Indian Astronomical Ephemeris 2020

THE

INDIAN ASTRONOMICAL EPHEMERIS FOR THE YEAR 2020

POSITIONAL ASTRONOMY CENTRE INDIA METEOROLOGICAL DEPARTMENT MINISTRY OF EARTH SCIENCES PUBLISHED BY THE CONTROLLER OF PUBLICATIONS, CIVIL LINES, DELHI

PDGM . 69 . 2020 160-2019 (DSK - III)

THE

INDIAN ASTRONOMICAL EPHEMERIS FOR THE YEAR 2020

POSITIONAL ASTRONOMY CENTRE INDIA METEOROLOGICAL DEPARTMENT

Issued under the authority of

THE DIRECTOR GENERAL OF METEOROLOGY, NEW DELHI INDIA METEOROLOGICAL DEPARTMENT MINISTRY OF EARTH SCIENCES GOVERNMENT OF INDIA

Office of preparation POSITIONAL ASTRONOMY CENTRE INDIA METEOROLOGICAL DEPARTMENT SALT LAKE, KOLKATA - 700 091

Copies available from:

In India : The Controller of Publications Civil Lines, Delhi - 110 054 Government of India Book Depot, 8, K. S. Roy Road, Kolkata - 700 001 Government of India Kitab Mahal, Baba Kharak Singh Marg, New Delhi Government of India Book Depot, New Marine Lines, Mumbai - 20 ( And other agents selling Government of India publications)

Sale Price : Inland Rs. 600.00; Foreign £ 12.00 or $ 15.00

PREFACE

The Indian Astronomical Ephemeris is published annually by the India Meteorological Department (IMD) for providing data to astronomers. The speciality of this publication is that it contains calendric information which caters to the requirement of the country’s panchang makers and other users. Thus it has great civil and cultural significance. This has been the mandate given to the Positional Astronomy Centre at Kolkata by the Govt. of India. The calculations of the Indian Calendar portion, such as tithi, nakshatra etc. are given in Indian Standard Time (IST) and covers an extended period upto 21st March 2021 which is the end of the year 1942 Saka Era of the Indian National Calendar. A separate note has also been given to explain the terminology and the basis of different calculations relating to the Indian Calendar. The epoch of the standard reference system in this publication is J 2000.0 and the argument of the ephemerides is Terrestrial Time (TT). Resolutions of the International Astronomical Union (IAU) recommending the changes from time to time including a list of new IAU constants are given in Part VI - Indian Calendar and Explanation. Our sincere thanks are due to the Nautical Almanac Office, United States Naval Observatory and Her Majesty’s Nautical Almanac Office, U.K. The work of preparation and publication of the Indian Astronomical Ephemeris for 2020 has been done under the supervision of Shri S. Sen, Director, Positional Astronomy Centre, India Meteorological Department, Kolkata.

Dr. K. J. Ramesh Director General of Meteorology

Mausam Bhawan New Delhi - 110 003 29th July, 2019 A.D. (7 Sravana, 1941 Saka Era)

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CONTENTS Page Preface

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Time Scales

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2

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III

PART I ─ TIME, SUN, MOON, PLANETS Chronological Table Calendar

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Sidereal Time

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13

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Mean longitude and anomaly of Sun Ephemeris of the Sun

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18

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Ephemeris for physical observations of the Sun

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Ephemeris of the Moon

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46

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88

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Rectangular Co-ordinates of the Sun .

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Ephemeris for physical observations of the Moon Ephemerides of planets : Mercury

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96

Venus

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112

Mars

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126

Jupiter

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140

Saturn

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154

Uranus

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168

Neptune .

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182

Pluto

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196

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Osculating Elements of Planets .

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200

Centre of Mass of the Solar System

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202

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204

PART II ─ STARS Longitude and Latitude of Stars

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Mean Places of Stars .

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215

Apparent Places of Stars

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227

Besselian Day Numbers

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244

Second Order Day Numbers

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252

Position and Velocity of the Earth

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256

Precession and Nutation

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257

Apparent Places of Polaris

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272

Polaris Tables

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275

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280 288

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PART III ─ TABLES OF SUNRISE, SUNSET AND MOONRISE, MOONSET Sunrise, Sunset and Twilight ( Meridian of Greenwich )

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Duration of Twilight.

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Sunrise, Sunset and Twilight -- Correction for Southern Latitudes Sunrise and Sunset for certain Stations in India

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290

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292

Moonrise and Moonset for the Central Meridian and Certain Stations in India

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296

Moonrise and Moonset -- Reduction to L. M. T. of other Meridians

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312

Sunrise, Sunset and Moonrise, Moonset -- Correction for Latitude

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313

Reduction of Local Mean Time into the Indian Standard Time .

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314

Sunrise, Sunset and Moonrise, Moonset -- Method of Calculation

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315

Phases of the Moon

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317

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CONTENTS Page

PART IV ─ ECLIPSES, TRANSIT AND OCCULTATIONS Eclipses of the Sun and the Moon

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320

Occultations of Planets and Bright Stars

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338

PART V ─ ASTRONOMICAL PHENOMENA AND MISCELLANEOUS TABLES Phenomena : Elongations and Magnitudes of Planets

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Conjunctions, oppositions, etc., of Planets with the Sun (in Longitude) Conjunctions of Planets with the Moon and other Planets (in Longitude) Conjunctions of Planets with Bright Stars (in R.A.) Astronomical Diary

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342

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344

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345

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346

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347

Table

I --- Conversion of mean Solar into Sidereal Time

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351

Table

II --- Conversion of sidereal into Mean Solar Time

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352

Table

III --- Conversion of Arc to Time

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353

Table

IV --- Conversion of Time to Arc

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354

Table

V --- Conversion of Hours, Minutes and Seconds to Decimals of a Day

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355

Table

VI --- Conversion of Minutes and Seconds to Decimals of a Degree

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358

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359

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Table VII --- Interpolation Coefficients

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Table VIII --- Everett Coefficients of the Second Differences

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361

Table

IX --- Julian Day Number

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363

Table

X, Xa, Xb --- Atmospheric Refraction

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364

Table

XI --- Factors for Computing the Geocentric Co-ordinates of a Place

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367

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Table XII --- Conversion of Geographic to Geocentric Co-ordinates Latitude and Longitude of Places

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Semi-diurnal and Semi-nocturnal Arcs, etc.

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368

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369

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373

Natural Trigonometric Functions

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374

Standard Time

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375

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PART VI ─ INDIAN CALENDAR AND EXPLANATION Explanatory Note

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Phenomena & Mean Rahu, 2021

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383

Indian Calendar, Saka Era 1942– 1943

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384

Principal Festivals and Anniversaries for Holidays

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414

Moslem Festivals

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417

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417

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The Islamic Calendar (Hejira 1441 - 1442) The Parsi Calendar and Festivals

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418

The Jewish Calendar and Festivals

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418

Christian Festivals

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419

The Indian Lunar Calendar

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420

Ayanamsa

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423

Longitudes of Sun, Moon and Planets, 2021

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424

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Declination of Sun and Latitude and Declination of Moon, 2021 Latitude and Declination of Planets, 2021

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Longitude of Uranus, Neptune and Pluto, 20201

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428

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430

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432

Explanation

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433

Index

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PART - I TIME, SUN, MOON, PLANETS

2

TIME-SCALE, 2020 Julian date for Standard epoch 1900 January 0, 12h U.T. B 1950.0 = 1950 Jan. 0.923 B 2020.0 = 2020 Jan. 0.877 J 2020.5 = 2020 July 2.125 J 2000.0 = 2000 Jan. 1.5

= = = = =

JD JD JD JD JD

241 243 245 245 245

5020.0 3282.423 8849.377 9032.625 1545.0

Tabulations of Julian date against calendar date for 2020 are given on pages 4 to12 and for other years are given at Table IX of Part-V on page 359. The fraction of the year from 2020.5 is tabulated with the Besselian day numbers on pages 244-251. ____________________________________________________________________________________________

The lengths of the principal years and mean months at 2020.0 as derived from the Sun’s mean motion and mean Orbital elements respectively are: Length of the year (ephemeris days ) : Tropical (equinox to equinox ) Sidereal (fixed star to fixed star) Anomalistic (perigee to perigee) Eclipse (node to node)

d 365.242190 365.256363 365. 259635 346. 620074

= = = =

d 365 365 365 346

h 05 06 06 14

m 48 09 13 52

s 45.2 09.8 52.5 54.4

d 29.5305888 27.3215822 27.3216615 27.5545501 27.2122207

= = = = =

d 29 27 27 27 27

h 12 07 07 13 05

m 44 43 43 18 05

s 02.9 04.7 11.6 33.1 35.9

Length of the Month (ephemeris days) Synodic (new moon to new moon) Tropical (equinox to equinox) Sidereal (fixed star to fixed star) Anomalistic (perigee to perigee) Nodical (node to node)

Length of the day: Mean Sidereal Mean Solar

h 23 24

m 56 03

s 04.09053 of mean Solar time. 56.55537 of mean Sidereal time.

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CHRONOLOGICAL TABLE

CHRONOLOGICAL CYCLES Golden Number or Lunar Cycle

VII

Solar Cycle

13

Epact

5

Roman Indiction

13

Dominical Letter

ED

CHRONOLOGICAL ERAS The year 1942 of the Saka Era (Indian National Calendar) begins on March 21, 2020. The year 1942 of the Saka Era or Saka Shalivahana (Lunisolar, Traditional Calendar) begins on March 25, 2020. The year 1942 of the Saka Era (Solar, Traditional Calendar) begins on April 14, 2020. The year 5121 of the Kali Era begins on April 14, 2020. The year 2077 of the Vikram Samvat begins on March 25, 2020 (Chaitradi) and November 16, 2020 (Kartikadi) according to different systems of reckoning. The year 1427 of the Bengali San begins on April 14, 2020. The year 1196 of the Kollam Era begins on August 17, 2020. Jovian year (Barhaspatya Varsa or 60-year cycle of Jupiter) 48 Ananda begins on June 1, 2020 (North Indian Usage), and 34 Sarvari on March 25, 2020 (Lunar Chaitradi) or April 14, 2020 (Solar) (South Indian Usage). Vedanga Jyotisa year 1- Samvatsara of the 5-year cycle (389 th cycle of Paitamaha Siddhanta) begins on January 25, 2020. The year 2564 of the Buddha Nirvana era begins on May 7, 2020. The year 2547 of the Mahavira Nirvana Era begins on November 16, 2020. The year 1442 of the Mohammedan Era begins on August 21, 2020. The year 1390 of the Yazdejardi Era begins on August 16, 2020 according to the Indian Parsi (Shahenshahi) Calendar. The year 6733 of the Julian period begins on January 14, 2020. The year 5781 of the Jewish Era (A.M. ) begins on September 19, 2020. The year 2796 of the Greek Olympiad, being the 4th year of the 4-Year cycle ( 699 th Olympiad ) begins on July, 2020. The year 2773 of the Foundation of Rome ( A.U.C. ) begins on January 14, 2020. The year 2769 of the Nabonassar begins on April 18, 2020. The year 2332 of the Seleucidean era begins in the present-day usage of the Syrians on September 14 or October 14, 2020 according to different sects. The Gregorian Year 2020 begins on January 1, 2020.

4

CALENDAR, 2020 Day of Month

Day of Year

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.) 2458

Dec.

Dec. Jan.

Feb.

Indian Calendar Day of Month Day of Year

Phases of the Moon

28 29 30 31 1 2 3

362 363 364 365 1 2 3

Sat Sun Mon Tue Wed Thu Fri

-187.125 186.125 185.125 184.125 183.125 182.125 181.125

-0.0110 -0.0082 -0.0055 -0.0027 0.0000 0.0027 0.0055

845.5 846.5 847.5 848.5 849.5 850.5 851.5

1941 Saka Era Pausha 7 8 9 10 11 12 13

4 5 6 7 8 9 10

4 5 6 7 8 9 10

Sat Sun Mon Tue Wed Thu Fri

-180.125 179.125 178.125 177.125 176.125 175.125 174.125

0.0082 0.0110 0.0137 0.0164 0.0192 0.0219 0.0246

852.5 853.5 854.5 855.5 856.5 857.5 858.5

14 15 16 17 18 19 20

11 12 13 14 15 16 17

11 12 13 14 15 16 17

Sat Sun Mon Tue Wed Thu Fri

-173.125 172.125 171.125 170.125 169.125 168.125 167.125

0.0274 0.0301 0.0329 0.0356 0.0383 0.0411 0.0438

859.5 860.5 861.5 862.5 863.5 864.5 865.5

21 22 23 24 25 26 27

18 19 20 21 22 23 24

18 19 20 21 22 23 24

Sat Sun Mon Tue Wed Thu Fri

-166.125 165.125 164.125 163.125 162.125 161.125 160.125

0.0465 0.0493 0.0520 0.0548 0.0575 0.0602 0.0630

866.5 867.5 868.5 869.5 870.5 871.5 872.5

28 29 30 Magha 1 2 3 4

25 26 27 28 29 30 31

25 26 27 28 29 30 31

Sat Sun Mon Tue Wed Thu Fri

-159.125 158.125 157.125 156.125 155.125 154.125 153.125

0.0657 0.0684 0.0712 0.0739 0.0767 0.0794 0.0821

873.5 874.5 875.5 876.5 877.5 878.5 879.5

5 6 7 8 9 10 11

282 283 284 285 286 287 288 3-First Quarter 4h 45m U.T. 289 290 291 292 293 294 295 10-Full Moon 19h 21m U.T. 296 297 298 299 300 301 302 17-Last Quarter 12h 58m U.T. 303 304 305 306 307 308 309 24-New Moon 21h 42m U.T. 310 311 312 313 314 315 316

1 2 3 4 5 6 7

32 33 34 35 36 37 38

Sat Sun Mon Tue Wed Thu Fri

-152.125 151.125 150.125 149.125 148.125 147.125 -146.125

0.0849 0.0876 0.0904 0.0931 0.0958 0.0986 0.1013

880.5 881.5 882.5 883.5 884.5 885.5 886.5

12 13 14 15 16 17 18

317 318 2-First Quarter h m 319 1 42 U.T. 320 321 322 323

5

CALENDAR, 2020 Day of Month

Day of Year

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.) 2458

Feb.

Mar.

Indian Calendar Day of Month Day of Year

Phases of the Moon

8 9 10 11 12 13 14

39 40 41 42 43 44 45

Sat Sun Mon Tue Wed Thu Fri

-145.125 144.125 143.125 142.125 141.125 140.125 139.125

0.1040 0.1068 0.1095 0.1123 0.1150 0.1177 0.1205

887.5 888.5 889.5 890.5 891.5 892.5 893.5

1941 Saka Era Magha 19 20 21 22 23 24 25

15 16 17 18 19 20 21

46 47 48 49 50 51 52

Sat Sun Mon Tue Wed Thu Fri

-138.125 137.125 136.125 135.125 134.125 133.125 132.125

0.1232 0.1259 0.1287 0.1314 0.1342 0.1369 0.1396

894.5 895.5 896.5 897.5 898.5 899.5 900.5

26 27 28 29 30 Phalguna 1 2

22 23 24 25 26 27 28

53 54 55 56 57 58 59

Sat Sun Mon Tue Wed Thu Fri

-131.125 130.125 129.125 128.125 127.125 126.125 125.125

0.1424 0.1451 0.1478 0.1506 0.1533 0.1561 0.1588

901.5 902.5 903.5 904.5 905.5 906.5 907.5

3 4 5 6 7 8 9

338 339 23-New Moon h m 340 15 32 U.T. 341 342 343 344

29 1 2 3 4 5 6

60 61 62 63 64 65 66

Sat Sun Mon Tue Wed Thu Fri

-124.125 123.125 122.125 121.125 120.125 119.125 118.125

0.1615 0.1643 0.1670 0.1698 0.1725 0.1752 0.1780

908.5 909.5 910.5 911.5 912.5 913.5 914.5

10 11 12 13 14 15 16

345 346 347 2-First Quarter h m 348 19 57 U.T. 349 350 351

7 8 9 10 11 12 13

67 68 69 70 71 72 73

Sat Sun Mon Tue Wed Thu Fri

-117.125 116.125 115.125 114.125 113.125 112.125 111.125

0.1807 0.1834 0.1862 0.1889 0.1917 0.1944 0.1971

915.5 916.5 917.5 918.5 919.5 920.5 921.5

17 18 19 20 21 22 23

352 353 354 9-Full Moon h m 355 17 48 U.T. 356 357 358

14 15 16 17 18 19 20

74 75 76 77 78 79 80

Sat Sun Mon Tue Wed Thu Fri

-110.125 109.125 108.125 107.125 106.125 105.125 -104.125

0.1999 0.2026 0.2053 0.2081 0.2108 0.2136 0.2163

922.5 923.5 924.5 925.5 926.5 927.5 928.5

24 25 26 27 28 29 30

359 360 361 16-Last Quarter h m 362 9 34 U.T. 363 364 365

324 325 9-Full Moon h m 326 7 33 U.T. 327 328 329 330 331 15-Last Quarter h m 332 22 17 U.T. 333 334 335 336 337

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CALENDAR, 2020 Day of Month

Day of Year

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.) 2458

Mar.

Apr.

May

Indian Calendar Day of Month Day of Year

Phases of the Moon

21 22 23 24 25 26 27

81 82 83 84 85 86 87

Sat Sun Mon Tue Wed Thu Fri

-103.125 102.125 101.125 100.125 99.125 98.125 97.125

0.2190 0.2218 0.2245 0.2272 0.2300 0.2327 0.2355

929.5 930.5 931.5 932.5 933.5 934.5 935.5

1942 Saka Era Chaitra 1 2 3 4 5 6 7

1 2 3 4 24-New Moon h m 5 9 28 U.T. 6 7

28 29 30 31 1 2 3

88 89 90 91 92 93 94

Sat Sun Mon Tue Wed Thu Fri

-96.125 95.125 94.125 93.125 92.125 91.125 90.125

0.2382 0.2409 0.2437 0.2464 0.2491 0.2519 0.2546

936.5 937.5 938.5 939.5 940.5 941.5 942.5

8 9 10 11 12 13 14

8 9 10 11 12 1-First Quarter h m 13 10 21 U.T. 14

4 5 6 7 8 9 10

95 96 97 98 99 100 101

Sat Sun Mon Tue Wed Thu Fri

-89.125 88.125 87.125 86.125 85.125 84.125 83.125

0.2574 0.2601 0.2628 0.2656 0.2683 0.2711 0.2738

943.5 944.5 945.5 946.5 947.5 948.5 949.5

15 16 17 18 19 20 21

15 16 17 18 19 8-Full Moon h m 20 2 35 U.T. 21

11 12 13 14 15 16 17

102 103 104 105 106 107 108

Sat Sun Mon Tue Wed Thu Fri

-82.125 81.125 80.125 79.125 78.125 77.125 76.125

0.2765 0.2793 0.2820 0.2847 0.2875 0.2902 0.2930

950.5 951.5 952.5 953.5 954.5 955.5 956.5

22 23 24 25 26 27 28

22 23 24 25 14-Last Quarter h m 26 22 56 U.T. 27 28

18 19 20 21 22 23 24

109 110 111 112 113 114 115

Sat Sun Mon Tue Wed Thu Fri

-75.125 74.125 73.125 72.125 71.125 70.125 69.125

0.2957 0.2984 0.3012 0.3039 0.3066 0.3094 0.3121

957.5 958.5 959.5 960.5 961.5 962.5 963.5

29 30 31 Vaisakha 1 2 3 4

25 26 27 28 29 30 1

116 117 118 119 120 121 122

Sat Sun Mon Tue Wed Thu Fri

-68.125 67.125 66.125 65.125 64.125 63.125 -62.125

0.3149 0.3176 0.3203 0.3231 0.3258 0.3285 0.3313

964.5 965.5 966.5 967.5 968.5 969.5 970.5

5 6 7 8 9 10 11

29 30 31 32 33 34 23-New Moon h m 35 2 26 U.T. 36 37 38 39 40 41 30-First Quarter h m 42 20 38 U.T.

7

CALENDAR, 2020 Day of Year

Day of Month

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.) 2458

May

June

Indian Calendar Day of Month Day of Year

2 3 4 5 6 7 8

123 124 125 126 127 128 129

Sat Sun Mon Tue Wed Thu Fri

-61.125 60.125 59.125 58.125 57.125 56.125 55.125

0.3340 0.3368 0.3395 0.3422 0.3450 0.3477 0.3505

971.5 972.5 973.5 974.5 975.5 976.5 977.5

1942 Saka Era Vaisakha 12 13 14 15 16 17 18

9 10 11 12 13 14 15

130 131 132 133 134 135 136

Sat Sun Mon Tue Wed Thu Fri

-54.125 53.125 52.125 51.125 50.125 49.125 48.125

0.3532 0.3559 0.3587 0.3614 0.3641 0.3669 0.3696

978.5 979.5 980.5 981.5 982.5 983.5 984.5

19 20 21 22 23 24 25

16 17 18 19 20 21 22

137 138 139 140 141 142 143

Sat Sun Mon Tue Wed Thu Fri

-47.125 46.125 45.125 44.125 43.125 42.125 41.125

0.3724 0.3751 0.3778 0.3806 0.3833 0.3860 0.3888

985.5 986.5 987.5 988.5 989.5 990.5 991.5

26 27 28 29 30 31 Jyaistha 1

23 24 25 26 27 28 29

144 145 146 147 148 149 150

Sat Sun Mon Tue Wed Thu Fri

-40.125 39.125 38.125 37.125 36.125 35.125 34.125

0.3915 0.3943 0.3970 0.3997 0.4025 0.4052 0.4079

992.5 993.5 994.5 995.5 996.5 997.5 998.5

2 3 4 5 6 7 8

30 31 1 2 3 4 5

151 152 153 154 155 156 157

Sat Sun Mon Tue Wed Thu Fri

-33.125 32.125 31.125 30.125 29.125 28.125 27.125

0.4107 999.5 0.4134 2459000.5 0.4162 001.5 0.4189 002.5 0.4216 003.5 0.4244 004.5 0.4271 005.5

9 10 11 12 13 14 15

6 7 8 9 10 11 12

158 159 160 161 162 163 164

Sat Sun Mon Tue Wed Thu Fri

-26.125 25.125 24.125 23.125 22.125 21.125 -20.125

0.4299 0.4326 0.4353 0.4381 0.4408 0.4435 0.4463

16 17 18 19 20 21 22

006.5 007.5 008.5 009.5 010.5 011.5 012.5

Phases of the Moon

43 44 45 46 47 48 7-Full Moon h m 49 10 45 U.T. 50 51 52 53 54 55 14-Last Quarter h m 56 14 03 U.T. 57 58 59 60 61 62 63 22-New Moon 17h 39m U.T. 64 65 66 67 68 69 70 71 30-First Quarter h m 72 3 30 U.T. 73 74 75 76 77 5-Full Moon 19h 12m U.T. 78 79 80 81 82 83 84

8

CALENDAR, 2020 Day of Month

June

July

Day of Year

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.)

Indian Calendar Day of Month Day of Year

2459 1942 Saka Era 013.5l Jyaishtha 23 014.5l 24 015.5l 25 016.5l 26 017.5l 27 018.5l 28 019.5l 29

Phases of the Moon

13 14 15 16 17 18 19

165 166 167 168 169 170 171

Sat Sun Mon Tue Wed Thu Fri

-19.125 18.125 17.125 16.125 15.125 14.125 13.125

0.4490 0.4518 0.4545 0.4572 0.4600 0.4627 0.4654

85 13-Last Quarter h m 86 6 24 U.T. 87 88 89 90 91

20 21 22 23 24 25 26

172 173 174 175 176 177 178

Sat Sun Mon Tue Wed Thu Fri

-12.125 11.125 10.125 9.125 8.125 7.125 6.125

0.4682 0.4709 0.4737 0.4764 0.4791 0.4819 0.4846

020.5l 021.5l 022.5l 023.5l 024.5l 025.5l 026.5l

30 31 Ashadha 1 2 3 4 5

27 28 29 30 1 2 3

179 180 181 182 183 184 185

Sat Sun Mon Tue Wed Thu Fri

-5.125 4.125 3.125 2.125 1.125 -0.125 +0.875

0.4873 0.4901 0.4928 0.4956 0.4983 0.5010 0.5038

027.5l 028.5l 029.5l 030.5l 031.5l 032.5l 033.5l

6 7 8 9 10 11 12

99 100 28-First Quarter h m 101 8 16 U.T. 102 103 104 105

4 5 6 7 8 9 10

186 187 188 189 190 191 192

Sat Sun Mon Tue Wed Thu Fri

+1.875 2.875 3.875 4.875 5.875 6.875 7.875

0.5065 0.5093 0.5120 0.5147 0.5175 0.5202 0.5229

034.5l 035.5l 036.5l 037.5l 038.5l 039.5l 040.5l

13 14 15 16 17 18 19

106 107 5-Full Moon h m 108 4 44 U.T. 109 110 111 112

11 12 13 14 15 16 17

193 194 195 196 197 198 199

Sat Sun Mon Tue Wed Thu Fri

+8.875 9.875 10.875 11.875 12.875 13.875 14.875

0.5257 0.5284 0.5312 0.5339 0.5366 0.5394 0.5421

041.5l 042.5l 043.5l 044.5l 045.5l 046.5l 047.5l

20 21 22 23 24 25 26

113 114 12-Last Quarter h m 115 23 29 U.T. 116 117 118 119

18 19 20 21 22 23 24

200 201 202 203 204 205 206

Sat Sun Mon Tue Wed Thu Fri

+15.875 16.875 17.875 18.875 19.875 20.875 +21.875

0.5448 0.5476 0.5503 0.5531 0.5558 0.5585 0.5613

048.5l 049.5l 050.5l 051.5l 052.5l 053.5l 054.5l

27 28 29 30 31 Sravana 1 2

92 93 21-New Moon h m 94 6 41 U.T. 95 96 97 98

120 121 122 20-New Moon h m 123 17 33 U.T. 124 125 126

9

CALENDAR, 2020 Day of Month

Day of Year

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.) 2459

Indian Calendar Day of Month Day of Year

Phases of the Moon

July

25 26 27 28 29 30 31

207 208 209 210 211 212 213

Sat Sun Mon Tue Wed Thu Fri

+22.875 23.875 24.875 25.875 26.875 27.875 28.875

0.5640 0.5667 0.5695 0.5722 0.5750 0.5777 0.5804

055.5 056.5 057.5 058.5 059.5 060.5 061.5

1942 Saka Era Sravana 3 4 5 6 7 8 9

Aug.

1 2 3 4 5 6 7

214 215 216 217 218 219 220

Sat Sun Mon Tue Wed Thu Fri

+29.875 30.875 31.875 32.875 33.875 34.875 35.875

0.5832 0.5859 0.5887 0.5914 0.5941 0.5969 0.5996

062.5 063.5 064.5 065.5 066.5 067.5 068.5

10 11 12 13 14 15 16

134 135 136 3-Full Moon h m 137 15 59 U.T. 138 139 140

8 9 10 11 12 13 14

221 222 223 224 225 226 227

Sat Sun Mon Tue Wed Thu Fri

+36.875 37.875 38.875 39.875 40.875 41.875 42.875

0.6023 0.6051 0.6078 0.6106 0.6133 0.6160 0.6188

069.5 070.5 071.5 072.5 073.5 074.5 075.5

17 18 19 20 21 22 23

141 142 143 144 11-Last Quarter h m 145 16 45 U.T. 146 147

15 16 17 18 19 20 21

228 229 230 231 232 233 234

Sat Sun Mon Tue Wed Thu Fri

+43.875 44.875 45.875 46.875 47.875 48.875 49.875

0.6215 0.6242 0.6270 0.6297 0.6325 0.6352 0.6379

076.5 077.5 078.5 079.5 080.5 081.5 082.5

24 25 26 27 28 29 30

148 149 150 151 152 19-New Moon h m 153 2 42 U.T. 154

22 23 24 25 26 27 28

235 236 237 238 239 240 241

Sat Sun Mon Tue Wed Thu Fri

+50.875 51.875 52.875 53.875 54.875 55.875 56.875

0.6407 0.6434 0.6461 0.6489 0.6516 0.6544 0.6571

083.5 084.5 085.5 086.5 087.5 088.5 089.5

31 Bhadra 1 2 3 4 5 6

29 30 31 1 2 3 4

242 243 244 245 246 247 248

Sat Sun Mon Tue Wed Thu Fri

+57.875 58.875 59.875 60.875 61.875 62.875 +63.875

0.6598 0.6626 0.6653 0.6680 0.6708 0.6735 0.6763

090.5 091.5 092.5 093.5 094.5 095.5 096.5

7 8 9 10 11 12 13

Sept.

127 128 129 27-First Quarter h m 130 12 33 U.T. 131 132 133

155 156 157 158 25-First Quarter h m 159 17 58 U.T. 160 161 162 163 164 165 166 2-Full Moon h m 167 5 22 U.T. 168

10

CALENDAR, 2020 Day of Month

Day of Year

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.) 2459

Sept.

Oct.

Indian Calendar Day of Month Day of Year

Phases of the Moon

5 6 7 8 9 10 11

249 250 251 252 253 254 255

Sat Sun Mon Tue Wed Thu Fri

+64.875 65.875 66.875 67.875 68.875 69.875 70.875

0.6790 0.6817 0.6845 0.6872 0.6900 0.6927 0.6954

097.5 098.5 099.5 100.5 101.5 102.5 103.5

1942 Saka Era Bhadra 14 15 16 17 18 19 20

12 13 14 15 16 17 18

256 257 258 259 260 261 262

Sat Sun Mon Tue Wed Thu Fri

+71.875 72.875 73.875 74.875 75.875 76.875 77.875

0.6982 0.7009 0.7036 0.7064 0.7091 0.7119 0.7146

104.5 105.5 106.5 107.5 108.5 109.5 110.5

21 22 23 24 25 26 27

19 20 21 22 23 24 25

263 264 265 266 267 268 269

Sat Sun Mon Tue Wed Thu Fri

+78.875 79.875 80.875 81.875 82.875 83.875 84.875

0.7173 0.7201 0.7228 0.7255 0.7283 0.7310 0.7338

111.5 112.5 113.5 114.5 115.5 116.5 117.5

28 29 30 31 Asvina 1 2 3

26 27 28 29 30 1 2

270 271 272 273 274 275 276

Sat Sun Mon Tue Wed Thu Fri

+85.875 86.875 87.875 88.875 89.875 90.875 91.875

0.7365 0.7392 0.7420 0.7447 0.7474 0.7502 0.7529

118.5 119.5 120.5 121.5 122.5 123.5 124.5

4 5 6 7 8 9 10

190 191 192 193 194 195 1-Full Moon h m 196 21 05 U.T.

3 4 5 6 7 8 9

277 278 279 280 281 282 283

Sat Sun Mon Tue Wed Thu Fri

+92.875 93.875 94.875 95.875 96.875 97.875 98.875

0.7557 0.7584 0.7611 0.7639 0.7666 0.7694 0.7721

125.5 126.5 127.5 128.5 129.5 130.5 131.5

11 12 13 14 15 16 17

197 198 199 200 201 202 203

10 11 12 13 14 15 16

284 285 286 287 288 289 290

Sat Sun Mon Tue Wed Thu Fri

+99.875 100.875 101.875 102.875 103.875 104.875 +105.875

0.7748 0.7776 0.7803 0.7830 0.7858 0.7885 0.7913

132.5 133.5 134.5 135.5 136.5 137.5 138.5

18 19 20 21 22 23 24

204 10-Last Quarter h m 205 0 40 U.T. 206 207 208 209 210 16-New Moon 19h 31m U.T.

169 170 171 172 173 174 10-Last Quarter h m 175 9 26 U.T. 176 177 178 179 180 181 17-New Moon h m 182 11 00 U.T. 183 184 185 186 187 188 24-First Quarter h m 189 1 55 U.T.

11

CALENDAR, 2020 Day of Month

Day of Year

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.) 2459

Oct.

Nov.

Indian Calendar Day of Month Day of Year

Phases of the Moon

17 18 19 20 21 22 23

291 292 293 294 295 296 297

Sat Sun Mon Tue Wed Thu Fri

+106.875 107.875 108.875 109.875 110.875 111.875 112.875

0.7940 0.7967 0.7995 0.8022 0.8049 0.8077 0.8104

139.5 140.5 141.5 142.5 143.5 144.5 145.5

1942 Saka Era Asvina 25 26 27 28 29 30 Kartika 1

24 25 26 27 28 29 30

298 299 300 301 302 303 304

Sat Sun Mon Tue Wed Thu Fri

+113.875 114.875 115.875 116.875 117.875 118.875 119.875

0.8132 0.8159 0.8186 0.8214 0.8241 0.8268 0.8296

146.5 147.5 148.5 149.5 150.5 151.5 152.5

2 3 4 5 6 7 8

31 1 2 3 4 5 6

305 306 307 308 309 310 311

Sat Sun Mon Tue Wed Thu Fri

+120.875 121.875 122.875 123.875 124.875 125.875 126.875

0.8323 0.8351 0.8378 0.8405 0.8433 0.8460 0.8488

153.5 154.5 155.5 156.5 157.5 158.5 159.5

9 10 11 12 13 14 15

225 31-Full Moon h m 226 14 49 U.T. 227 228 229 230 231

7 8 9 10 11 12 13

312 313 314 315 316 317 318

Sat Sun Mon Tue Wed Thu Fri

+127.875 128.875 129.875 130.875 131.875 132.875 133.875

0.8515 0.8542 0.8570 0.8597 0.8624 0.8652 0.8679

160.5 161.5 162.5 163.5 164.5 165.5 166.5

16 17 18 19 20 21 22

232 233 8-Last Quarter h m 234 13 46 U.T. 235 236 237 238

14 15 16 17 18 19 20

319 320 321 322 323 324 325

Sat Sun Mon Tue Wed Thu Fri

+134.875 135.875 136.875 137.875 138.875 139.875 140.875

0.8707 0.8734 0.8761 0.8789 0.8816 0.8843 0.8871

167.5 168.5 169.5 170.5 171.5 172.5 173.5

23 24 25 26 27 28 29

239 240 15-New Moon h m 241 5 07 U.T. 242 243 244 245

21 22 23 24 25 26 27

326 327 328 329 330 331 332

Sat Sun Mon Tue Wed Thu Fri

+141.875 142.875 143.875 144.875 145.875 146.875 +147.875

0.8898 0.8926 0.8953 0.8980 0.9008 0.9035 0.9062

174.5 30 175.5 Agrahayana 1 176.5 2 177.5 3 178.5 4 179.5 5 180.5 6

211 212 213 214 215 216 217 23-First Quarter 13h 23m U.T. 218 219 220 221 222 223 224

246 247 22-First Quarter h m 248 4 45 U.T. 249 250 251 252

12

CALENDAR, 2020 Day of Month

Day of Year

Day of Week

Days since J 2020.5

Fraction of Year since Jan. 1.0

Julian Day (at 0h U.T.) 2459

Nov.

Dec.

Indian Calendar Day of Month Day of Year

Phases of the Moon

28 29 30 1 2 3 4

333 334 335 336 337 338 339

Sat Sun Mon Tue Wed Thu Fri

+148.875 149.875 150.875 151.875 152.875 153.875 154.875

0.9090 0.9117 0.9145 0.9172 0.9199 0.9227 0.9254

1942 Saka Era 181.5 Agrahayana 7 182.5 8 183.5 9 184.5 10 185.5 11 186.5 12 187.5 13

253 254 255 30-Full Moon h m 256 9 30 U.T. 257 258 259

5 6 7 8 9 10 11

340 341 342 343 344 345 346

Sat Sun Mon Tue Wed Thu Fri

+155.875 156.875 157.875 158.875 159.875 160.875 161.875

0.9282 0.9309 0.9336 0.9364 0.9391 0.9418 0.9446

188.5 189.5 190.5 191.5 192.5 193.5 194.5

14 15 16 17 18 19 20

260 261 262 263 8-Last Quarter h m 264 0 37 U.T. 265 266

12 13 14 15 16 17 18

347 348 349 350 351 352 353

Sat Sun Mon Tue Wed Thu Fri

+162.875 163.875 164.875 165.875 166.875 167.875 168.875

0.9473 0.9501 0.9528 0.9555 0.9583 0.9610 0.9637

195.5 196.5 197.5 198.5 199.5 200.5 201.5

21 22 23 24 25 26 27

267 268 269 14-New Moon h m 270 16 17 U.T. 271 272 273

19 20 21 22 23 24 25

354 355 356 357 358 359 360

Sat Sun Mon Tue Wed Thu Fri

+169.875 170.875 171.875 172.875 173.875 174.875 175.875

0.9665 0.9692 0.9720 0.9747 0.9774 0.9802 0.9829

202.5 203.5 204.5 205.5 206.5 207.5 208.5

28 29 30 Pausha 1 2 3 4

274 275 276 21-First Quarter h m 277 23 41 U.T. 278 279 280

26 361 Sat +176.875 0.9856 209.5 5 281 27 362 Sun 177.875 0.9884 210.5 6 282 28 363 Mon 178.875 0.9911 211.5 7 283 29 364 Tue 179.875 0.9939 212.5 8 284 30 365 Wed 180.875 0.9966 213.5 9 285 30-Full Moon h m 31 366 Thu 181.875 0.9993 214.5 10 286 3 28 U.T. 32 1 Fri +182.875 1.0021 215.5 11 287 The new epoch is the middle of the Julian year, denoted by J 2020.5 (i.e. 2020, July 2.125) where the length of the Julian year is taken to be 365.25 days. The Fraction of year is reckoned from January 1, 0 h U.T and is based on the tropical year of 365.2422 days. The Julian Day begins at noon. In order to obtain the Julian Day Number completed at noon as given in Table IX, increase the above figure by 0.5. The Day of year of the Gregorian Calendar is reckoned from January 1, and that of the Indian Calendar from Chaitra 1.

13

SIDEREAL TIME, 2020 Greenwich Mean Greenwich Equation Transit of Mean Sidereal Time at of the 0h U.T. (G.H.A. Equinox- Equinox (U.T. at of the Equinox) es at 0h 0h G.M.S.T.) U.T.

Date

Greenwich Mean Greenwich Equation Transit of Mean Sidereal Time at of the 0h U.T. (G.H.A. Equinox- Equinox (U.T. at of the Equinox) es at 0h 0h G.M.S.T.) U.T.

Date

0 1 2 3 4 5

h 6 6 6 6 6 6

m 36 40 44 48 52 56

s 32.679 29.234 25.790 22.345 18.900 15.456

s -1.007 1.009 1.012 1.015 1.019 1.021

h 17 17 17 17 17 17

m 20 16 12 08 04 00

s 36.376 Feb. 40.467 44.557 48.648 52.738 56.829

15 16 17 18 19 20

h 9 9 9 9 9 9

m 37 41 45 49 53 57

s 54.226 50.781 47.337 43.892 40.447 37.003

s -0.979 0.979 0.977 0.973 0.968 0.964

h 14 14 14 14 14 14

m 19 15 11 07 04 00

s 44.540 48.631 52.721 56.812 00.902 04.993

6 7 8 9 10 11

7 7 7 7 7 7

00 04 08 12 15 19

12.011 08.567 05.122 01.677 58.233 54.788

-1.021 1.018 1.013 1.005 0.995 0.986

16 16 16 16 16 16

57 53 49 45 41 37

00.919 05.010 09.100 13.191 17.281 21.372

21 22 23 24 25 26

10 10 10 10 10 10

01 05 09 13 17 21

33.558 30.114 26.669 23.224 19.780 16.335

-0.962 0.962 0.964 0.969 0.976 0.984

23 23 23 23 23 23

54 50 46 42 38 34

30.788 34.879 38.969 43.060 47.150 51.241

12 13 14 15 16 17

7 7 7 7 7 7

23 27 31 35 39 43

51.343 47.899 44.454 41.010 37.565 34.120

-0.978 0.974 0.973 0.976 0.980 0.985

16 16 16 16 16 16

33 29 25 21 17 13

25.462 29.553 33.643 37.734 Mar. 41.825 45.915

27 28 29 1 2 3

10 10 10 10 10 10

25 29 33 37 40 44

12.890 09.446 06.001 02.556 59.112 55.667

-0.993 1.000 1.007 1.011 1.012 1.012

23 23 23 23 23 23

30 26 23 19 15 11

55.331 59.422 03.512 07.603 11.693 15.784

18 19 20 21 22 23

7 7 7 7 8 8

47 51 55 59 03 07

30.676 27.231 23.786 20.342 16.897 13.452

-0.987 0.988 0.985 0.980 0.972 0.965

16 16 16 15 15 15

09 05 01 58 54 50

50.006 54.096 58.187 02.277 06.368 10.458

4 5 6 7 8 9

10 10 10 11 11 11

48 52 56 00 04 08

52.223 48.778 45.333 41.889 38.444 34.999

-1.009 1.004 1.000 0.998 0.998 1.002

23 23 22 22 22 22

07 03 59 55 51 47

19.874 23.965 28.055 32.146 36.237 40.327

24 25 26 27 28 29

8 8 8 8 8 8

11 15 19 22 26 30

10.008 06.563 03.119 59.674 56.229 52.785

-0.959 0.954 0.952 0.953 0.956 0.960

15 15 15 15 15 15

46 42 38 34 30 26

14.549 18.639 22.730 26.820 30.911 35.001

10 11 12 13 14 15

11 11 11 11 11 11

12 16 20 24 28 32

31.555 28.110 24.666 21.221 17.776 14.332

-1.010 1.019 1.028 1.034 1.037 1.037

22 22 22 22 22 22

43 39 35 31 28 24

44.418 48.508 52.599 56.689 00.780 04.870

30 31 Feb. 1 2 3 4

8 8 8 8 8 8

34 38 42 46 50 54

49.340 45.895 42.451 39.006 35.562 32.117

-0.966 0.972 0.976 0.979 0.980 0.979

15 15 15 15 15 15

22 18 14 10 06 02

39.092 43.182 47.273 51.364 55.454 59.545

16 17 18 19 20 21

11 11 11 11 11 11

36 40 44 47 51 55

10.887 07.442 03.998 60.553 57.108 53.664

-1.034 1.030 1.027 1.026 1.026 1.029

22 22 22 22 22 22

20 16 12 08 04 00

08.961 13.051 17.142 21.232 25.323 29.413

5 6 7 8 9 10

8 9 9 9 9 9

58 02 06 10 14 18

28.672 25.228 21.783 18.338 14.894 11.449

-0.974 0.968 0.961 0.955 0.951 0.951

14 14 14 14 14 14

59 55 51 47 43 39

03.635 07.726 11.816 15.907 19.997 24.088

22 23 24 25 26 27

11 12 12 12 12 12

59 03 07 11 15 19

50.219 46.775 43.330 39.885 36.441 32.996

-1.035 1.043 1.051 1.060 1.069 1.076

21 21 21 21 21 21

56 52 48 44 40 36

33.504 37.594 41.685 45.775 49.866 53.957

11 12 13 14 15

9 9 9 9 9

22 26 30 33 37

08.004 04.560 01.115 57.671 54.226

-0.955 0.962 0.969 0.975 -0.979

14 14 14 14 14

35 31 27 23 19

28.178 32.269 36.359 40.450 44.540 Apr.

28 29 30 31 1

12 12 12 12 12

23 27 31 35 39

29.551 26.107 22.662 19.218 15.773

-1.082 1.084 1.085 1.083 -1.080

21 21 21 21 21

32 29 25 21 17

58.047 02.138 06.228 10.319 14.409

Jan.

N.B.-Apparent Sidereal Time = Mean Sidereal Time + Equation of Equinoxes for the instant

14

SIDEREAL TIME, 2020 Greenwich Mean Greenwich Equation Transit of Mean Sidereal Time at of the 0h U.T. (G.H.A. Equinox- Equinox (U.T. at of the Equinox) es at 0h 0h G.M.S.T.) U.T.

Date

Apr.

May

Greenwich Mean Greenwich Equation Transit of Mean Sidereal Time at of the 0h U.T. (G.H.A. Equinox- Equinox (U.T. at of the Equinox) es at 0h 0h G.M.S.T.) U.T.

Date

1 2 3 4 5 6

h 12 12 12 12 12 12

m 39 43 47 51 55 58

s 15.773 12.328 08.884 05.439 01.994 58.550

s -1.080 1.076 1.073 1.072 1.075 1.081

h 21 21 21 21 21 20

m 17 13 09 05 01 57

s 14.409 May 18.500 22.590 26.681 30.771 34.862

17 18 19 20 21 22

h 15 15 15 15 15 16

m 40 44 48 52 56 00

s 37.320 33.875 30.431 26.986 23.541 20.097

s -1.111 1.117 1.122 1.126 1.129 1.129

h 18 18 18 18 18 17

m 16 12 08 04 00 56

s 22.574 26.664 30.755 34.845 38.936 43.026

7 8 9 10 11 12

13 13 13 13 13 13

02 06 10 14 18 22

55.105 51.660 48.216 44.771 41.327 37.882

-1.090 1.098 1.106 1.109 1.109 1.105

20 20 20 20 20 20

53 49 45 41 37 33

38.952 43.043 47.133 51.224 55.315 59.405

23 24 25 26 27 28

16 16 16 16 16 16

04 08 12 16 20 23

16.652 13.207 09.763 06.318 02.874 59.429

-1.126 1.121 1.114 1.106 1.099 1.094

17 17 17 17 17 17

52 48 44 40 37 33

47.117 51.207 55.298 59.388 03.479 07.569

13 14 15 16 17 18

13 13 13 13 13 13

26 30 34 38 42 46

34.437 30.993 27.548 24.103 20.659 17.214

-1.100 1.096 1.092 1.091 1.092 1.096

20 20 20 20 20 20

30 26 22 18 14 10

03.496 07.586 11.677 15.767 June 19.858 23.948

29 30 31 1 2 3

16 16 16 16 16 16

27 31 35 39 43 47

55.984 52.540 49.095 45.650 42.206 38.761

-1.091 1.091 1.094 1.098 1.103 1.105

17 17 17 17 17 17

29 25 21 17 13 09

11.660 15.750 19.841 23.932 28.022 32.113

19 20 21 22 23 24

13 13 13 14 14 14

50 54 58 02 05 09

13.770 10.325 06.880 03.436 59.991 56.546

-1.102 1.109 1.117 1.124 1.130 1.134

20 20 19 19 19 19

06 02 58 54 50 46

28.039 32.129 36.220 40.310 44.401 48.491

4 5 6 7 8 9

16 16 16 17 17 17

51 55 59 03 07 11

35.316 31.872 28.427 24.983 21.538 18.093

-1.104 1.099 1.091 1.081 1.072 1.064

17 17 16 16 16 16

05 01 57 53 49 45

36.203 40.294 44.384 48.475 52.565 56.656

25 26 27 28 29 30

14 14 14 14 14 14

13 17 21 25 29 33

53.102 49.657 46.212 42.768 39.323 35.879

-1.136 1.135 1.132 1.127 1.122 1.117

19 19 19 19 19 19

42 38 35 31 27 23

52.582 56.673 00.763 04.854 08.944 13.035

10 11 12 13 14 15

17 17 17 17 17 17

15 19 23 27 30 34

14.649 11.204 07.759 04.315 60.870 57.426

-1.059 1.056 1.057 1.060 1.063 1.067

16 16 16 16 16 16

42 38 34 30 26 22

00.746 04.837 08.927 13.018 17.108 21.199

1 2 3 4 5 6

14 14 14 14 14 14

37 41 45 49 53 57

32.434 28.989 25.545 22.100 18.655 15.211

-1.114 1.114 1.117 1.122 1.129 1.135

19 19 19 19 19 18

19 15 11 07 03 59

17.125 21.216 25.306 29.397 33.487 37.578

16 17 18 19 20 21

17 17 17 17 17 17

38 42 46 50 54 58

53.981 50.536 47.092 43.647 40.202 36.758

-1.071 1.073 1.072 1.069 1.064 1.056

16 16 16 16 16 15

18 14 10 06 02 58

25.290 29.380 33.471 37.561 41.652 45.742

7 8 9 10 11 12

15 15 15 15 15 15

01 05 09 13 16 20

11.766 08.322 04.877 01.432 57.988 54.543

-1.138 1.137 1.133 1.125 1.118 1.110

18 18 18 18 18 18

55 51 47 43 39 36

41.668 45.759 49.849 53.940 58.030 02.121

22 23 24 25 26 27

18 18 18 18 18 18

02 06 10 14 18 22

33.313 29.868 26.424 22.979 19.535 16.090

-1.047 1.039 1.031 1.027 1.026 1.028

15 15 15 15 15 15

54 50 46 43 39 35

49.833 53.923 58.014 02.104 06.195 10.285

13 14 15 16 17

15 15 15 15 15

24 28 32 36 40

51.098 47.654 44.209 40.764 37.320

-1.106 1.103 1.104 1.107 -1.111

18 18 18 18 18

32 28 24 20 16

06.211 10.302 14.393 18.483 July 22.574

28 29 30 1 2

18 18 18 18 18

26 30 34 38 41

12.645 09.201 05.756 02.311 58.867

-1.031 1.036 1.038 1.038 -1.035

15 15 15 15 15

31 27 23 19 15

14.376 18.466 22.557 26.647 30.738

N.B.-Apparent Sidereal Time = Mean Sidereal Time + Equation of Equinoxes for the instant

15

SIDEREAL TIME, 2020 Greenwich Mean Greenwich Equation Transit of Mean Sidereal Time at of the 0h U.T. (G.H.A. Equinox- Equinox (U.T. at of the Equinox) es at 0h 0h G.M.S.T.) U.T.

Date

July

Aug.

Greenwich Mean Greenwich Equation Transit of Mean Sidereal Time at of the 0h U.T. (G.H.A. Equinox- Equinox (U.T. at of the Equinox) es at 0h 0h G.M.S.T.) U.T.

Date

1 2 3 4 5 6

h 18 18 18 18 18 18

m 38 41 45 49 53 57

s 02.311 58.867 55.422 51.978 48.533 45.088

s -1.038 1.035 1.028 1.019 1.009 1.001

h 15 15 15 15 15 14

m 19 15 11 07 03 59

s h m s 26.647 Aug. 16 21 39 23.858 30.738 17 21 43 20.414 34.829 18 21 47 16.969 38.919 19 21 51 13.524 43.010 20 21 55 10.080 47.100 21 21 59 06.635

s -0.979 0.974 0.971 0.970 0.974 0.980

h 22 22 22 22 22 21

m 16 13 09 05 01 57

s 56.516 00.607 04.697 08.788 12.878 16.969

7 8 9 10 11 12

19 19 19 19 19 19

01 05 09 13 17 21

41.644 38.199 34.754 31.310 27.865 24.420

-0.995 0.991 0.991 0.994 0.998 1.002

14 14 14 14 14 14

55 51 47 44 40 36

51.191 55.281 59.372 03.462 07.553 11.643

22 23 24 25 26 27

22 22 22 22 22 22

03 06 10 14 18 22

03.191 59.746 56.301 52.857 49.412 45.967

-0.988 0.996 1.001 1.003 1.001 0.997

21 21 21 21 21 21

53 49 45 41 37 33

21.059 25.150 29.240 33.331 37.422 41.512

13 14 15 16 17 18

19 19 19 19 19 19

25 29 33 37 41 45

20.976 17.531 14.087 10.642 07.197 03.753

-1.006 1.009 1.011 1.009 1.006 1.000

14 14 14 14 14 14

32 28 24 20 16 12

15.734 19.824 23.915 28.005 32.096 Sept. 36.186

28 29 30 31 1 2

22 22 22 22 22 22

26 30 34 38 42 46

42.523 39.078 35.634 32.189 28.744 25.300

-0.992 0.988 0.984 0.984 0.986 0.991

21 21 21 21 21 21

29 25 21 17 14 10

45.603 49.693 53.784 57.874 01.965 06.055

19 20 21 22 23 24

19 19 19 20 20 20

48 52 56 00 04 08

60.308 56.863 53.419 49.974 46.530 43.085

-0.992 0.984 0.977 0.973 0.972 0.974

14 14 14 23 23 23

08 04 00 55 51 47

40.277 44.367 48.458 14.253 18.344 22.434

3 4 5 6 7 8

22 22 22 23 23 23

50 54 58 02 06 10

21.855 18.410 14.966 11.521 08.076 04.632

-0.998 1.007 1.015 1.024 1.030 1.035

21 21 20 20 20 20

06 02 58 54 50 46

10.146 14.236 18.327 22.417 26.508 30.598

25 26 27 28 29 30

20 20 20 20 20 20

12 16 20 24 28 32

39.640 36.196 32.751 29.306 25.862 22.417

-0.979 0.985 0.990 0.992 0.991 0.987

23 23 23 23 23 23

43 39 35 31 27 23

26.525 30.615 34.706 38.796 42.887 46.977

9 10 11 12 13 14

23 23 23 23 23 23

14 17 21 25 29 33

01.187 57.743 54.298 50.853 47.409 43.964

-1.037 1.036 1.034 1.031 1.027 1.024

20 20 20 20 20 20

42 38 34 30 26 22

34.689 38.780 42.870 46.961 51.051 55.142

31 1 2 3 4 5

20 20 20 20 20 20

36 40 44 48 52 56

18.972 15.528 12.083 08.639 05.194 01.749

-0.980 0.972 0.966 0.961 0.959 0.959

23 23 23 23 23 23

19 15 11 08 04 00

51.068 55.158 59.249 03.339 07.430 11.520

15 16 17 18 19 20

23 23 23 23 23 23

37 41 45 49 53 57

40.519 37.075 33.630 30.186 26.741 23.296

-1.024 1.028 1.035 1.044 1.053 1.060

20 20 20 20 20 19

18 15 11 07 03 59

59.232 03.323 07.413 11.504 15.594 19.685

6 7 8 9 10 11

20 21 21 21 21 21

59 03 07 11 15 19

58.305 54.860 51.415 47.971 44.526 41.082

-0.963 0.969 0.975 0.982 0.987 0.991

22 22 22 22 22 22

56 52 48 44 40 36

15.611 19.702 23.792 27.883 31.973 36.064

21 22 23 24 25 26

0 0 0 0 0 0

01 05 09 13 17 21

19.852 16.407 12.962 09.518 06.073 02.628

-1.064 1.064 1.061 1.057 1.053 1.050

23 23 23 23 23 23

54 50 46 42 39 35

44.457 48.548 52.638 56.729 00.819 04.910

12 13 14 15 16

21 21 21 21 21

23 27 31 35 39

37.637 34.192 30.748 27.303 23.858

-0.993 0.993 0.990 0.985 -0.979

22 22 22 22 22

32 28 24 20 16

40.154 44.245 48.335 52.426 56.516 Oct.

27 28 29 30 1

0 0 0 0 0

24 28 32 36 40

59.184 55.739 52.295 48.850 45.405

-1.049 1.052 1.057 1.064 -1.073

23 23 23 23 23

31 27 23 19 15

09.000 13.091 17.181 21.272 25.362

N.B.-Apparent Sidereal Time = Mean Sidereal Time + Equation of Equinoxes for the instant

16

SIDEREAL TIME, 2020 Greenwich Mean Greenwich Equation Transit of Mean Sidereal Time at of the 0h U.T. (G.H.A. Equinox- Equinox (U.T. at of the Equinox) es at 0h 0h G.M.S.T.) U.T.

Date

Oct.

Nov.

Greenwich Mean Greenwich Equation Transit of Mean Sidereal Time at of the 0h U.T. (G.H.A. Equinox- Equinox (U.T. at of the Equinox) es at 0h 0h G.M.S.T.) U.T.

Date

1 2 3 4 5 6

h 0 0 0 0 0 1

m 40 44 48 52 56 00

s 45.405 41.961 38.516 35.071 31.627 28.182

s -1.073 1.082 1.090 1.097 1.103 1.105

h 23 23 23 23 22 22

m 15 11 07 03 59 55

s 25.362 Nov. 16 29.453 17 33.543 18 37.634 19 41.725 20 45.815 21

h 3 3 3 3 3 4

m 42 46 49 53 57 01

s 06.952 03.508 60.063 56.618 53.174 49.729

s -1.132 1.124 1.114 1.105 1.098 1.094

h 20 20 20 20 19 19

m 14 10 06 02 58 54

s 33.527 37.617 41.708 45.798 49.889 53.979

7 8 9 10 11 12

1 1 1 1 1 1

04 08 12 16 20 24

24.738 21.293 17.848 14.404 10.959 07.514

-1.106 1.104 1.101 1.097 1.094 1.093

22 22 22 22 22 22

51 47 43 40 36 32

49.906 53.996 58.087 02.177 06.268 10.358

22 23 24 25 26 27

4 4 4 4 4 4

05 09 13 17 21 25

46.284 42.840 39.395 35.951 32.506 29.061

-1.093 1.094 1.098 1.103 1.107 1.111

19 19 19 19 19 19

50 47 43 39 35 31

58.070 02.161 06.251 10.342 14.432 18.523

13 14 15 16 17 18

1 1 1 1 1 1

28 31 35 39 43 47

04.070 60.625 57.180 53.736 50.291 46.847

-1.095 1.099 1.107 1.116 1.123 1.128

22 22 22 22 22 22

28 24 20 16 12 08

14.449 18.539 22.630 26.720 Dec. 30.811 34.901

28 29 30 1 2 3

4 4 4 4 4 4

29 33 37 41 45 49

25.617 22.172 18.727 15.283 11.838 08.394

-1.112 1.112 1.108 1.103 1.096 1.088

19 19 19 19 19 19

27 23 19 15 11 07

22.613 26.704 30.794 34.885 38.975 43.066

19 20 21 22 23 24

1 1 1 2 2 2

51 55 59 03 07 11

43.402 39.957 36.513 33.068 29.623 26.179

-1.128 1.124 1.118 1.111 1.106 1.103

22 22 21 21 21 21

04 00 56 52 48 44

38.992 43.083 47.173 51.264 55.354 59.445

4 5 6 7 8 9

4 4 5 5 5 5

53 57 00 04 08 12

04.949 01.504 58.060 54.615 51.170 47.726

-1.080 1.073 1.069 1.067 1.068 1.072

19 18 18 18 18 18

03 59 55 51 48 44

47.156 51.247 55.337 59.428 03.518 07.609

25 26 27 28 29 30

2 2 2 2 2 2

15 19 23 27 31 35

22.734 19.290 15.845 12.400 08.956 05.511

-1.103 1.106 1.111 1.118 1.125 1.132

21 21 21 21 21 21

41 37 33 29 25 21

03.535 07.626 11.716 15.807 19.897 23.988

10 11 12 13 14 15

5 5 5 5 5 5

16 20 24 28 32 36

44.281 40.836 37.392 33.947 30.503 27.058

-1.075 1.078 1.078 1.073 1.064 1.053

18 18 18 18 18 18

40 36 32 28 24 20

11.699 15.790 19.881 23.971 28.062 32.152

31 1 2 3 4 5

2 2 2 2 2 2

39 42 46 50 54 58

02.066 58.622 55.177 51.732 48.288 44.843

-1.138 1.141 1.143 1.141 1.138 1.133

21 21 21 21 21 20

17 13 09 05 01 57

28.078 32.169 36.259 40.350 44.440 48.531

16 17 18 19 20 21

5 5 5 5 5 6

40 44 48 52 56 00

23.613 20.169 16.724 13.279 09.835 06.390

-1.041 1.031 1.023 1.019 1.019 1.020

18 18 18 18 18 17

16 12 08 04 00 56

36.243 40.333 44.424 48.514 52.605 56.695

6 7 8 9 10 11

3 3 3 3 3 3

02 06 10 14 18 22

41.399 37.954 34.509 31.065 27.620 24.175

-1.127 1.122 1.118 1.117 1.118 1.122

20 20 20 20 20 20

53 49 46 42 38 34

52.622 56.712 00.803 04.893 08.984 13.074

22 23 24 25 26 27

6 6 6 6 6 6

04 07 11 15 19 23

02.946 59.501 56.056 52.612 49.167 45.722

-1.024 1.027 1.030 1.031 1.030 1.027

17 17 17 17 17 17

53 49 45 41 37 33

00.786 04.876 08.967 13.057 17.148 21.239

12 13 14 15 16

3 3 3 3 3

26 30 34 38 42

20.731 17.286 13.842 10.397 06.952

-1.128 1.134 1.138 1.137 -1.132

20 20 20 20 20

30 26 22 18 14

17.165 21.255 25.346 29.436 33.527 Dec

28 29 30 31 32

6 6 6 6 6

27 31 35 39 43

42.278 38.833 35.388 31.944 28.499

-1.021 1.014 1.005 0.996 -0.988

17 17 17 17 17

29 25 21 17 13

25.329 29.420 33.510 37.601 41.691

N.B.-Apparent Sidereal Time = Mean Sidereal Time + Equation of Equinoxes for the instant

17

SUN, 2020 MEAN LONGITUDE AND ANOMALY Date

Horizontal Parallax

Mean Longitude

Mean Anomaly

Horizontal Parallax

Date

Mean Longitude

Mean Anomaly

1 11 21 31 10 20

" 8.94 8.94 8.94 8.93 8.91 8.9

° 280 289 299 309 319 329

 07 59 50 41 33 24

" 39.318 02.623 25.928 49.233 12.538 35.843

° 356.846 Jul 6.702 16.558 26.414 Aug 36.270 46.126

9 19 29 8 18 28

" 8.65 8.65 8.66 8.67 8.69 8.71

°  107 24 117 15 127 06 136 58 146 49 156 40

" 02.112 25.417 48.722 12.027 35.332 58.637

° 184.110 193.966 203.822 213.678 223.534 233.390

Mar

1 11 21 31 Apr 10 20

8.88 8.85 8.83 8.8 8.78 8.75

339 349 358 8 18 28

15 07 58 50 41 32

59.148 22.453 45.758 09.063 32.368 55.673

55.982 Sep 65.838 75.694 85.550 Oct 95.406 105.262

7 17 27 7 17 27

8.73 8.75 8.77 8.8 8.82 8.85

166 176 186 196 205 215

32 23 15 06 57 49

21.942 45.247 08.552 31.857 55.162 18.467

243.246 253.102 262.958 272.814 282.670 292.526

30 May 10 20 30 Jun 9 19

8.73 8.71 8.69 8.67 8.66 8.65

38 48 58 67 77 87

24 15 07 58 49 41

18.978 42.283 05.588 28.892 52.197 15.502

115.118 Nov 124.974 134.830 144.686 Dec 154.542 164.398

6 16 26 6 16 26

8.87 8.89 8.91 8.93 8.94 8.94

225 235 245 255 265 274

40 32 23 14 06 57

41.772 05.077 28.382 51.687 14.992 38.297

302.382 312.238 322.094 331.950 341.806 351.662

29 9

8.65 8.65

97 107

32 24

38.807 02.112

174.254 184.110

36 46

8.94 284 8.94 294

49 40

01.602 24.907

1.518 11.374

Jan

Feb

Jul

18

SUN, 2020 FOR 0h TERRESTRIAL TIME Date

Jan. 0 1 2 3 4 5

Geometric Longitude* Latitude Apparent Longitude Aberra- Prec. in Nut. in Nut. in True (Mean Equinox ( Ecliptic (True equinox of date) tion Long. Long. Obliquity Obliquity of date ) of date ) ( J 2020.5 (23° 26') of date ) ° ' '' '' ° ' '' '' '' '' '' '' 278 59 58.46 -0.40 278 59 21.19 20.84 -25.58 -16.47 -1.75 10.29 280 01 08.58 0.47 280 00 31.28 20.84 25.44 16.49 1.70 10.34 281 02 18.57 0.50 281 01 41.23 20.84 25.30 16.54 1.67 10.37 282 03 28.40 0.50 282 02 51.00 20.84 25.16 16.60 1.65 10.39 283 04 38.04 0.47 283 04 00.59 20.84 25.02 16.66 1.65 10.39 284 05 47.38 0.43 284 05 09.89 20.84 24.88 16.69 1.66 10.38

6 7 8 9 10 11

285 286 287 288 289 290

06 08 09 10 11 12

56.46 05.21 13.67 21.80 29.61 37.13

-0.36 0.25 -0.11 +0.00 0.14 0.29

285 286 287 288 289 290

06 07 08 09 10 12

18.97 27.77 36.31 44.57 52.54 00.22

20.84 20.84 20.84 20.84 20.84 20.84

-24.74 -16.69 24.60 16.65 24.46 16.56 24.33 16.43 24.19 16.28 24.05 16.12

-1.68 1.70 1.72 1.72 1.71 1.67

10.36 10.33 10.31 10.30 10.32 10.35

12 13 14 15 16 17

291 292 293 294 295 296

13 14 15 17 18 19

44.44 51.50 58.41 05.16 11.80 18.25

+0.43 0.58 0.65 0.72 0.76 0.76

291 292 293 294 295 296

13 14 15 16 17 18

07.64 14.78 21.71 28.42 34.98 41.36

20.84 20.84 20.84 20.84 20.84 20.84

-23.91 -16.00 23.77 15.92 23.63 15.91 23.49 15.95 23.35 16.02 23.21 16.10

-1.61 1.54 1.46 1.40 1.36 1.34

10.41 10.49 10.56 10.62 10.66 10.67

18 19 20 21 22 23

297 298 299 300 301 302

20 21 22 23 24 25

24.57 30.67 36.50 41.97 47.05 51.65

+0.72 0.65 0.54 0.43 0.32 0.18

297 298 299 300 301 302

19 20 21 23 24 25

47.64 53.74 59.62 05.17 10.37 15.10

20.83 20.83 20.83 20.83 20.83 20.82

-23.08 -16.15 22.94 16.15 22.80 16.10 22.66 16.02 22.52 15.90 22.38 15.78

-1.35 1.37 1.39 1.40 1.40 1.37

10.67 10.65 10.63 10.61 10.62 10.64

24 25 26 27 28 29

303 304 305 306 307 308

26 27 29 30 31 32

55.63 58.91 01.41 03.04 03.75 03.41

+0.04 -0.07 0.18 0.29 0.36 0.40

303 304 305 306 307 308

26 27 28 29 30 31

19.18 22.54 25.07 26.70 27.36 26.94

20.82 20.82 20.82 20.82 20.81 20.81

-22.24 -15.67 22.10 15.60 21.96 15.57 21.83 15.57 21.69 15.62 21.55 15.70

-1.33 1.27 1.21 1.14 1.08 1.03

10.68 10.74 10.80 10.87 10.92 10.97

30 31 Feb. 1 2 3 4

309 310 311 312 313 314

33 33 34 35 36 37

01.96 59.32 55.49 50.36 43.91 36.15

-0.40 0.40 0.36 0.29 0.18 -0.07

309 310 311 312 313 314

32 33 34 35 36 36

25.40 22.68 18.77 13.60 07.13 59.40

20.81 20.81 20.80 20.80 20.80 20.79

-21.41 -15.79 21.27 15.88 21.13 15.96 20.99 16.01 20.85 16.03 20.72 16.00

-1.00 0.98 0.97 0.98 0.99 1.00

11.01 11.02 11.03 11.02 11.01 11.00

5 6 7 8 9 10

315 316 317 318 319 320

38 39 40 40 41 42

26.94 16.41 04.46 51.12 36.45 20.51

+0.04 0.18 0.32 0.47 0.58 0.68

315 316 317 318 319 320

37 38 39 40 41 41

50.27 39.84 28.01 14.77 00.17 44.23

20.79 20.79 20.79 20.78 20.78 20.77

-20.58 -15.93 20.44 15.83 20.30 15.71 20.16 15.61 20.02 15.55 19.88 15.55

-1.00 0.99 0.95 0.90 0.82 0.73

10.99 11.00 11.04 11.09 11.17 11.25

11 321 43 03.30 +0.76 12 322 43 44.92 0.79 13 323 44 25.39 0.79 14 324 45 04.76 0.76 15 325 45 42.98 +0.72 *To obtain the geometric longitude referred precession from J 2020.5.

321 322 323 324 325 to the

42 26.96 20.77 -19.74 43 08.47 20.77 19.60 43 48.83 20.76 19.47 44 28.10 20.76 19.33 45 06.26 20.75 -19.19 mean equinox of J 2000.0, add

-15.62 -0.66 11.33 15.72 0.61 11.38 15.84 0.58 11.41 15.95 0.58 11.41 -16.00 -0.59 11.39 -17' 10".958 and subtract

19

SUN, 2020 FOR 0 TERRESTRIAL TIME h

Apparent Right Ascension

Date

Apparent Declination

True Distance from the Earth

Semi Diameter

Ephemeris Transit

0 1 2 3 4 5

h 18 18 18 18 18 19

m 39 43 47 52 56 01

s 07.80 33.11 58.12 22.77 47.06 10.94

º -23 23 22 22 22 22

' 07 03 58 53 47 41

" 53.76 31.98 42.54 25.57 41.24 29.72

0.983 3175 0.983 2931 0.983 2733 0.983 2583 0.983 2484 0.983 2439

' 16 16 16 16 16 16

" 15.93 15.95 15.97 15.98 15.99 16.00

h 12 12 12 12 12 12

m 02 03 03 04 04 05

s 50.60 19.22 47.51 15.44 42.98 10.11

6 7 8 9 10 11

19 19 19 19 19 19

05 09 14 18 23 27

34.40 57.39 19.91 41.91 03.39 24.32

-22 22 22 22 22 21

34 27 20 12 03 55

51.20 45.88 13.99 15.76 51.43 01.25

0.983 2449 0.983 2516 0.983 2645 0.983 2835 0.983 3090 0.983 3410

16 16 16 16 16 16

16.00 15.99 15.98 15.96 15.93 15.90

12 12 12 12 12 12

05 06 06 06 07 07

36.78 02.99 28.70 53.88 18.53 42.62

12 13 14 15 16 17

19 19 19 19 19 19

31 36 40 44 49 53

44.68 04.45 23.61 42.14 00.04 17.29

-21 21 21 21 21 20

45 36 25 15 04 53

45.48 04.37 58.19 27.20 31.68 11.91

0.983 3796 0.983 4248 0.983 4763 0.983 5341 0.983 5977 0.983 6669

16 16 16 16 16 16

15.86 15.82 15.77 15.71 15.65 15.58

12 12 12 12 12 12

08 08 08 09 09 09

06.12 29.03 51.33 13.00 34.02 54.39

18 19 20 21 22 23

19 20 20 20 20 20

57 01 06 10 14 18

33.87 49.76 04.96 19.44 33.18 46.18

-20 20 20 20 19 19

41 29 16 03 50 37

28.20 20.87 50.25 56.68 40.53 02.14

0.983 7412 0.983 8203 0.983 9040 0.983 9918 0.984 0835 0.984 1789

16 16 16 16 16 16

15.51 15.43 15.34 15.26 15.17 15.07

12 12 12 12 12 12

10 10 10 11 11 11

14.07 33.06 51.34 08.89 25.70 41.75

24 25 26 27 28 29

20 20 20 20 20 20

22 27 31 35 39 43

58.41 09.87 20.52 30.38 39.42 47.63

-19 19 18 18 18 18

23 08 53 38 23 07

01.89 40.16 57.31 53.73 29.81 45.93

0.984 2780 0.984 3805 0.984 4865 0.984 5960 0.984 7091 0.984 8258

16 16 16 16 16 16

14.97 14.87 14.77 14.66 14.55 14.43

12 12 12 12 12 12

11 12 12 12 12 13

57.03 11.53 25.22 38.11 50.18 01.43

30 31 Feb. 1 2 3 4

20 20 20 21 21 21

47 52 56 00 04 08

55.03 01.59 07.31 12.21 16.27 19.50

-17 17 17 17 16 16

51 35 18 01 44 26

42.50 19.92 38.59 38.92 21.33 46.24

0.984 9462 0.985 0706 0.985 1991 0.985 3317 0.985 4688 0.985 6106

16 16 16 16 16 16

14.31 14.19 14.06 13.93 13.80 13.66

12 12 12 12 12 12

13 13 13 13 13 13

11.85 21.44 30.19 38.11 45.19 51.44

5 6 7 8 9 10

21 21 21 21 21 21

12 16 20 24 28 32

21.90 23.48 24.24 24.19 23.33 21.68

-16 15 15 15 14 14

08 50 32 13 54 35

54.07 45.24 20.16 39.26 42.95 31.62

0.985 7572 0.985 9088 0.986 0658 0.986 2282 0.986 3963 0.986 5700

16 16 16 16 16 16

13.51 13.36 13.21 13.05 12.88 12.71

12 12 12 12 12 12

13 14 14 14 14 14

56.86 01.46 05.24 08.22 10.40 11.80

11 12 13 14 15

21 21 21 21 21

36 40 44 48 52

19.25 16.05 12.10 07.42 02.02

-14 13 13 13 -12

16 56 36 16 56

05.67 25.48 31.42 23.88 03.27

0.986 7493 0.986 9340 0.987 1239 0.987 3187 0.987 5179

16 16 16 16 16

12.53 12.35 12.16 11.97 11.77

12 12 12 12 12

14 14 14 14 14

12.42 12.29 11.42 09.82 07.50

Jan.

20

SUN, 2020 FOR 0h TERRESTRIAL TIME Date

Feb. 15 16 17 18 19 20

Geometric Longitude* Latitude Apparent Longitude Aberra- Prec. in Nut. in Nut. in True (Mean Equinox ( Ecliptic (True equinox of date) tion Long. Long. Obliquity Obliquity of date ) of date ) ( J 2020.5 (23° 26') of date ) ° ' '' '' ° ' '' '' '' '' '' '' 325 45 42.98 +0.72 325 45 06.26 20.75 -19.19 -16.00 -0.59 11.39 326 46 20.09 0.61 326 45 43.38 20.75 19.05 16.01 0.61 11.37 327 46 56.05 0.50 327 46 19.38 20.75 18.91 15.97 0.63 11.35 328 47 30.83 0.40 328 46 54.23 20.74 18.77 15.90 0.63 11.35 329 48 04.34 0.25 329 47 27.82 20.74 18.63 15.83 0.61 11.37 330 48 36.56 0.14 330 48 00.11 20.73 18.49 15.76 0.57 11.40

21 22 23 24 25 26

331 332 333 334 335 336

49 49 50 50 50 51

07.37 36.74 04.61 30.85 55.44 18.25

+0.00 -0.11 0.18 0.25 0.32 0.32

331 332 333 334 335 336

48 49 49 49 50 50

30.96 00.34 28.16 54.34 18.82 41.50

20.73 20.72 20.72 20.71 20.71 20.70

-18.35 -15.73 18.22 15.73 18.08 15.77 17.94 15.85 17.80 15.96 17.66 16.10

-0.52 0.46 0.40 0.34 0.29 0.26

11.45 11.51 11.57 11.63 11.68 11.71

27 28 29 Mar. 1 2 3

337 338 339 340 341 342

51 51 52 52 52 52

39.30 58.43 15.66 30.88 44.11 55.25

-0.32 0.29 0.22 0.14 -0.04 +0.07

337 338 339 340 341 342

51 51 51 51 52 52

02.41 21.42 38.56 53.71 06.92 18.08

20.70 20.69 20.69 20.68 20.68 20.67

-17.52 -16.23 17.38 16.36 17.24 16.46 17.10 16.53 16.96 16.55 16.83 16.54

-0.24 0.24 0.25 0.27 0.29 0.30

11.73 11.73 11.72 11.70 11.67 11.66

4 5 6 7 8 9

343 344 345 346 347 348

53 53 53 53 53 53

04.27 11.22 16.04 18.73 19.38 17.97

+0.22 0.32 0.47 0.58 0.68 0.76

343 344 345 346 347 348

52 52 52 52 52 52

27.16 34.18 39.07 41.81 42.46 40.98

20.67 20.66 20.66 20.65 20.65 20.64

-16.69 -16.49 16.55 16.42 16.41 16.35 16.27 16.31 16.13 16.32 15.99 16.39

-0.30 0.29 0.25 0.19 0.12 -0.05

11.65 11.67 11.70 11.76 11.83 11.90

10 11 12 13 14 15

349 350 351 352 353 354

53 53 53 52 52 52

14.59 09.30 02.24 53.37 42.83 30.58

+0.79 0.83 0.79 0.76 0.65 0.54

349 350 351 352 353 354

52 52 52 52 52 51

37.49 32.05 24.85 15.89 05.30 53.06

20.64 20.63 20.63 20.62 20.62 20.61

-15.85 -16.51 15.71 16.67 15.58 16.81 15.44 16.91 15.30 16.96 15.16 16.95

+0.00 0.03 +0.02 -0.01 0.04 0.08

11.95 11.98 11.97 11.94 11.90 11.87

16 17 18 19 20 21

355 356 357 358 359 0

52 52 51 51 51 50

16.67 01.05 43.75 24.71 03.91 41.27

+0.43 0.29 0.18 +0.07 -0.04 0.14

355 356 357 358 359 0

51 51 51 50 50 50

39.20 23.65 06.41 47.40 26.59 03.91

20.60 20.60 20.59 20.59 20.58 20.57

-15.02 -16.90 14.88 16.85 14.74 16.80 14.60 16.77 14.46 16.78 14.33 16.83

-0.10 0.10 0.08 0.05 -0.01 +0.04

11.85 11.84 11.86 11.89 11.93 11.98

22 23 24 25 26 27

1 2 3 4 5 6

50 49 49 48 48 47

16.81 50.39 22.05 51.67 19.22 44.67

-0.22 0.25 0.29 0.29 0.25 0.22

1 2 3 4 5 6

49 49 48 48 47 47

39.36 12.83 44.35 13.82 41.24 06.58

20.57 20.56 20.56 20.55 20.55 20.54

-14.19 -16.92 14.05 17.05 13.91 17.19 13.77 17.34 13.63 17.48 13.49 17.60

+0.08 0.12 0.14 0.14 0.13 0.10

12.02 12.05 12.07 12.07 12.06 12.03

28 7 47 07.92 0.11 7 29 8 46 29.01 -0.04 8 30 9 45 47.79 +0.11 9 31 10 45 04.30 0.22 10 Apr. 1 11 44 18.48 +0.36 11 *To obtain the geometric longitude referred to the precession from J 2020.5.

46 29.75 20.53 -13.35 45 50.80 20.53 13.21 45 09.58 20.52 13.08 44 26.12 20.52 12.94 43 40.37 20.51 -12.80 mean equinox of J 2000.0, add

-17.69 +0.07 12.00 17.73 +0.03 11.96 17.74 -0.00 11.92 17.71 0.03 11.89 -17.65 -0.04 11.88 -17' 10".958 and subtract

21

SUN, 2020 h FOR 0 TERRESTRIAL TIME Apparent Right Ascension

Date

Apparent Declination

True Distance from the Earth

Semi Diameter

Ephemeris Transit

Feb. 15 16 17 18 19 20

h 21 21 21 22 22 22

m 52 55 59 03 07 11

s 02.02 55.91 49.10 41.60 33.43 24.58

º -12 12 12 11 11 11

' 56 35 14 53 32 11

" 03.27 29.98 44.44 47.06 38.26 18.48

0.987 5179 0.987 7212 0.987 9281 0.988 1383 0.988 3515 0.988 5673

' 16 16 16 16 16 16

" 11.77 11.57 11.37 11.16 10.96 10.74

h 12 12 12 12 12 12

m 14 14 14 13 13 13

s 07.50 04.47 00.76 56.35 51.28 45.54

21 22 23 24 25 26

22 22 22 22 22 22

15 19 22 26 30 34

15.08 04.93 54.15 42.74 30.72 18.10

-10 10 10 9 9 8

49 28 06 44 22 59

48.13 07.63 17.42 17.90 09.50 52.64

0.988 7855 0.989 0060 0.989 2286 0.989 4531 0.989 6795 0.989 9078

16 16 16 16 16 16

10.53 10.31 10.09 09.87 09.65 09.43

12 12 12 12 12 12

13 13 13 13 13 12

39.15 32.12 24.47 16.20 07.32 57.86

27 28 29 Mar. 1 2 3

22 22 22 22 22 22

38 41 45 49 53 56

04.90 51.14 36.82 21.97 06.60 50.74

-8 8 7 7 7 6

37 14 52 29 06 43

27.72 55.17 15.40 28.82 35.85 36.89

0.990 1381 0.990 3702 0.990 6044 0.990 8407 0.991 0793 0.991 3202

16 16 16 16 16 16

09.20 08.98 08.75 08.52 08.28 08.05

12 12 12 12 12 12

12 12 12 12 12 11

47.83 37.23 26.09 14.43 02.25 49.58

4 5 6 7 8 9

23 23 23 23 23 23

00 04 08 11 15 19

34.39 17.57 00.32 42.63 24.55 06.08

-6 5 5 5 4 4

20 57 34 10 47 23

32.35 22.64 08.15 49.29 26.44 59.95

0.991 5637 0.991 8101 0.992 0594 0.992 3120 0.992 5679 0.992 8275

16 16 16 16 16 16

07.81 07.57 07.33 07.08 06.83 06.58

12 12 12 12 12 12

11 11 11 10 10 10

36.44 22.84 08.81 54.36 39.53 24.33

10 11 12 13 14 15

23 23 23 23 23 23

22 26 30 33 37 41

47.25 28.10 08.64 48.91 28.93 08.72

-4 3 3 2 2 2

00 36 13 49 26 02

30.20 57.51 22.21 44.65 05.16 24.10

0.993 0908 0.993 3576 0.993 6279 0.993 9014 0.994 1776 0.994 4563

16 16 16 16 16 16

06.32 06.06 05.80 05.53 05.26 04.99

12 12 12 12 12 12

10 09 09 09 09 08

08.79 52.94 36.79 20.38 03.73 46.86

16 17 18 19 20 21

23 23 23 23 23 0

44 48 52 55 59 03

48.30 27.70 06.92 45.99 24.93 03.75

-1 1 0 -0 +0 0

38 14 51 27 03 19

41.83 58.72 15.15 31.49 48.12 54.59

0.994 7371 0.995 0194 0.995 3029 0.995 5873 0.995 8723 0.996 1576

16 16 16 16 16 16

04.72 04.45 04.17 03.90 03.62 03.35

12 12 12 12 12 12

08 08 07 07 07 07

29.79 12.54 55.13 37.58 19.90 02.12

22 23 24 25 26 27

0 0 0 0 0 0

06 10 13 17 21 24

42.46 21.10 59.68 38.21 16.71 55.20

+0 1 1 1 2 2

43 07 30 54 18 41

36.26 16.52 55.00 31.32 05.11 36.01

0.996 4430 0.996 7282 0.997 0131 0.997 2977 0.997 5817 0.997 8652

16 16 16 16 16 16

03.07 02.79 02.52 02.25 01.97 01.70

12 12 12 12 12 12

06 06 06 05 05 05

44.25 26.31 08.32 50.29 32.24 14.19

28 29 30 31 Apr. 1

0 0 0 0 0

28 32 35 39 43

33.70 12.23 50.81 29.44 08.15

+3 3 3 4 +4

05 28 51 15 38

03.63 27.61 47.58 03.18 14.02

0.998 1482 0.998 4306 0.998 7127 0.998 9944 0.999 2759

16 16 16 16 16

01.43 01.15 00.88 00.61 00.34

12 12 12 12 12

04 04 04 04 03

56.16 38.16 20.21 02.32 44.53

22

SUN, 2020 FOR 0h TERRESTRIAL TIME Date

Apr. 1 2 3 4 5 6

Geometric Longitude* Latitude Apparent Longitude Aberra- Prec. in Nut. in Nut. in True (Mean Equinox ( Ecliptic (True equinox of date) tion Long. Long. Obliquity Obliquity of date ) of date ) ( J 2020.5 (23° 26') of date ) ° ' '' '' ° ' '' '' '' '' '' '' 11 44 18.48 +0.36 11 43 40.37 20.51 -12.80 -17.65 -0.04 11.88 12 43 30.36 0.47 12 42 52.31 20.50 12.66 17.59 -0.03 11.89 13 42 39.83 0.58 13 42 01.84 20.50 12.52 17.54 0.00 11.92 14 41 47.01 0.68 14 41 09.02 20.49 12.38 17.53 +0.05 11.97 15 40 51.89 0.76 15 40 13.87 20.49 12.24 17.58 0.10 12.02 16 39 54.46 0.83 16 39 16.34 20.48 12.10 17.68 0.15 12.06

7 8 9 10 11 12

17 18 19 20 21 22

38 37 36 35 34 33

54.83 53.09 49.33 43.57 35.99 26.63

+0.83 0.79 0.76 0.68 0.58 0.43

17 18 19 20 21 22

38 37 36 35 33 32

16.58 14.70 10.84 05.03 57.46 48.16

20.48 20.47 20.46 20.46 20.45 20.45

-11.96 -17.82 11.83 17.96 11.69 18.08 11.55 18.13 11.41 18.13 11.27 18.07

+0.17 0.16 0.12 0.07 +0.01 -0.03

12.08 12.07 12.03 11.98 11.92 11.87

13 14 15 16 17 18

23 24 25 26 27 28

32 31 29 28 27 25

15.48 02.64 48.09 31.81 13.89 54.21

+0.32 0.18 +0.07 -0.04 0.14 0.22

23 24 25 26 27 28

31 30 29 27 26 25

37.09 24.34 09.85 53.60 35.66 15.92

20.44 20.43 20.43 20.42 20.42 20.41

-11.13 -17.99 10.99 17.91 10.85 17.85 10.71 17.83 10.58 17.85 10.44 17.92

-0.06 0.06 0.05 -0.02 +0.01 0.04

11.85 11.84 11.85 11.88 11.91 11.94

19 20 21 22 23 24

29 30 31 32 33 34

24 23 21 20 18 17

32.83 09.71 44.76 18.01 49.43 18.96

-0.29 0.29 0.29 0.29 0.22 0.14

29 30 31 32 33 34

23 22 21 19 18 16

54.46 31.22 06.16 39.29 10.62 40.08

20.41 20.40 20.39 20.39 20.38 20.38

-10.30 -18.01 10.16 18.13 10.02 18.26 9.88 18.38 9.74 18.48 9.60 18.55

+0.06 0.07 0.06 0.04 +0.01 -0.04

11.96 11.97 11.96 11.94 11.90 11.85

25 26 27 28 29 30

35 36 37 38 39 40

15 14 12 10 09 07

46.57 12.23 35.91 57.54 17.15 34.69

-0.04 +0.07 0.18 0.32 0.43 0.54

35 36 37 38 39 40

15 13 11 10 08 06

07.67 33.35 57.08 18.80 38.51 56.12

20.37 20.37 20.36 20.36 20.35 20.35

-9.46 -18.57 9.33 18.56 9.19 18.51 9.05 18.43 8.91 18.34 8.77 18.26

-0.09 0.14 0.18 0.20 0.21 0.19

11.80 11.75 11.71 11.68 11.68 11.69

May 1 2 3 4 5 6

41 42 43 44 44 45

05 04 02 00 58 56

50.12 03.52 14.85 24.16 31.55 37.02

+0.65 0.72 0.79 0.79 0.79 0.76

41 42 43 43 44 45

05 03 01 59 57 55

11.62 25.02 36.30 45.53 52.81 58.19

20.34 20.34 20.33 20.33 20.32 20.32

-8.63 -18.21 8.49 18.21 8.35 18.26 8.21 18.35 8.08 18.46 7.94 18.56

-0.16 0.12 0.09 0.06 0.07 0.10

11.72 11.76 11.80 11.82 11.81 11.78

7 8 9 10 11 12

46 47 48 49 50 51

54 52 50 48 46 44

40.71 42.72 43.12 42.04 39.54 35.69

+0.65 0.58 0.43 0.29 0.18 +0.04

46 47 48 49 50 51

54 52 50 48 46 43

01.84 03.86 04.34 03.38 01.02 57.29

20.31 20.31 20.30 20.30 20.29 20.29

-7.80 -18.61 7.66 18.60 7.52 18.52 7.38 18.40 7.24 18.27 7.10 18.16

-0.15 0.22 0.28 0.32 0.33 0.33

11.72 11.66 11.60 11.56 11.54 11.54

13 52 42 30.54 14 53 40 24.14 15 54 38 16.52 16 55 36 07.65 17 56 33 57.62 *To obtain the geometric longitude precession from J 2020.5.

-0.11 52 0.22 53 0.29 54 0.36 55 -0.40 56 referred to the

41 52.22 20.28 -6.96 39 45.86 20.28 6.82 37 38.24 20.27 6.69 35 29.33 20.27 6.55 33 19.22 20.27 -6.41 mean equinox of J 2000.0, add

-18.08 -0.31 11.56 18.04 0.28 11.59 18.05 0.25 11.62 18.10 0.22 11.64 -18.17 -0.21 11.66 -17' 10".958 and subtract

23

SUN, 2020 FOR 0 TERRESTRIAL TIME h

Apparent Right Ascension

Date

Apr.

May

Apparent Declination

True Distance from the Earth

Semi Diameter

Ephemeris Transit

1 2 3 4 5 6

h 0 0 0 0 0 1

m 43 46 50 54 57 01

s 08.15 46.96 25.88 04.93 44.13 23.50

º +4 5 5 5 6 6

' 38 01 24 47 10 32

" 14.02 19.75 20.00 14.41 02.64 44.34

0.999 2759 0.999 5574 0.999 8391 1.000 1212 1.000 4040 1.000 6877

' 16 16 15 15 15 15

" 00.34 00.07 59.80 59.53 59.26 58.99

h 12 12 12 12 12 12

m 03 03 03 02 02 02

s 44.53 26.83 09.26 51.84 34.57 17.49

7 8 9 10 11 12

1 1 1 1 1 1

05 08 12 16 19 23

03.07 42.85 22.88 03.17 43.75 24.64

+6 7 7 8 8 8

55 17 40 02 24 46

19.19 46.89 07.14 19.66 24.13 20.25

1.000 9725 1.001 2585 1.001 5456 1.001 8338 1.002 1227 1.002 4121

15 15 15 15 15 15

58.71 58.44 58.16 57.89 57.61 57.34

12 12 12 12 12 12

02 01 01 01 00 00

00.62 43.98 27.59 11.47 55.65 40.15

13 14 15 16 17 18

1 1 1 1 1 1

27 30 34 38 41 45

05.86 47.42 29.33 11.62 54.29 37.36

+9 9 9 10 10 10

08 29 51 12 33 54

07.69 46.13 15.22 34.62 44.00 43.00

1.002 7016 1.002 9907 1.003 2791 1.003 5665 1.003 8525 1.004 1367

15 15 15 15 15 15

57.06 56.78 56.51 56.23 55.96 55.69

12 12 11 11 11 11

00 00 59 59 59 59

24.97 10.15 55.70 41.62 27.94 14.66

19 20 21 22 23 24

1 1 1 2 2 2

49 53 56 00 04 08

20.84 04.75 49.08 33.87 19.11 04.81

+11 11 11 12 12 12

15 36 56 16 36 56

31.28 08.50 34.32 48.39 50.37 39.92

1.004 4189 1.004 6989 1.004 9764 1.005 2512 1.005 5232 1.005 7923

15 15 15 15 15 15

55.42 55.16 54.89 54.63 54.37 54.12

11 11 11 11 11 11

59 58 58 58 58 58

01.81 49.38 37.39 25.86 14.78 04.17

25 26 27 28 29 30

2 2 2 2 2 2

11 15 19 23 27 30

50.99 37.66 24.81 12.45 00.60 49.25

+13 13 13 14 14 14

16 35 54 13 32 50

16.69 40.34 50.54 46.92 29.16 56.92

1.006 0584 1.006 3214 1.006 5814 1.006 8385 1.007 0928 1.007 3443

15 15 15 15 15 15

53.87 53.62 53.37 53.13 52.89 52.65

11 11 11 11 11 11

57 57 57 57 57 57

54.03 44.38 35.22 26.56 18.39 10.74

1 2 3 4 5 6

2 2 2 2 2 2

34 38 42 46 50 53

38.41 28.08 18.28 09.01 00.27 52.09

+15 15 15 16 16 16

09 27 44 02 19 36

09.85 07.62 49.91 16.41 26.81 20.84

1.007 5934 1.007 8402 1.008 0850 1.008 3281 1.008 5697 1.008 8101

15 15 15 15 15 15

52.41 52.18 51.95 51.72 51.49 51.26

11 11 11 11 11 11

57 56 56 56 56 56

03.60 56.98 50.89 45.33 40.32 35.86

7 8 9 10 11 12

2 3 3 3 3 3

57 01 05 09 13 17

44.46 37.40 30.92 25.02 19.71 14.98

+16 17 17 17 17 18

52 09 25 41 56 11

58.23 18.72 22.04 07.93 36.11 46.29

1.009 0494 1.009 2875 1.009 5245 1.009 7600 1.009 9939 1.010 2258

15 15 15 15 15 15

51.04 50.81 50.59 50.37 50.15 49.93

11 11 11 11 11 11

56 56 56 56 56 56

31.96 28.63 25.88 23.71 22.12 21.12

13 14 15 16 17

3 3 3 3 3

21 25 29 33 37

10.84 07.28 04.30 01.91 00.09

+18 18 18 19 +19

26 41 55 09 22

38.20 11.54 26.03 21.39 57.34

1.010 4554 1.010 6823 1.010 9062 1.011 1267 1.011 3437

15 15 15 15 15

49.72 49.50 49.29 49.08 48.88

11 11 11 11 11

56 56 56 56 56

20.71 20.89 21.65 22.99 24.91

24

SUN, 2020 FOR 0h TERRESTRIAL TIME Date

May 17 18 19 20 21 22

Geometric Longitude* Latitude Apparent Longitude Aberra- Prec. in Nut. in Nut. in True (Mean Equinox ( Ecliptic (True equinox of date) tion Long. Long. Obliquity Obliquity of date ) of date ) ( J 2020.5 (23° 26') of date ) ° ' '' '' ° ' '' '' '' '' '' '' 56 33 57.62 -0.40 56 33 19.22 20.27 -6.41 -18.17 -0.21 11.66 57 31 46.34 0.40 57 31 07.86 20.26 6.27 18.26 0.21 11.65 58 29 33.90 0.36 58 28 55.34 20.26 6.13 18.35 0.23 11.64 59 27 20.19 0.32 59 26 41.57 20.25 5.99 18.42 0.26 11.60 60 25 05.30 0.25 60 24 26.64 20.25 5.85 18.46 0.30 11.56 61 22 49.11 0.14 61 22 10.45 20.25 5.71 18.46 0.35 11.51

23 24 25 26 27 28

62 63 64 65 66 67

20 18 15 13 11 08

31.69 12.96 52.88 31.45 08.66 44.42

-0.04 +0.07 0.22 0.32 0.43 0.54

62 63 64 65 66 67

19 17 15 12 10 08

53.08 34.44 14.47 53.17 30.50 06.36

20.24 20.24 20.23 20.23 20.23 20.22

-5.57 -18.41 5.44 18.33 5.30 18.22 5.16 18.09 5.02 17.97 4.88 17.88

-0.40 0.44 0.46 0.47 0.45 0.42

11.46 11.42 11.39 11.39 11.40 11.43

29 30 31 June 1 2 3

68 69 70 70 71 72

06 03 01 58 56 53

18.79 51.76 23.27 53.44 22.27 49.81

+0.61 0.68 0.72 0.72 0.65 0.58

68 69 70 70 71 72

05 03 00 58 55 53

40.78 13.75 45.22 15.31 44.08 11.58

20.22 20.22 20.21 20.21 20.21 20.21

-4.74 -17.83 4.60 17.84 4.46 17.88 4.32 17.96 4.19 18.03 4.05 18.07

-0.37 0.33 0.30 0.29 0.30 0.34

11.47 11.52 11.55 11.56 11.54 11.50

4 5 6 7 8 9

73 74 75 76 77 78

51 48 46 43 40 38

16.18 41.48 05.75 29.17 51.76 13.70

+0.50 0.36 0.22 +0.07 -0.07 0.18

73 74 75 76 77 78

50 48 45 42 40 37

37.97 03.35 27.76 51.34 14.09 36.16

20.20 20.20 20.20 20.19 20.19 20.19

-3.91 -18.05 3.77 17.97 3.63 17.84 3.49 17.68 3.35 17.52 3.21 17.39

-0.39 0.44 0.48 0.50 0.49 0.46

11.45 11.40 11.36 11.34 11.34 11.37

10 11 12 13 14 15

79 80 81 82 83 84

35 32 30 27 24 22

34.99 55.76 16.00 35.77 55.12 14.09

-0.29 0.40 0.47 0.50 0.54 0.50

79 80 81 82 83 84

34 32 29 26 24 21

57.54 18.35 38.58 58.31 17.60 36.50

20.19 20.19 20.18 20.18 20.18 20.18

-3.07 -17.31 2.93 17.27 2.80 17.28 2.66 17.32 2.52 17.39 2.38 17.45

-0.42 0.38 0.34 0.31 0.29 0.29

11.41 11.45 11.49 11.52 11.54 11.54

16 17 18 19 20 21

85 86 87 88 89 90

19 16 14 11 08 05

32.68 50.89 08.74 26.18 43.26 59.98

-0.47 0.43 0.32 0.22 -0.11 +0.00

85 86 87 88 89 90

18 16 13 10 08 05

55.04 13.22 31.08 48.58 05.75 22.60

20.17 20.17 20.17 20.17 20.17 20.17

-2.24 -17.51 2.10 17.54 1.96 17.53 1.82 17.48 1.68 17.39 1.55 17.27

-0.30 0.33 0.36 0.39 0.42 0.44

11.52 11.50 11.46 11.43 11.40 11.38

22 23 24 25 26 27

91 92 92 93 94 95

03 00 57 55 52 49

16.22 32.06 47.39 02.22 16.53 30.27

+0.14 0.25 0.36 0.47 0.54 0.58

91 91 92 93 94 95

02 59 57 54 51 48

38.98 54.96 10.40 25.31 39.64 53.35

20.17 20.16 20.16 20.16 20.16 20.16

-1.41 -17.12 1.27 16.98 1.13 16.86 0.99 16.79 0.85 16.77 0.71 16.80

-0.43 0.41 0.36 0.30 0.24 0.19

11.38 11.41 11.45 11.51 11.57 11.62

28 96 46 43.51 +0.58 96 46 06.53 20.16 -0.57 29 97 43 56.18 0.54 97 43 19.13 20.16 0.43 30 98 41 08.35 0.47 98 40 31.26 20.16 0.30 July 1 99 38 20.12 0.40 99 37 43.03 20.16 0.16 2 100 35 31.48 +0.25 100 34 54.44 20.16 -0.02 *To obtain the geometric longitude referred to the mean equinox of J 2000.0, add precession from J 2020.5.

-16.86 -0.16 11.65 16.93 0.15 11.66 16.98 0.16 11.64 16.98 0.20 11.61 -16.92 -0.23 11.57 -17' 10".958 and subtract

25

SUN, 2020 FOR 0 TERRESTRIAL TIME h

Apparent Right Ascension

Date

Apparent Declination

True Distance from the Earth

Semi Diameter

Ephemeris Transit

May 17 18 19 20 21 22

h 3 3 3 3 3 3

m 37 40 44 48 52 56

s 00.09 58.85 58.17 58.04 58.47 59.44

º +19 19 19 20 20 20

' 22 36 49 01 14 25

" 57.34 13.60 09.90 45.98 01.56 56.40

1.011 3437 1.011 5568 1.011 7657 1.011 9702 1.012 1702 1.012 3654

' 15 15 15 15 15 15

" 48.88 48.68 48.49 48.29 48.11 47.92

h 11 11 11 11 11 11

m 56 56 56 56 56 56

s 24.91 27.39 30.44 34.04 38.19 42.86

23 24 25 26 27 28

4 4 4 4 4 4

01 05 09 13 17 21

00.93 02.94 05.45 08.45 11.91 15.81

+20 20 20 21 21 21

37 48 59 10 20 29

30.24 42.82 33.92 03.29 10.68 55.88

1.012 5557 1.012 7411 1.012 9215 1.013 0969 1.013 2674 1.013 4332

15 15 15 15 15 15

47.75 47.57 47.40 47.24 47.08 46.92

11 11 11 11 11 11

56 56 56 57 57 57

48.06 53.76 59.94 06.61 13.73 21.30

29 30 31 June 1 2 3

4 4 4 4 4 4

25 29 33 37 41 45

20.15 24.91 30.07 35.61 41.52 47.79

+21 21 21 22 22 22

39 48 56 05 13 20

18.66 18.81 56.11 10.40 01.50 29.25

1.013 5943 1.013 7512 1.013 9040 1.014 0530 1.014 1986 1.014 3410

15 15 15 15 15 15

46.77 46.63 46.48 46.35 46.21 46.08

11 11 11 11 11 11

57 57 57 57 58 58

29.29 37.70 46.50 55.68 05.22 15.11

4 5 6 7 8 9

4 4 4 5 5 5

49 54 58 02 06 10

54.42 01.37 08.65 16.23 24.09 32.23

+22 22 22 22 22 22

27 34 40 46 51 56

33.52 14.19 31.15 24.27 53.45 58.57

1.014 4806 1.014 6173 1.014 7514 1.014 8826 1.015 0111 1.015 1364

15 15 15 15 15 15

45.95 45.82 45.69 45.57 45.45 45.34

11 11 11 11 11 11

58 58 58 58 59 59

25.35 35.90 46.77 57.93 09.37 21.08

10 11 12 13 14 15

5 5 5 5 5 5

14 18 22 27 31 35

40.62 49.24 58.07 07.09 16.28 25.62

+23 23 23 23 23 23

01 05 09 13 16 18

39.52 56.21 48.51 16.37 19.68 58.38

1.015 2584 1.015 3768 1.015 4914 1.015 6018 1.015 7078 1.015 8090

15 15 15 15 15 15

45.22 45.11 45.01 44.90 44.80 44.71

11 11 11 12 12 12

59 59 59 00 00 00

33.02 45.20 57.57 10.13 22.85 35.71

16 17 18 19 20 21

5 5 5 5 5 6

39 43 47 52 56 00

35.09 44.66 54.30 04.00 13.72 23.44

+23 23 23 23 23 23

21 23 24 25 26 26

12.42 01.74 26.31 26.10 01.10 11.29

1.015 9054 1.015 9965 1.016 0822 1.016 1623 1.016 2366 1.016 3050

15 15 15 15 15 15

44.62 44.54 44.46 44.38 44.31 44.25

12 12 12 12 12 12

00 01 01 01 01 01

48.68 01.73 14.85 28.01 41.17 54.32

22 23 24 25 26 27

6 6 6 6 6 6

04 08 12 17 21 25

33.13 42.75 52.29 01.71 10.97 20.07

+23 23 23 23 23 23

25 25 24 22 20 18

56.68 17.28 13.12 44.21 50.60 32.32

1.016 3673 1.016 4236 1.016 4739 1.016 5182 1.016 5568 1.016 5898

15 15 15 15 15 15

44.19 44.14 44.09 44.05 44.01 43.98

12 12 12 12 12 12

02 02 02 02 02 03

07.42 20.44 33.36 46.15 58.78 11.23

28 29 30 July 1 2

6 6 6 6 6

29 33 37 41 46

28.96 37.63 46.07 54.24 02.14

+23 23 23 23 +23

15 12 09 05 00

49.45 42.04 10.20 14.02 53.64

1.016 6177 1.016 6407 1.016 6592 1.016 6734 1.016 6838

15 15 15 15 15

43.96 43.94 43.92 43.91 43.90

12 12 12 12 12

03 03 03 03 04

23.46 35.47 47.22 58.70 09.89

26

SUN, 2020 FOR 0h TERRESTRIAL TIME Date

July 1 2 3 4 5 6

Geometric Longitude* Latitude Apparent Longitude Aberra- Prec. in Nut. in Nut. in True (Mean Equinox ( Ecliptic (True equinox of date) tion Long. Long. Obliquity Obliquity of date ) of date ) ( J 2020.5 (23° 26') of date ) ° ' '' '' ° ' '' '' '' '' '' '' 99 38 20.12 +0.40 99 37 43.03 20.16 -0.16 -16.98 -0.20 11.61 100 35 31.48 0.25 100 34 54.44 20.16 -0.02 16.92 0.23 11.57 101 32 42.56 +0.14 101 32 05.64 20.16 +0.12 16.81 0.26 11.55 102 29 53.43 -0.00 102 29 16.66 20.16 0.26 16.66 0.27 11.54 103 27 04.18 0.14 103 26 27.56 20.16 0.40 16.50 0.25 11.55 104 24 14.95 0.29 104 23 38.47 20.16 0.54 16.36 0.22 11.58

7 8 9 10 11 12

105 106 107 108 109 110

21 18 15 12 10 07

25.79 36.83 48.13 59.76 11.78 24.27

-0.40 0.50 0.58 0.65 0.65 0.65

105 106 107 108 109 110

20 18 15 12 09 06

49.42 00.50 11.81 23.40 35.35 47.77

20.16 20.16 20.16 20.16 20.16 20.16

+0.68 -16.26 0.82 16.21 0.96 16.21 1.09 16.25 1.23 16.31 1.37 16.39

-0.16 0.10 -0.04 +0.01 0.05 0.07

11.64 11.70 11.76 11.81 11.84 11.87

13 14 15 16 17 18

111 112 112 113 114 115

04 01 59 56 53 50

37.23 50.71 04.74 19.37 34.57 50.35

-0.61 0.58 0.47 0.40 0.29 0.14

111 112 112 113 114 115

04 01 58 55 52 50

00.66 14.09 28.09 42.74 58.01 13.88

20.16 20.16 20.16 20.16 20.16 20.17

+1.51 -16.46 1.65 16.51 1.79 16.53 1.93 16.51 2.07 16.44 2.21 16.34

+0.08 0.07 0.06 0.04 0.02 0.02

11.87 11.86 11.85 11.83 11.81 11.80

19 20 21 22 23 24

116 117 118 119 120 121

48 45 42 39 37 34

06.71 23.65 41.14 59.11 17.56 36.43

-0.04 +0.11 0.22 0.32 0.40 0.43

116 117 118 119 120 121

47 44 42 39 36 34

30.37 47.44 05.04 23.08 41.54 00.37

20.17 20.17 20.17 20.17 20.17 20.18

+2.34 -16.22 2.48 16.09 2.62 15.98 2.76 15.91 2.90 15.89 3.04 15.93

+0.03 0.06 0.12 0.19 0.26 0.33

11.81 11.84 11.90 11.97 12.04 12.11

25 26 27 28 29 30

122 123 124 125 126 127

31 29 26 23 21 18

55.70 15.34 35.37 55.82 16.65 37.97

+0.43 0.43 0.36 0.29 0.18 +0.07

122 123 124 125 126 127

31 28 25 23 20 18

19.56 39.11 59.05 19.46 40.31 01.69

20.18 20.18 20.18 20.18 20.19 20.19

+3.18 -16.01 3.32 16.10 3.46 16.18 3.60 16.22 3.73 16.20 3.87 16.13

+0.39 0.41 0.41 0.40 0.38 0.36

12.16 12.19 12.19 12.17 12.15 12.13

31 Aug. 1 2 3 4 5

128 129 130 131 132 133

15 13 10 08 05 02

59.82 22.27 45.42 09.39 34.20 59.96

-0.07 0.22 0.32 0.47 0.58 0.65

128 129 130 131 132 133

15 12 10 07 04 02

23.65 46.22 09.48 33.53 58.37 24.11

20.19 20.19 20.20 20.20 20.20 20.20

+4.01 -16.02 4.15 15.90 4.29 15.79 4.43 15.71 4.57 15.67 4.71 15.69

+0.35 0.37 0.41 0.47 0.54 0.61

12.12 12.14 12.18 12.23 12.30 12.37

6 7 8 9 10 11

134 134 135 136 137 138

00 57 55 52 50 47

26.80 54.72 23.85 54.24 25.94 58.98

-0.72 0.72 0.76 0.72 0.68 0.61

133 134 135 136 137 138

59 57 54 52 49 47

50.89 18.72 47.74 18.01 49.62 22.60

20.21 20.21 20.21 20.22 20.22 20.22

+4.85 -15.75 4.98 15.84 5.12 15.94 5.26 16.05 5.40 16.14 5.54 16.21

+0.67 0.72 0.76 0.77 0.78 0.77

12.43 12.48 12.51 12.53 12.53 12.52

12 139 45 33.43 13 140 43 09.32 14 141 40 46.68 15 142 38 25.48 16 143 36 05.75 *To obtain the geometric longitude precession from J 2020.5.

-0.50 0.40 0.29 0.14 -0.04 referred

139 140 141 142 143 to the

44 57.01 20.23 +5.68 42 32.90 20.23 5.82 40 10.31 20.23 5.96 37 49.19 20.24 6.10 35 29.54 20.24 +6.24 mean equinox of J 2000.0, add

-16.24 +0.76 12.51 16.23 0.74 12.49 16.18 0.74 12.49 16.10 0.74 12.49 -16.01 +0.77 12.52 -17' 10".958 and subtract

27

SUN, 2020 FOR 0h TERRESTRIAL TIME Apparent Right Ascension

Date

July

Aug.

Apparent Declination

True Distance from the Earth

Semi Diameter

Ephemeris Transit

1 2 3 4 5 6

h 6 6 6 6 6 7

m 41 46 50 54 58 02

s 54.24 02.14 09.74 17.02 23.98 30.59

º +23 23 22 22 22 22

' 05 00 56 51 45 39

" 14.02 53.64 09.17 00.75 28.53 32.64

1.016 6734 1.016 6838 1.016 6906 1.016 6939 1.016 6938 1.016 6904

' 15 15 15 15 15 15

" 43.91 43.90 43.89 43.89 43.89 43.89

h 12 12 12 12 12 12

m 03 04 04 04 04 04

s 58.70 09.89 20.77 31.33 41.56 51.42

7 8 9 10 11 12

7 7 7 7 7 7

06 10 14 18 22 27

36.84 42.71 48.19 53.26 57.91 02.13

+22 22 22 22 22 21

33 26 19 11 04 55

13.22 30.42 24.38 55.27 03.24 48.47

1.016 6837 1.016 6734 1.016 6594 1.016 6416 1.016 6198 1.016 5936

15 15 15 15 15 15

43.90 43.91 43.92 43.94 43.96 43.98

12 12 12 12 12 12

05 05 05 05 05 05

00.92 10.04 18.76 27.07 34.96 42.40

13 14 15 16 17 18

7 7 7 7 7 7

31 35 39 43 47 51

05.90 09.21 12.05 14.40 16.25 17.59

+21 21 21 21 21 20

47 38 28 19 09 58

11.14 11.44 49.57 05.75 00.17 33.08

1.016 5630 1.016 5275 1.016 4872 1.016 4416 1.016 3906 1.016 3340

15 15 15 15 15 15

44.01 44.04 44.08 44.12 44.17 44.22

12 12 12 12 12 12

05 05 06 06 06 06

49.39 55.91 01.95 07.50 12.53 17.04

19 20 21 22 23 24

7 7 8 8 8 8

55 59 03 07 11 15

18.40 18.66 18.37 17.50 16.05 14.00

+20 20 20 20 20 19

47 36 25 13 01 48

44.71 35.29 05.08 14.33 03.29 32.22

1.016 2717 1.016 2033 1.016 1290 1.016 0485 1.015 9621 1.015 8697

15 15 15 15 15 15

44.28 44.34 44.41 44.49 44.57 44.65

12 12 12 12 12 12

06 06 06 06 06 06

21.01 24.44 27.30 29.58 31.27 32.36

25 26 27 28 29 30

8 8 8 8 8 8

19 23 27 30 34 38

11.34 08.06 04.17 59.66 54.52 48.76

+19 19 19 18 18 18

35 22 09 55 41 26

41.38 31.05 01.49 12.98 05.83 40.33

1.015 7717 1.015 6683 1.015 5599 1.015 4469 1.015 3296 1.015 2084

15 15 15 15 15 15

44.74 44.84 44.94 45.05 45.16 45.27

12 12 12 12 12 12

06 06 06 06 06 06

32.84 32.71 31.95 30.57 28.56 25.92

31 1 2 3 4 5

8 8 8 8 8 9

42 46 50 54 58 02

42.38 35.38 27.75 19.52 10.67 01.22

+18 17 17 17 17 16

11 56 41 26 10 53

56.76 55.43 36.62 00.63 07.72 58.18

1.015 0836 1.014 9555 1.014 8243 1.014 6901 1.014 5531 1.014 4132

15 15 15 15 15 15

45.38 45.50 45.63 45.75 45.88 46.01

12 12 12 12 12 12

06 06 06 06 06 05

22.66 18.79 14.29 09.19 03.49 57.18

6 7 8 9 10 11

9 9 9 9 9 9

05 09 13 17 21 24

51.18 40.55 29.33 17.55 05.21 52.31

+16 16 16 15 15 15

37 20 03 46 29 11

32.30 50.34 52.59 39.34 10.87 27.49

1.014 2704 1.014 1247 1.013 9758 1.013 8237 1.013 6683 1.013 5092

15 15 15 15 15 15

46.14 46.28 46.42 46.56 46.70 46.85

12 12 12 12 12 12

05 05 05 05 05 05

50.29 42.82 34.77 26.15 16.98 07.25

12 13 14 15 16

9 9 9 9 9

28 32 36 39 43

38.86 24.88 10.37 55.34 39.80

+14 14 14 13 +13

53 35 16 58 39

29.48 17.15 50.82 10.78 17.37

1.013 3465 1.013 1797 1.013 0089 1.012 8337 1.012 6540

15 15 15 15 15

47.01 47.16 47.32 47.48 47.65

12 12 12 12 12

04 04 04 04 04

56.98 46.18 34.85 23.00 10.64

28

SUN, 2020 FOR 0h TERRESTRIAL TIME Date

Aug. 16 17 18 19 20 21

Geometric Longitude* Latitude Apparent Longitude Aberra- Prec. in Nut. in Nut. in True (Mean Equinox ( Ecliptic (True equinox of date) tion Long. Long. Obliquity Obliquity of date ) of date ) ( J 2020.5 (23° 26') of date ) ° ' '' '' ° ' '' '' '' '' '' '' 143 36 05.75 -0.04 143 35 29.54 20.24 +6.24 -16.01 +0.77 12.52 144 33 47.50 +0.11 144 33 11.38 20.24 6.37 15.92 0.82 12.57 145 31 30.68 0.18 145 30 54.61 20.25 6.51 15.87 0.89 12.64 146 29 15.29 0.29 146 28 39.22 20.25 6.65 15.87 0.97 12.71 147 27 01.21 0.32 147 26 25.08 20.25 6.79 15.92 1.05 12.79 148 24 48.48 0.32 148 24 12.24 20.26 6.93 16.03 1.11 12.85

22 23 24 25 26 27

149 150 151 152 153 154

22 20 18 16 14 11

36.97 26.70 17.59 09.68 02.94 57.38

+0.32 0.29 0.22 +0.11 -0.00 0.14

149 150 151 152 153 154

22 19 17 15 13 11

00.59 50.20 40.99 33.05 26.33 20.83

20.26 20.27 20.27 20.28 20.28 20.29

+7.07 -16.16 7.21 16.28 7.35 16.37 7.49 16.40 7.62 16.37 7.76 16.31

+1.14 1.15 1.13 1.11 1.08 1.07

12.88 12.89 12.87 12.84 12.82 12.80

28 29 30 31 Sept. 1 2

155 156 157 158 159 159

09 07 05 03 01 59

53.07 50.09 48.43 48.23 49.50 52.34

-0.29 0.40 0.50 0.61 0.72 0.76

155 156 157 158 159 159

09 07 05 03 01 59

16.60 13.69 12.08 11.88 13.12 15.86

20.29 20.29 20.30 20.30 20.31 20.31

+7.90 -16.23 8.04 16.15 8.18 16.10 8.32 16.09 8.46 16.12 8.60 16.21

+1.08 1.11 1.16 1.22 1.28 1.34

12.81 12.84 12.89 12.95 13.01 13.07

3 4 5 6 7 8

160 161 162 163 164 165

57 56 54 52 50 48

56.83 03.07 11.08 20.91 32.66 46.39

-0.79 0.79 0.79 0.76 0.68 0.58

160 161 162 163 164 165

57 55 53 51 49 48

20.23 26.33 34.19 43.88 55.52 09.18

20.32 20.32 20.33 20.33 20.34 20.34

+8.74 -16.32 8.88 16.46 9.01 16.60 9.15 16.74 9.29 16.84 9.43 16.92

+1.39 1.42 1.44 1.44 1.42 1.40

13.11 13.15 13.16 13.16 13.14 13.12

9 10 11 12 13 14

166 167 168 169 170 171

47 45 43 42 40 38

02.10 19.87 39.72 01.64 25.68 51.83

-0.47 0.36 0.25 -0.11 +0.00 0.11

166 167 168 169 170 171

46 44 43 41 39 38

24.85 42.61 02.50 24.47 48.56 14.75

20.35 20.35 20.36 20.36 20.37 20.37

+9.57 -16.95 9.71 16.95 9.85 16.91 9.99 16.85 10.13 16.79 10.26 16.75

+1.38 1.36 1.35 1.36 1.39 1.44

13.09 13.07 13.06 13.07 13.10 13.15

15 16 17 18 19 20

172 173 174 175 176 177

37 35 34 32 31 30

20.03 50.35 22.62 56.84 32.94 10.84

+0.18 0.25 0.29 0.25 0.22 0.14

172 173 174 175 176 177

36 35 33 32 30 29

42.95 13.20 45.36 19.43 55.37 33.14

20.38 20.39 20.39 20.40 20.40 20.41

+10.40 -16.75 10.54 16.81 10.68 16.92 10.82 17.07 10.96 17.22 11.10 17.34

+1.50 1.57 1.62 1.66 1.66 1.63

13.21 13.27 13.33 13.36 13.36 13.34

21 22 23 24 25 26

178 179 180 181 182 183

28 27 26 24 23 22

50.49 31.84 14.86 59.56 45.91 33.94

+0.07 -0.07 0.18 0.32 0.47 0.58

178 179 180 181 182 183

28 26 25 24 23 21

12.72 54.06 37.13 21.89 08.30 56.38

20.41 20.42 20.42 20.43 20.44 20.44

+11.24 -17.40 11.38 17.40 11.52 17.36 11.65 17.28 11.79 17.21 11.93 17.17

+1.59 1.55 1.52 1.51 1.52 1.55

13.29 13.25 13.22 13.20 13.21 13.24

27 184 21 23.70 28 185 20 15.27 29 186 19 08.65 30 187 18 03.87 Oct. 1 188 17 01.05 *To obtain the geometric longitude precession from J 2020.5.

-0.68 0.76 0.83 0.86 -0.86 referred

184 185 186 187 188 to the

20 46.14 20.45 +12.07 19 37.67 20.45 12.21 18 30.96 20.46 12.35 17 26.05 20.47 12.49 16 23.09 20.47 +12.63 mean equinox of J 2000.0, add

-17.16 +1.59 13.28 17.19 1.64 13.33 17.28 1.68 13.37 17.40 1.71 13.40 -17.54 +1.73 13.42 -17' 10".958 and subtract

29

SUN, 2020 FOR 0h TERRESTRIAL TIME Apparent Right Ascension

Date

Apparent Declination

True Distance from the Earth

Semi Diameter

Ephemeris Transit

Aug. 16 17 18 19 20 21

h 9 9 9 9 9 10

m 43 47 51 54 58 02

s 39.80 23.75 07.20 50.15 32.61 14.59

º +13 13 13 12 12 12

' 39 20 00 41 21 01

" 17.37 10.90 51.71 20.12 36.47 41.08

1.012 6540 1.012 4695 1.012 2801 1.012 0857 1.011 8863 1.011 6818

' 15 15 15 15 15 15

" 47.65 47.83 48.00 48.19 48.37 48.56

h 12 12 12 12 12 12

m 04 03 03 03 03 03

s 10.64 57.78 44.42 30.57 16.24 01.44

22 23 24 25 26 27

10 10 10 10 10 10

05 09 13 16 20 24

56.10 37.14 17.74 57.90 37.63 16.96

+11 11 11 10 10 9

41 21 00 40 19 58

34.29 16.43 47.84 08.85 19.80 21.03

1.011 4726 1.011 2587 1.011 0407 1.010 8188 1.010 5936 1.010 3653

15 15 15 15 15 15

48.76 48.96 49.17 49.37 49.59 49.80

12 12 12 12 12 12

02 02 02 01 01 01

46.17 30.44 14.27 57.66 40.64 23.21

28 29 30 31 Sept. 1 2

10 10 10 10 10 10

27 31 35 38 42 46

55.90 34.46 12.67 50.53 28.07 05.31

+9 9 8 8 8 7

37 15 54 32 11 49

12.87 55.65 29.69 55.30 12.79 22.45

1.010 1343 1.009 9011 1.009 6658 1.009 4288 1.009 1901 1.008 9500

15 15 15 15 15 15

50.02 50.24 50.46 50.68 50.91 51.13

12 12 12 12 11 11

01 00 00 00 59 59

05.40 47.23 28.70 09.85 50.70 31.25

3 4 5 6 7 8

10 10 10 11 11 11

49 53 56 00 04 07

42.27 18.98 55.45 31.70 07.77 43.66

+7 7 6 6 5 5

27 05 43 20 58 35

24.59 19.51 07.51 48.87 23.91 52.94

1.008 7086 1.008 4657 1.008 2216 1.007 9760 1.007 7290 1.007 4804

15 15 15 15 15 15

51.36 51.59 51.82 52.05 52.28 52.52

11 11 11 11 11 11

59 58 58 58 57 57

11.54 51.58 31.40 11.01 50.44 29.71

9 10 11 12 13 14

11 11 11 11 11 11

11 14 18 22 25 29

19.40 55.01 30.50 05.91 41.24 16.51

+5 4 4 4 3 3

13 50 27 04 41 18

16.25 34.18 47.02 55.11 58.78 58.36

1.007 2301 1.006 9780 1.006 7239 1.006 4676 1.006 2089 1.005 9477

15 15 15 15 15 15

52.76 52.99 53.24 53.48 53.72 53.97

11 11 11 11 11 11

57 56 56 56 55 55

08.83 47.83 26.72 05.53 44.28 22.97

15 16 17 18 19 20

11 11 11 11 11 11

32 36 40 43 47 50

51.73 26.94 02.13 37.33 12.55 47.81

+2 2 2 1 1 0

55 32 09 46 23 59

54.20 46.64 36.04 22.75 07.12 49.52

1.005 6836 1.005 4166 1.005 1465 1.004 8732 1.004 5968 1.004 3175

15 15 15 15 15 15

54.22 54.47 54.73 54.99 55.25 55.52

11 11 11 11 11 11

55 54 54 53 53 53

01.64 40.29 18.94 57.61 36.30 15.05

21 22 23 24 25 26

11 11 12 12 12 12

54 57 01 05 08 12

23.13 58.53 34.02 09.62 45.35 21.24

+0 0 0 0 +0 -1

36 13 10 33 56 20

30.29 09.81 11.55 33.45 55.50 17.38

1.004 0356 1.003 7515 1.003 4654 1.003 1780 1.002 8895 1.002 6003

15 15 15 15 15 15

55.79 56.06 56.33 56.60 56.88 57.16

11 11 11 11 11 11

52 52 52 51 51 51

53.86 32.75 11.74 50.85 30.10 09.51

27 28 29 30 Oct. 1

12 12 12 12 12

15 19 23 26 30

57.30 33.55 10.02 46.73 23.71

-1 2 2 2 -3

43 06 30 53 16

38.72 59.20 18.47 36.22 52.10

1.002 3109 1.002 0214 1.001 7322 1.001 4436 1.001 1555

15 15 15 15 15

57.43 57.71 57.99 58.26 58.54

11 11 11 11 11

50 50 50 49 49

49.11 28.92 08.96 49.26 29.83

30

SUN, 2020 FOR 0h TERRESTRIAL TIME Date

Oct. 1 2 3 4 5 6

Geometric Longitude* Latitude Apparent Longitude Aberra- Prec. in Nut. in Nut. in True (Mean Equinox ( Ecliptic (True equinox of date) tion Long. Long. Obliquity Obliquity of date ) of date ) ( J 2020.5 (23° 26') of date ) ° ' '' '' ° ' '' '' '' '' '' '' 188 17 01.05 -0.86 188 16 23.09 20.47 +12.63 -17.54 +1.73 13.42 189 16 00.19 0.83 189 15 22.07 20.48 12.77 17.69 1.74 13.42 190 15 01.36 0.79 190 14 23.10 20.48 12.91 17.83 1.72 13.41 191 14 04.64 0.72 191 13 26.26 20.49 13.04 17.94 1.69 13.38 192 13 10.05 0.65 192 12 31.57 20.50 13.18 18.03 1.65 13.34 193 12 17.65 0.54 193 11 39.12 20.50 13.32 18.07 1.61 13.29

7 8 9 10 11 12

194 195 196 197 198 199

11 10 09 09 08 07

27.44 39.54 53.92 10.59 29.62 50.97

-0.40 0.29 0.14 -0.04 +0.07 0.14

194 195 196 197 198 199

10 10 09 08 07 07

48.90 01.02 15.44 32.17 51.24 12.61

20.51 20.51 20.52 20.52 20.53 20.54

+13.46 -18.08 13.60 18.05 13.74 18.00 13.88 17.94 14.02 17.89 14.16 17.87

+1.57 1.55 1.53 1.54 1.56 1.60

13.26 13.23 13.21 13.21 13.24 13.27

13 14 15 16 17 18

200 201 202 203 204 205

07 06 06 05 05 04

14.64 40.60 08.83 39.25 11.73 46.25

+0.22 0.25 0.25 0.22 0.14 +0.04

200 201 202 203 204 205

06 06 05 05 04 04

36.25 02.12 30.23 00.49 32.84 07.28

20.54 20.55 20.55 20.56 20.56 20.57

+14.29 -17.90 14.43 17.98 14.57 18.10 14.71 18.24 14.85 18.36 14.99 18.44

+1.65 1.69 1.72 1.72 1.69 1.63

13.32 13.36 13.39 13.39 13.36 13.30

19 20 21 22 23 24

206 207 208 209 210 211

04 04 03 03 03 02

22.67 00.95 41.02 22.77 06.28 51.44

-0.07 0.18 0.32 0.47 0.61 0.72

206 207 208 209 210 211

03 03 03 02 02 02

43.70 22.03 02.20 44.05 27.64 12.84

20.58 20.58 20.59 20.59 20.60 20.61

+15.13 -18.44 15.27 18.38 15.41 18.28 15.55 18.17 15.68 18.09 15.82 18.04

+1.57 1.51 1.48 1.47 1.48 1.50

13.23 13.18 13.14 13.13 13.14 13.16

25 26 27 28 29 30

212 213 214 215 216 217

02 02 02 02 02 01

38.30 26.83 17.09 09.11 02.90 58.44

-0.79 0.86 0.90 0.90 0.86 0.83

212 213 214 215 216 217

01 01 01 01 01 01

59.70 48.18 38.35 30.25 23.92 19.34

20.61 20.62 20.62 20.63 20.63 20.64

+15.96 -18.04 16.10 18.08 16.24 18.16 16.38 18.27 16.52 18.39 16.66 18.51

+1.54 1.57 1.59 1.60 1.60 1.57

13.19 13.23 13.25 13.26 13.25 13.23

31 Nov. 1 2 3 4 5

218 219 220 221 222 223

01 01 01 01 02 02

55.84 55.12 56.26 59.38 04.44 11.49

-0.76 0.65 0.54 0.43 0.29 0.18

218 219 220 221 222 223

01 01 01 01 01 01

16.64 15.85 16.97 20.10 25.21 32.34

20.65 20.65 20.66 20.66 20.67 20.67

+16.80 -18.60 16.94 18.66 17.07 18.68 17.21 18.66 17.35 18.61 17.49 18.53

+1.54 1.49 1.44 1.38 1.34 1.31

13.19 13.14 13.08 13.03 12.99 12.96

6 7 8 9 10 11

224 225 226 227 228 229

02 02 02 03 03 03

20.55 31.66 44.85 00.06 17.37 36.66

-0.04 +0.07 0.14 0.22 0.29 0.29

224 225 226 227 228 229

01 01 02 02 02 02

41.48 52.68 05.93 21.16 38.44 57.66

20.68 20.68 20.69 20.69 20.70 20.70

+17.63 -18.43 17.77 18.35 17.91 18.28 18.05 18.26 18.19 18.28 18.32 18.35

+1.30 1.31 1.34 1.37 1.41 1.44

12.95 12.95 12.98 13.01 13.05 13.07

12 230 03 57.93 +0.25 13 231 04 21.15 0.22 14 232 04 46.23 0.11 15 233 05 13.01 +0.00 16 234 05 41.45 -0.14 *To obtain the geometric longitude referred precession from J 2020.5.

230 231 232 233 234 to the

03 18.83 20.71 +18.46 03 41.94 20.71 18.60 04 06.96 20.72 18.74 04 33.74 20.72 18.88 05 02.26 20.72 +19.02 mean equinox of J 2000.0, add

-18.45 +1.44 13.08 18.54 1.42 13.05 18.60 1.37 13.00 18.59 1.31 12.94 -18.51 +1.24 12.87 -17' 10".958 and subtract

31

SUN, 2020 FOR 0h TERRESTRIAL TIME Apparent Right Ascension

Date

Oct.

Nov.

Apparent Declination

True Distance from the Earth

Semi Diameter

Ephemeris Transit

1 2 3 4 5 6

h 12 12 12 12 12 12

m 30 34 37 41 44 48

s 23.71 00.97 38.55 16.47 54.76 33.42

º -3 3 4 4 4 5

' 16 40 03 26 49 12

" 52.10 05.79 16.97 25.31 30.47 32.12

1.001 1555 1.000 8683 1.000 5820 1.000 2965 1.000 0121 0.999 7286

' 15 15 15 15 15 15

" 58.54 58.81 59.09 59.36 59.63 59.91

h 11 11 11 11 11 11

m 49 49 48 48 48 47

s 29.83 10.71 51.91 33.46 15.38 57.70

7 8 9 10 11 12

12 12 12 13 13 13

52 55 59 03 06 10

12.50 52.00 31.95 12.37 53.28 34.69

-5 5 6 6 7 7

35 58 21 43 06 29

29.91 23.50 12.53 56.66 35.50 08.69

0.999 4459 0.999 1641 0.998 8829 0.998 6022 0.998 3219 0.998 0418

16 16 16 16 16 16

00.18 00.45 00.72 00.99 01.26 01.53

11 11 11 11 11 11

47 47 47 46 46 46

40.43 23.59 07.22 51.32 35.91 21.03

13 14 15 16 17 18

13 13 13 13 13 13

14 17 21 25 29 32

16.63 59.10 42.13 25.73 09.91 54.68

-7 8 8 8 9 9

51 13 36 58 20 42

35.84 56.55 10.41 16.98 15.97 07.10

0.997 7615 0.997 4810 0.997 1999 0.996 9182 0.996 6357 0.996 3525

16 16 16 16 16 16

01.80 02.07 02.34 02.61 02.88 03.16

11 11 11 11 11 11

46 45 45 45 45 45

06.67 52.87 39.63 26.97 14.90 03.43

19 20 21 22 23 24

13 13 13 13 13 13

36 40 44 48 51 55

40.08 26.10 12.75 00.06 48.02 36.65

-10 10 10 11 11 11

03 25 46 08 29 50

49.80 23.61 48.12 02.92 07.60 01.76

0.996 0688 0.995 7848 0.995 5010 0.995 2175 0.994 9350 0.994 6538

16 16 16 16 16 16

03.43 03.71 03.98 04.26 04.53 04.80

11 11 11 11 11 11

44 44 44 44 44 44

52.57 42.34 32.75 23.81 15.54 07.95

25 26 27 28 29 30

13 14 14 14 14 14

59 03 07 10 14 18

25.96 15.98 06.72 58.19 50.40 43.38

-12 12 12 13 13 13

10 31 51 11 31 51

45.00 16.91 37.12 45.23 40.86 23.63

0.994 3742 0.994 0966 0.993 8213 0.993 5486 0.993 2787 0.993 0118

16 16 16 16 16 16

05.07 05.34 05.61 05.88 06.14 06.40

11 11 11 11 11 11

44 43 43 43 43 43

01.05 54.87 49.41 44.69 40.73 37.54

31 1 2 3 4 5

14 14 14 14 14 14

22 26 30 34 38 42

37.13 31.68 27.03 23.19 20.19 18.01

-14 14 14 15 15 15

10 30 49 07 26 44

53.16 09.06 10.97 58.50 31.26 48.87

0.992 7481 0.992 4877 0.992 2308 0.991 9772 0.991 7272 0.991 4806

16 16 16 16 16 16

06.65 06.91 07.16 07.41 07.65 07.89

11 11 11 11 11 11

43 43 43 43 43 43

35.13 33.51 32.70 32.71 33.55 35.23

6 7 8 9 10 11

14 14 14 14 15 15

46 50 54 58 02 06

16.68 16.21 16.58 17.82 19.92 22.89

-16 16 16 16 17 17

02 20 38 55 12 28

50.94 37.06 06.86 19.91 15.82 54.18

0.991 2373 0.990 9973 0.990 7604 0.990 5264 0.990 2950 0.990 0661

16 16 16 16 16 16

08.13 08.36 08.59 08.82 09.05 09.27

11 11 11 11 11 11

43 43 43 43 43 44

37.75 41.13 45.37 50.48 56.45 03.29

12 13 14 15 16

15 15 15 15 15

10 14 18 22 26

26.72 31.42 36.99 43.41 50.68

-17 18 18 18 -18

45 01 16 32 47

14.57 16.59 59.83 23.88 28.35

0.989 8394 0.989 6146 0.989 3915 0.989 1700 0.988 9502

16 16 16 16 16

09.50 09.72 09.93 10.15 10.37

11 11 11 11 11

44 44 44 44 44

11.00 19.57 29.00 39.29 50.41

32

SUN, 2020 FOR 0h TERRESTRIAL TIME Date

Nov. 16 17 18 19 20 21

Geometric Longitude* Latitude Apparent Longitude Aberra- Prec. in Nut. in Nut. in True (Mean Equinox ( Ecliptic (True equinox of date) tion Long. Long. Obliquity Obliquity of date ) of date ) ( J 2020.5 (23° 26') of date ) ° ' '' '' ° ' '' '' '' '' '' '' 234 05 41.45 -0.14 234 05 02.26 20.72 +19.02 -18.51 +1.24 12.87 235 06 11.45 0.25 235 05 32.39 20.73 19.16 18.38 1.19 12.82 236 06 42.86 0.40 236 06 03.96 20.73 19.30 18.22 1.17 12.79 237 07 15.62 0.54 237 06 36.86 20.74 19.44 18.06 1.17 12.79 238 07 49.67 0.65 238 07 11.03 20.74 19.58 17.95 1.19 12.81 239 08 24.92 0.76 239 07 46.34 20.75 19.71 17.88 1.23 12.85

22 23 24 25 26 27

240 241 242 243 244 245

09 09 10 10 11 12

01.42 39.03 17.83 57.76 38.81 21.03

-0.83 0.86 0.86 0.86 0.83 0.76

240 241 242 243 244 245

08 09 09 10 10 11

22.85 00.43 39.17 19.02 59.99 42.14

20.75 20.76 20.76 20.76 20.77 20.77

+19.85 -17.86 19.99 17.89 20.13 17.95 20.27 18.03 20.41 18.10 20.55 18.16

+1.26 1.29 1.31 1.31 1.29 1.26

12.88 12.91 12.93 12.93 12.91 12.88

28 29 30 Dec. 1 2 3

246 247 248 249 250 251

13 13 14 15 16 16

04.40 48.96 34.67 21.60 09.73 59.13

-0.65 0.54 0.43 0.29 0.14 -0.00

246 247 248 249 250 251

12 13 13 14 15 16

25.49 10.06 55.81 42.83 31.07 20.60

20.78 20.78 20.78 20.79 20.79 20.79

+20.69 -18.19 20.83 18.18 20.97 18.12 21.10 18.03 21.24 17.92 21.38 17.78

+1.22 1.17 1.13 1.09 1.06 1.05

12.83 12.79 12.74 12.70 12.67 12.66

4 5 6 7 8 9

252 253 254 255 256 257

17 18 19 20 21 22

49.76 41.71 34.93 29.48 25.30 22.42

+0.11 0.22 0.29 0.36 0.36 0.36

252 253 254 255 256 257

17 18 18 19 20 21

11.36 03.42 56.70 51.28 47.08 44.14

20.80 20.80 20.80 20.80 20.81 20.81

+21.52 -17.65 21.66 17.54 21.80 17.47 21.94 17.45 22.08 17.47 22.22 17.52

+1.07 1.10 1.14 1.19 1.23 1.25

12.67 12.70 12.74 12.79 12.83 12.85

10 11 12 13 14 15

258 259 260 261 262 263

23 24 25 26 27 28

20.77 20.32 21.01 22.72 25.36 28.83

+0.32 0.25 0.14 +0.00 -0.14 0.29

258 259 260 261 262 263

22 23 24 25 26 27

42.42 41.93 42.62 44.40 47.18 50.83

20.81 20.81 20.82 20.82 20.82 20.82

+22.36 -17.58 22.49 17.63 22.63 17.62 22.77 17.54 22.91 17.40 23.05 17.22

+1.25 1.22 1.17 1.12 1.08 1.05

12.85 12.82 12.77 12.72 12.67 12.64

16 17 18 19 20 21

264 265 266 267 268 269

29 30 31 32 33 35

32.97 37.74 42.96 48.64 54.62 00.92

-0.40 0.54 0.65 0.72 0.76 0.79

264 265 266 267 268 269

28 30 31 32 33 34

55.16 00.11 05.45 11.18 17.17 23.45

20.83 20.83 20.83 20.83 20.83 20.83

+23.19 -17.02 23.33 16.85 23.47 16.73 23.61 16.67 23.75 16.66 23.88 16.69

+1.06 1.09 1.14 1.19 1.24 1.28

12.65 12.68 12.72 12.78 12.83 12.86

22 23 24 25 26 27

270 271 272 273 274 275

36 37 38 39 40 41

07.43 14.16 21.02 28.07 35.27 42.58

-0.79 0.76 0.68 0.58 0.47 0.36

270 271 272 273 274 275

35 36 37 38 39 41

29.90 36.58 43.39 50.42 57.64 04.99

20.84 20.84 20.84 20.84 20.84 20.84

+24.02 -16.74 24.16 16.79 24.30 16.84 24.44 16.86 24.58 16.84 24.72 16.79

+1.30 1.31 1.30 1.28 1.25 1.22

12.89 12.89 12.88 12.86 12.83 12.80

28 276 42 50.02 -0.22 29 277 43 57.58 -0.07 30 278 45 05.29 +0.04 31 279 46 13.15 0.18 32 280 47 21.21 +0.29 *To obtain the geometric longitude referred precession from J 2020.5.

276 277 278 279 280 to the

42 12.53 20.84 +24.86 43 20.21 20.84 25.00 44 28.07 20.84 25.14 45 36.07 20.84 25.27 46 44.26 20.84 +25.41 mean equinox of J 2000.0, add

-16.70 +1.20 12.77 16.57 1.19 12.76 16.43 1.19 12.77 16.28 1.22 12.79 -16.16 +1.26 12.83 -17' 10".958 and subtract

33

SUN, 2020 FOR 0h TERRESTRIAL TIME Apparent Right Ascension

Date

Apparent Declination

True Distance from the Earth

Semi Diameter

Ephemeris Transit

Nov. 16 17 18 19 20 21

h 15 15 15 15 15 15

m 26 30 35 39 43 47

s 50.68 58.79 07.73 17.48 28.04 39.38

º -18 19 19 19 19 19

' 47 02 16 30 44 57

" 28.35 12.81 36.88 40.14 22.20 42.67

0.988 9502 0.988 7321 0.988 5159 0.988 3020 0.988 0907 0.987 8824

' 16 16 16 16 16 16

" 10.37 10.58 10.79 11.00 11.21 11.42

h 11 11 11 11 11 11

m 44 45 45 45 45 45

s 50.41 02.36 15.14 28.72 43.11 58.28

22 23 24 25 26 27

15 15 16 16 16 16

51 56 00 04 08 13

51.50 04.39 18.04 32.44 47.57 03.43

-20 20 20 20 20 21

10 23 35 47 58 09

41.18 17.39 30.93 21.48 48.72 52.33

0.987 6774 0.987 4760 0.987 2786 0.987 0855 0.986 8969 0.986 7130

16 16 16 16 16 16

11.62 11.82 12.01 12.20 12.39 12.57

11 11 11 11 11 11

46 46 46 47 47 47

14.23 30.94 48.41 06.62 25.57 45.22

28 29 30 Dec. 1 2 3

16 16 16 16 16 16

17 21 25 30 34 38

19.99 37.26 55.20 13.81 33.06 52.94

-21 21 21 21 21 22

20 30 40 50 59 07

32.01 47.46 38.41 04.57 05.69 41.50

0.986 5342 0.986 3605 0.986 1921 0.986 0291 0.985 8716 0.985 7196

16 16 16 16 16 16

12.74 12.92 13.08 13.24 13.40 13.55

11 11 11 11 11 11

48 48 48 49 49 49

05.59 26.63 48.35 10.72 33.73 57.35

4 5 6 7 8 9

16 16 16 16 17 17

43 47 51 56 00 05

13.42 34.49 56.12 18.29 40.97 04.14

-22 22 22 22 22 22

15 23 30 37 44 50

51.74 36.18 54.56 46.65 12.22 11.05

0.985 5731 0.985 4319 0.985 2960 0.985 1651 0.985 0391 0.984 9176

16 16 16 16 16 16

13.69 13.83 13.97 14.10 14.22 14.34

11 11 11 11 11 11

50 50 51 51 52 52

21.57 46.37 11.71 37.59 03.97 30.82

10 11 12 13 14 15

17 17 17 17 17 17

09 13 18 22 27 31

27.76 51.82 16.28 41.11 06.27 31.73

-22 23 23 23 23 23

55 00 05 09 13 16

42.95 47.71 25.16 35.14 17.51 32.13

0.984 8004 0.984 6872 0.984 5777 0.984 4716 0.984 3688 0.984 2692

16 16 16 16 16 16

14.46 14.57 14.68 14.78 14.88 14.98

11 11 11 11 11 11

52 53 53 54 54 55

58.12 25.84 53.94 22.38 51.14 20.16

16 17 18 19 20 21

17 17 17 17 17 17

35 40 44 49 53 58

57.43 23.35 49.43 15.65 41.97 08.35

-23 23 23 23 23 23

19 21 23 24 25 26

18.88 37.65 28.34 50.86 45.15 11.17

0.984 1729 0.984 0800 0.983 9907 0.983 9053 0.983 8240 0.983 7472

16 16 16 16 16 16

15.08 15.17 15.26 15.34 15.42 15.50

11 11 11 11 11 11

55 56 56 57 57 58

49.42 18.87 48.48 18.21 48.02 17.87

22 23 24 25 26 27

18 18 18 18 18 18

02 07 11 15 20 24

34.76 01.17 27.53 53.83 20.03 46.10

-23 23 23 23 23 23

26 25 24 23 21 18

08.90 38.33 39.48 12.37 17.06 53.61

0.983 6751 0.983 6080 0.983 5462 0.983 4899 0.983 4393 0.983 3946

16 16 16 16 16 16

15.57 15.64 15.70 15.75 15.80 15.85

11 11 11 12 12 12

58 59 59 00 00 01

47.74 17.59 47.38 17.09 46.68 16.12

28 29 30 31 32

18 18 18 18 18

29 33 38 42 46

12.00 37.71 03.20 28.43 53.38

-23 23 23 23 -22

16 12 08 04 59

02.10 42.62 55.27 40.18 57.47

0.983 3560 0.983 3236 0.983 2976 0.983 2780 0.983 2649

16 16 16 16 16

15.89 15.92 15.95 15.97 15.98

12 12 12 12 12

01 02 02 03 03

45.38 14.43 43.24 11.78 40.02

34

SUN, 2020 EQUATORIAL RECTANGULAR CO-ORDINATES FOR 0h TERRESTRIAL TIME MEAN EQUATOR AND EQUINOX OF J 2020.5 AND J 2000.0 Date Jan.

X 2020.5

X 2000.0

Y 2020.5

Y 2000.0

Z 2020.5

Z 2000.0

0 1 2 3 4 5

+0.149 8509 0.167 1135 0.184 3227 0.201 4730 0.218 5591 0.235 5758

+0.149 0809 0.166 3458 0.183 5575 0.200 7105 0.217 7997 0.234 8196

-0.891 7657 0.889 1687 0.886 2947 0.883 1448 0.879 7203 0.876 0226

-0.891 7640 0.889 1670 0.886 2930 0.883 1431 0.879 7187 0.876 0209

-0.386 2797 0.385 1199 0.383 8400 0.382 4405 0.380 9219 0.379 2849

-0.386 5815 0.385 4561 0.384 2105 0.382 8451 0.381 3605 0.379 7574

6 7 8 9 10 11

+0.252 5179 0.269 3803 0.286 1580 0.302 8462 0.319 4399 0.335 9345

+0.251 7651 0.268 6313 0.285 4129 0.302 1052 0.318 7033 0.335 2025

-0.872 0529 0.867 8129 0.863 3040 0.858 5279 0.853 4861 0.848 1802

-0.872 0513 0.867 8113 0.863 3024 0.858 5263 0.853 4845 0.848 1787

-0.377 5300 0.375 6579 0.373 6693 0.371 5650 0.369 3457 0.367 0121

-0.378 0362 0.376 1977 0.374 2425 0.372 1714 0.369 9851 0.367 6844

12 13 14 15 16 17

+0.352 3252 0.368 6073 0.384 7762 0.400 8270 0.416 7550 0.432 5551

+0.351 5980 0.367 8853 0.384 0594 0.400 1158 0.416 0495 0.431 8555

-0.842 6119 0.836 7827 0.830 6941 0.824 3478 0.817 7453 0.810 8883

-0.842 6103 0.836 7811 0.830 6926 0.824 3463 0.817 7438 0.810 8868

-0.364 5650 0.362 0050 0.359 3331 0.356 5497 0.353 6557 0.350 6519

-0.365 2699 0.362 7424 0.360 1026 0.357 3512 0.354 4889 0.351 5165

18 19 20 21 22 23

+0.448 2224 0.463 7519 0.479 1385 0.494 3770 0.509 4625 0.524 3898

+0.447 5291 0.463 0649 0.478 4581 0.493 7034 0.508 7959 0.523 7305

-0.803 7786 0.796 4182 0.788 8091 0.780 9535 0.772 8540 0.764 5129

-0.803 7772 0.796 4168 0.788 8077 0.780 9521 0.772 8526 0.764 5115

-0.347 5389 0.344 3177 0.340 9891 0.337 5541 0.334 0136 0.330 3688

-0.348 4347 0.345 2444 0.341 9464 0.338 5417 0.335 0313 0.331 4162

24 25 26 27 28 29

+0.539 1541 0.553 7505 0.568 1742 0.582 4206 0.596 4851 0.610 3633

+0.538 5022 0.553 1062 0.567 5378 0.581 7922 0.595 8649 0.609 7516

-0.755 9331 0.747 1173 0.738 0687 0.728 7903 0.719 2853 0.709 5570

-0.755 9317 0.747 1160 0.738 0674 0.728 7890 0.719 2840 0.709 5557

-0.326 6209 0.322 7709 0.318 8203 0.314 7703 0.310 6224 0.306 3778

-0.327 6976 0.323 8767 0.319 9548 0.315 9332 0.311 8132 0.307 5963

30 31 Feb. 1 2 3 4

+0.624 0510 0.637 5439 0.650 8381 0.663 9296 0.676 8146 0.689 4894

+0.623 4479 0.636 9497 0.650 2528 0.663 3535 0.676 2478 0.688 9321

-0.699 6087 0.689 4441 0.679 0664 0.668 4794 0.657 6866 0.646 6916

-0.699 6075 0.689 4429 0.679 0653 0.668 4783 0.657 6854 0.646 6905

-0.302 0382 0.297 6050 0.293 0797 0.288 4639 0.283 7592 0.278 9672

-0.303 2839 0.298 8775 0.294 3787 0.289 7889 0.285 1098 0.280 3430

5 6 7 8 9 10

+0.701 9504 0.714 1943 0.726 2178 0.738 0176 0.749 5907 0.760 9340

+0.701 4029 0.713 6566 0.725 6901 0.737 5002 0.749 0836 0.760 4374

-0.635 4981 0.624 1098 0.612 5303 0.600 7634 0.588 8125 0.576 6813

-0.635 4970 0.624 1088 0.612 5293 0.600 7624 0.588 8116 0.576 6804

-0.274 0894 0.269 1276 0.264 0834 0.258 9583 0.253 7540 0.248 4722

-0.275 4900 0.270 5526 0.265 5322 0.260 4306 0.255 2494 0.249 9900

11 12 13 14 15

+0.772 0444 0.782 9188 0.793 5541 0.803 9470 +0.814 0944

+0.771 5584 0.782 4437 0.793 0899 0.803 4939 +0.813 6525

-0.564 3731 0.551 8915 0.539 2400 0.526 4221 -0.513 4415

-0.564 3722 0.551 8907 0.539 2392 0.526 4213 -0.513 4407

-0.243 1142 0.237 6817 0.232 1761 0.226 5991 -0.220 9523

-0.244 6541 0.239 2432 0.233 7588 0.228 2025 -0.222 5758

35

SUN, 2020 EQUATORIAL RECTANGULAR CO-ORDINATES FOR 0h TERRESTRIAL TIME MEAN EQUATOR AND EQUINOX OF J 2020.5 AND J 2000.0 Date

X 2020.5

X 2000.0

Y 2020.5

Y 2000.0

Z 2020.5

Z 2000.0

Feb. 15 16 17 18 19 20

+0.814 0944 0.823 9928 0.833 6391 0.843 0302 0.852 1629 0.861 0342

+0.813 6525 0.823 5623 0.833 2201 0.842 6228 0.851 7673 0.860 6504

-0.513 4415 0.500 3019 0.487 0074 0.473 5619 0.459 9697 0.446 2350

-0.513 4407 0.500 3012 0.487 0066 0.473 5612 0.459 9690 0.446 2344

-0.220 9523 0.215 2371 0.209 4554 0.203 6088 0.197 6992 0.191 7283

-0.222 5758 0.216 8803 0.211 1178 0.205 2898 0.199 3984 0.193 4451

21 22 23 24 25 26

+0.869 6412 0.877 9813 0.886 0517 0.893 8500 0.901 3739 0.908 6212

+0.869 2695 0.877 6217 0.885 7043 0.893 5150 0.901 0513 0.908 3111

-0.432 3623 0.418 3561 0.404 2209 0.389 9615 0.375 5825 0.361 0886

-0.432 3617 0.418 3555 0.404 2204 0.389 9610 0.375 5820 0.361 0882

-0.185 6982 0.179 6105 0.173 4675 0.167 2710 0.161 0231 0.154 7258

-0.187 4320 0.181 3610 0.175 2339 0.169 0529 0.162 8199 0.156 5370

27 28 29 Mar. 1 2 3

+0.915 5898 0.922 2779 0.928 6837 0.934 8057 0.940 6423 0.946 1922

+0.915 2923 0.921 9932 0.928 4118 0.934 5466 0.940 3962 0.945 9592

-0.346 4848 0.331 7756 0.316 9661 0.302 0610 0.287 0650 0.271 9832

-0.346 4843 0.331 7753 0.316 9657 0.302 0606 0.287 0647 0.271 9829

-0.148 3812 0.141 9914 0.135 5585 0.129 0846 0.122 5719 0.116 0223

-0.150 2063 0.143 8297 0.137 4096 0.130 9478 0.124 4466 0.117 9081

4 5 6 7 8 9

+0.951 4544 0.956 4276 0.961 1111 0.965 5041 0.969 6057 0.973 4155

+0.951 2344 0.956 2209 0.960 9176 0.965 3238 0.969 4388 0.973 2620

-0.256 8201 0.241 5806 0.226 2693 0.210 8909 0.195 4499 0.179 9508

-0.256 8199 0.241 5804 0.226 2691 0.210 8908 0.195 4498 0.179 9507

-0.109 4381 0.102 8212 0.096 1739 0.089 4981 0.082 7959 0.076 0691

-0.111 3342 0.104 7273 0.098 0892 0.091 4221 0.084 7280 0.078 0087

10 11 12 13 14 15

+0.976 9326 0.980 1565 0.983 0864 0.985 7214 0.988 0608 0.990 1037

+0.976 7926 0.980 0299 0.982 9733 0.985 6219 0.987 9749 0.990 0314

-0.164 3978 0.148 7953 0.133 1475 0.117 4589 0.101 7337 0.085 9765

-0.164 3978 0.148 7953 0.133 1476 0.117 4589 0.101 7338 0.085 9767

-0.069 3198 0.062 5497 0.055 7608 0.048 9549 0.042 1339 0.035 2998

-0.071 2663 0.064 5026 0.057 7195 0.050 9188 0.044 1025 0.037 2723

16 17 18 19 20 21

+0.991 8494 0.993 2972 0.994 4465 0.995 2969 0.995 8481 0.996 0999

+0.991 7907 0.993 2522 0.994 4152 0.995 2792 0.995 8441 0.996 1096

-0.070 1920 0.054 3849 0.038 5599 0.022 7219 -0.006 8760 +0.008 9731

-0.070 1922 0.054 3851 0.038 5601 0.022 7222 -0.006 8762 +0.008 9728

-0.028 4545 0.021 5999 0.014 7383 0.007 8716 -0.001 0019 +0.005 8685

-0.030 4304 0.023 5787 0.016 7193 0.009 8542 -0.002 9856 +0.003 8844

22 23 24 25 26 27

+0.996 0524 0.995 7055 0.995 0597 0.994 1153 0.992 8730 0.991 3333

+0.996 0758 0.995 7426 0.995 1105 0.994 1798 0.992 9510 0.991 4249

+0.024 8203 0.040 6605 0.056 4889 0.072 3003 0.088 0899 0.103 8527

+0.024 8199 0.040 6602 0.056 4885 0.072 2999 0.088 0895 +0.103 8522

+0.012 7377 0.019 6034 0.026 4635 0.033 3158 0.040 1582 0.046 9885

+0.010 7537 0.017 6202 0.024 4816 0.031 3359 0.038 1808 0.045 0142

28 29 30 31 Apr. 1

+0.989 4971 0.987 3655 0.984 9396 0.982 2206 +0.979 2099

+0.989 6024 0.987 4843 0.985 0719 0.982 3664 +0.979 3691

+0.119 5837 0.135 2780 0.150 9309 0.166 5377 +0.182 0935

+0.119 5831 0.135 2775 0.150 9304 0.166 5370 +0.182 0928

+0.053 8045 0.060 6042 0.067 3854 0.074 1461 +0.080 8841

+0.051 8340 0.058 6380 0.065 4241 0.072 1902 +0.078 9343

36

SUN, 2020 EQUATORIAL RECTANGULAR CO-ORDINATES FOR 0h TERRESTRIAL TIME MEAN EQUATOR AND EQUINOX OF J 2020.5 AND J 2000.0 Date Apr.

May

X 2020.5

X 2000.0

Y 2020.5

Y 2000.0

Z 2020.5

Z 2000.0

1 2 3 4 5 6

+0.979 2099 0.975 9089 0.972 3194 0.968 4430 0.964 2814 0.959 8364

+0.979 3691 0.976 0816 0.972 5054 0.968 6422 0.964 4938 0.960 0620

+0.182 0935 0.197 5938 0.213 0342 0.228 4102 0.243 7175 0.258 9521

+0.182 0928 0.197 5932 0.213 0335 0.228 4095 0.243 7168 0.258 9513

+0.080 8841 0.087 5975 0.094 2843 0.100 9425 0.107 5703 0.114 1658

+0.078 9343 0.085 6543 0.092 3483 0.099 0143 0.105 6504 0.112 2549

7 8 9 10 11 12

+0.955 1098 0.950 1032 0.944 8185 0.939 2570 0.933 4203 0.927 3101

+0.955 3484 0.950 3549 0.945 0831 0.939 5345 0.933 7106 0.927 6131

+0.274 1099 0.289 1869 0.304 1792 0.319 0829 0.333 8940 0.348 6084

+0.274 1091 0.289 1860 0.304 1783 0.319 0820 0.333 8930 0.348 6074

+0.120 7273 0.127 2531 0.133 7413 0.140 1905 0.146 5989 0.152 9647

+0.118 8258 0.125 3616 0.131 8605 0.138 3208 0.144 7408 0.151 1188

13 14 15 16 17 18

+0.920 9279 0.914 2754 0.907 3543 0.900 1668 0.892 7147 0.885 0003

+0.921 2435 0.914 6034 0.907 6948 0.900 5196 0.893 0797 0.885 3774

+0.363 2219 0.377 7304 0.392 1296 0.406 4152 0.420 5829 0.434 6284

+0.363 2209 0.377 7294 0.392 1286 0.406 4141 0.420 5818 0.434 6273

+0.159 2862 0.165 5616 0.171 7891 0.177 9670 0.184 0932 0.190 1661

+0.157 4531 0.163 7418 0.169 9832 0.176 1754 0.182 3166 0.188 4049

19 20 21 22 23 24

+0.877 0259 0.868 7940 0.860 3071 0.851 5679 0.842 5793 0.833 3442

+0.877 4151 0.869 1950 0.860 7199 0.851 9924 0.843 0153 0.833 7916

+0.448 5475 0.462 3359 0.475 9894 0.489 5040 0.502 8754 0.516 0997

+0.448 5463 0.462 3347 0.475 9882 0.489 5027 0.502 8741 0.516 0984

+0.196 1839 0.202 1445 0.208 0464 0.213 8876 0.219 6665 0.225 3812

+0.194 4385 0.200 4157 0.206 3345 0.212 1932 0.217 9900 0.223 7231

25 26 27 28 29 30

+0.823 8657 0.814 1469 0.804 1911 0.794 0017 0.783 5822 0.772 9362

+0.824 3244 0.814 6167 0.804 6719 0.794 4934 0.784 0847 0.773 4492

+0.529 1729 0.542 0911 0.554 8506 0.567 4477 0.579 8789 0.592 1406

+0.529 1716 0.542 0898 0.554 8493 0.567 4464 0.579 8775 0.592 1392

+0.231 0300 0.236 6112 0.242 1233 0.247 5644 0.252 9332 0.258 2280

+0.229 3909 0.234 9915 0.240 5234 0.245 9850 0.251 3745 0.256 6906

1 2 3 4 5 6

+0.762 0672 0.750 9790 0.739 6751 0.728 1593 0.716 4352 0.704 5062

+0.762 5907 0.751 5127 0.740 2190 0.728 7131 0.716 9987 0.705 0794

+0.604 2295 0.616 1426 0.627 8767 0.639 4290 0.650 7967 0.661 9770

+0.604 2281 0.616 1412 0.627 8753 0.639 4275 0.650 7952 0.661 9755

+0.263 4474 0.268 5901 0.273 6545 0.278 6396 0.283 5440 0.288 3667

+0.261 9317 0.267 0965 0.272 1835 0.277 1915 0.282 1194 0.286 9658

7 8 9 10 11 12

+0.692 3759 0.680 0475 0.667 5245 0.654 8101 0.641 9077 0.628 8207

+0.692 9585 0.680 6395 0.668 1256 0.655 4202 0.642 5266 0.629 4482

+0.672 9673 0.683 7649 0.694 3672 0.704 7713 0.714 9745 0.724 9739

+0.672 9657 0.683 7634 0.694 3656 0.704 7697 0.714 9729 0.724 9723

+0.293 1063 0.297 7620 0.302 3324 0.306 8166 0.311 2132 0.315 5211

+0.291 7297 0.296 4099 0.301 0054 0.305 5148 0.309 9372 0.314 2713

13 14 15 16 17

+0.615 5527 0.602 1071 0.588 4879 0.574 6987 +0.560 7437

+0.616 1885 0.602 7513 0.589 1401 0.575 3588 +0.561 4115

+0.734 7666 0.744 3497 0.753 7204 0.762 8759 +0.771 8134

+0.734 7649 0.744 3480 0.753 7187 0.762 8742 +0.771 8117

+0.319 7392 0.323 8661 0.327 9007 0.331 8418 +0.335 6883

+0.318 5158 0.322 6695 0.326 7313 0.330 6999 +0.334 5742

37

SUN, 2020 EQUATORIAL RECTANGULAR CO-ORDINATES FOR 0h TERRESTRIAL TIME MEAN EQUATOR AND EQUINOX OF J 2020.5 AND J 2000.0 Date

X 2020.5

X 2000.0

Y 2020.5

Y 2000.0

Z 2020.5

Z 2000.0

May 17 18 19 20 21 22

+0.560 7437 0.546 6267 0.532 3520 0.517 9238 0.503 3464 +0.488 6243

+0.561 4115 0.547 3020 0.533 0346 0.518 6135 0.504 0431 0.489 3276

+0.771 8134 0.780 5303 0.789 0238 0.797 2915 0.805 3308 0.813 1393

+0.771 8117 0.780 5286 0.789 0221 0.797 2898 0.805 3290 0.813 1376

+0.335 6883 0.339 4389 0.343 0925 0.346 6481 0.350 1045 0.353 4606

+0.334 5742 0.338 3529 0.342 0350 0.345 6194 0.349 1048 0.352 4904

23 24 25 26 27 28

+0.473 7618 0.458 7636 0.443 6344 0.428 3789 0.413 0019 0.397 5081

+0.474 4716 0.459 4798 0.444 3567 0.429 1071 0.413 7358 0.398 2474

+0.820 7148 0.828 0551 0.835 1580 0.842 0217 0.848 6443 0.855 0242

+0.820 7131 0.828 0533 0.835 1562 0.842 0199 0.848 6425 0.855 0224

+0.356 7156 0.359 8684 0.362 9181 0.365 8638 0.368 7047 0.371 4401

+0.355 7750 0.358 9576 0.362 0375 0.365 0136 0.367 8852 0.370 6514

29 30 31 June 1 2 3

+0.381 9024 0.366 1895 0.350 3742 0.334 4612 0.318 4550 0.302 3602

+0.382 6470 0.366 9391 0.351 1287 0.335 2203 0.319 2186 0.303 1280

+0.861 1598 0.867 0499 0.872 6931 0.878 0883 0.883 2346 0.888 1309

+0.861 1580 0.867 0480 0.872 6912 0.878 0865 0.883 2327 0.888 1291

+0.374 0693 0.376 5916 0.379 0066 0.381 3137 0.383 5126 0.385 6027

+0.373 3117 0.375 8654 0.378 3119 0.380 6508 0.382 8815 0.385 0038

4 5 6 7 8 9

+0.286 1812 0.269 9223 0.253 5877 0.237 1816 0.220 7083 0.204 1721

+0.286 9530 0.270 6978 0.254 3667 0.237 9640 0.221 4938 0.204 9605

+0.892 7765 0.897 1703 0.901 3115 0.905 1990 0.908 8319 0.912 2091

+0.892 7746 0.897 1685 0.901 3096 0.905 1972 0.908 8301 0.912 2072

+0.387 5839 0.389 4556 0.391 2176 0.392 8694 0.394 4107 0.395 8411

+0.387 0171 0.388 9212 0.390 7158 0.392 4003 0.393 9745 0.395 4378

10 11 12 13 14 15

+0.187 5774 0.170 9285 0.154 2300 0.137 4865 0.120 7027 0.103 8834

+0.188 3684 0.171 7219 0.155 0257 0.138 2842 0.121 5022 0.104 6843

+0.915 3295 0.918 1922 0.920 7961 0.923 1403 0.925 2239 0.927 0461

+0.915 3277 0.918 1903 0.920 7942 0.923 1384 0.925 2220 0.927 0443

+0.397 1602 0.398 3675 0.399 4627 0.400 4454 0.401 3152 0.402 0718

+0.396 7900 0.398 0305 0.399 1589 0.400 1750 0.401 0782 0.401 8683

16 17 18 19 20 21

+0.087 0332 0.070 1571 0.053 2601 0.036 3469 0.019 4228 +0.002 4928

+0.087 8355 0.070 9605 0.054 0643 0.037 1518 0.020 2281 +0.003 2983

+0.928 6063 0.929 9038 0.930 9380 0.931 7086 0.932 2151 0.932 4574

+0.928 6045 0.929 9019 0.930 9362 0.931 7067 0.932 2132 0.932 4555

+0.402 7148 0.403 2441 0.403 6593 0.403 9602 0.404 1468 0.404 2189

+0.402 5449 0.403 1078 0.403 5566 0.403 8913 0.404 1116 0.404 2173

22 23 24 25 26 27

-0.014 4380 0.031 3645 0.048 2815 0.065 1839 0.082 0667 0.098 9247

-0.013 6326 0.030 5594 0.047 4769 0.064 3801 0.081 2638 0.098 1230

+0.932 4353 0.932 1490 0.931 5986 0.930 7845 0.929 7072 0.928 3674

+0.932 4335 0.932 1471 0.931 5967 0.930 7826 0.929 7054 0.928 3656

+0.404 1763 0.404 0192 0.403 7476 0.403 3616 0.402 8614 0.402 2472

+0.404 2085 0.404 0851 0.403 8472 0.403 4948 0.403 0283 0.402 4477

28 29 30 July 1 2

-0.115 7532 0.132 5474 0.149 3025 0.166 0140 -0.182 6775

-0.114 9529 0.131 7487 0.148 5057 0.165 2193 -0.181 8851

+0.926 7658 0.924 9033 0.922 7809 0.920 3995 +0.917 7602

+0.926 7640 0.924 9015 0.922 7791 0.920 3978 +0.917 7584

+0.401 5195 0.400 6786 0.399 7249 0.398 6589 +0.397 4810

+0.401 7535 0.400 9461 0.400 0258 0.398 9930 +0.397 8483

38

SUN, 2020 EQUATORIAL RECTANGULAR CO-ORDINATES FOR 0h TERRESTRIAL TIME MEAN EQUATOR AND EQUINOX OF J 2020.5 AND J 2000.0 Date July

Aug.

X 2020.5

X 2000.0

Y 2020.5

Y 2000.0

Z 2020.5

Z 2000.0

1 2 3 4 5 6

-0.166 0140 0.182 6775 0.199 2887 0.215 8432 0.232 3369 0.248 7655

-0.165 2193 0.181 8851 0.198 4988 0.215 0561 0.231 5528 0.247 9846

+0.920 3995 0.917 7602 0.914 8638 0.911 7114 0.908 3039 0.904 6422

+0.920 3978 0.917 7584 0.914 8621 0.911 7097 0.908 3022 0.904 6405

+0.398 6589 0.397 4810 0.396 1918 0.394 7916 0.393 2809 0.391 6602

+0.398 9930 0.397 8483 0.396 5921 0.395 2249 0.393 7471 0.392 1591

7 8 9 10 11 12

-0.265 1247 0.281 4103 0.297 6178 0.313 7429 0.329 7811 0.345 7280

-0.264 3472 0.280 6364 0.296 8478 0.312 9769 0.329 0195 0.344 9708

+0.900 7271 0.896 5595 0.892 1404 0.887 4706 0.882 5512 0.877 3833

+0.900 7254 0.896 5578 0.892 1387 0.887 4689 0.882 5496 0.877 3817

+0.389 9298 0.388 0903 0.386 1420 0.384 0854 0.381 9208 0.379 6489

+0.390 4613 0.388 6542 0.386 7382 0.384 7136 0.382 5810 0.380 3408

13 14 15 16 17 18

-0.361 5789 0.377 3294 0.392 9749 0.408 5107 0.423 9322 0.439 2348

-0.360 8265 0.376 5819 0.392 2325 0.407 7736 0.423 2007 0.438 5091

+0.871 9680 0.866 3066 0.860 4003 0.854 2506 0.847 8589 0.841 2270

+0.871 9664 0.866 3049 0.860 3987 0.854 2490 0.847 8574 0.841 2254

+0.377 2701 0.374 7849 0.372 1939 0.369 4977 0.366 6969 0.363 7923

+0.377 9936 0.375 5397 0.372 9798 0.370 3146 0.367 5445 0.364 6703

19 20 21 22 23 24

-0.454 4139 0.469 4647 0.484 3825 0.499 1629 0.513 8012 0.528 2929

-0.453 6941 0.468 7510 0.483 6753 0.498 4622 0.513 1072 0.527 6060

+0.834 3565 0.827 2492 0.819 9073 0.812 3328 0.804 5281 0.796 4956

+0.834 3549 0.827 2477 0.819 9058 0.812 3313 0.804 5266 0.796 4941

+0.360 7845 0.357 6743 0.354 4626 0.351 1502 0.347 7382 0.344 2276

+0.361 6927 0.358 6125 0.355 4305 0.352 1475 0.348 7647 0.345 2829

25 26 27 28 29 30

-0.542 6339 0.556 8198 0.570 8468 0.584 7109 0.598 4084 0.611 9358

-0.541 9541 0.556 1474 0.570 1819 0.584 0537 0.597 7592 0.611 2947

+0.788 2379 0.779 7577 0.771 0577 0.762 1406 0.753 0093 0.743 6665

+0.788 2365 0.779 7563 0.771 0563 0.762 1393 0.753 0080 0.743 6652

+0.340 6195 0.336 9151 0.333 1156 0.329 2221 0.325 2360 0.321 1584

+0.341 7033 0.338 0272 0.334 2555 0.330 3896 0.326 4307 0.322 3801

31 1 2 3 4 5

-0.625 2895 0.638 4661 0.651 4622 0.664 2744 0.676 8993 0.689 3336

-0.624 6566 0.637 8417 0.650 8464 0.663 6674 0.676 3013 0.688 7447

+0.734 1149 0.724 3571 0.714 3959 0.704 2338 0.693 8735 0.683 3175

+0.734 1136 0.724 3559 0.714 3947 0.704 2326 0.693 8723 0.683 3164

+0.316 9905 0.312 7337 0.308 3891 0.303 9577 0.299 4410 0.294 8399

+0.318 2388 0.314 0082 0.309 6894 0.305 2835 0.300 7919 0.296 2155

6 7 8 9 10 11

-0.701 5737 0.713 6164 0.725 4581 0.737 0954 0.748 5248 0.759 7428

-0.700 9942 0.713 0463 0.724 8977 0.736 5447 0.747 9841 0.759 2122

+0.672 5686 0.661 6293 0.650 5024 0.639 1907 0.627 6971 0.616 0244

+0.672 5674 0.661 6282 0.650 5013 0.639 1897 0.627 6961 0.616 0234

+0.290 1556 0.285 3894 0.280 5425 0.275 6159 0.270 6111 0.265 5292

+0.291 5556 0.286 8134 0.281 9899 0.277 0865 0.272 1044 0.267 0448

12 13 14 15 16

-0.770 7460 0.781 5310 0.792 0942 0.802 4324 -0.812 5420

-0.770 2257 0.781 0210 0.791 5948 0.801 9437 -0.812 0641

+0.604 1757 0.592 1541 0.579 9627 0.567 6048 +0.555 0837

+0.604 1747 0.592 1531 0.579 9618 0.567 6039 +0.555 0828

+0.260 3715 0.255 1393 0.249 8341 0.244 4571 +0.239 0099

+0.261 9090 0.256 6983 0.251 4140 0.246 0576 +0.240 6305

39

SUN, 2020 EQUATORIAL RECTANGULAR CO-ORDINATES FOR 0h TERRESTRIAL TIME MEAN EQUATOR AND EQUINOX OF J 2020.5 AND J 2000.0 Date

X 2020.5

X 2000.0

Y 2020.5

Y 2000.0

Z 2020.5

Z 2000.0

Aug. 16 17 18 19 20 21

-0.812 5420 0.822 4196 0.832 0621 0.841 4660 0.850 6283 0.859 5459

-0.812 0641 0.821 9527 0.831 6063 0.841 0214 0.850 1951 0.859 1242

+0.555 0837 0.542 4030 0.529 5663 0.516 5774 0.503 4401 0.490 1585

+0.555 0828 0.542 4022 0.529 5655 0.516 5766 0.503 4393 0.490 1577

+0.239 0099 0.233 4939 0.227 9107 0.222 2618 0.216 5489 0.210 7738

+0.240 6305 0.235 1341 0.229 5700 0.223 9398 0.218 2452 0.212 4878

22 23 24 25 26 27

-0.868 2161 0.876 6362 0.884 8038 0.892 7166 0.900 3726 0.907 7697

-0.867 8060 0.876 2378 0.884 4173 0.892 3421 0.900 0101 0.907 4194

+0.476 7367 0.463 1789 0.449 4893 0.435 6721 0.421 7313 0.407 6712

+0.476 7360 0.463 1782 0.449 4887 0.435 6715 0.421 7308 0.407 6707

+0.204 9383 0.199 0441 0.193 0931 0.187 0872 0.181 0282 0.174 9178

+0.206 6695 0.200 7920 0.194 8573 0.188 8670 0.182 8232 0.176 7275

28 29 30 31 Sept. 1 2

-0.914 9062 0.921 7800 0.928 3895 0.934 7329 0.940 8084 0.946 6143

-0.914 5681 0.921 4543 0.928 0762 0.934 4321 0.940 5203 0.946 3389

+0.393 4956 0.379 2087 0.364 8142 0.350 3160 0.335 7182 0.321 0244

+0.393 4951 0.379 2082 0.364 8137 0.350 3156 0.335 7178 0.321 0241

+0.168 7579 0.162 5503 0.156 2966 0.149 9986 0.143 6580 0.137 2765

+0.170 5818 0.164 3878 0.158 1472 0.151 8618 0.145 5333 0.139 1633

3 4 5 6 7 8

-0.952 1489 0.957 4105 0.962 3974 0.967 1078 0.971 5401 0.975 6927

-0.951 8863 0.957 1607 0.962 1605 0.966 8839 0.971 3293 0.975 4950

+0.306 2387 0.291 3649 0.276 4069 0.261 3688 0.246 2545 0.231 0682

+0.306 2384 0.291 3646 0.276 4067 0.261 3686 0.246 2543 0.231 0680

+0.130 8558 0.124 3977 0.117 9037 0.111 3757 0.104 8153 0.098 2244

+0.132 7536 0.126 3058 0.119 8218 0.113 3031 0.106 7515 0.100 1688

9 10 11 12 13 14

-0.979 5639 0.983 1522 0.986 4560 0.989 4738 0.992 2043 0.994 6459

-0.979 3794 0.982 9809 0.986 2980 0.989 3292 0.992 0730 0.994 5281

+0.215 8140 0.200 4960 0.185 1185 0.169 6860 0.154 2027 0.138 6732

+0.215 8138 0.200 4959 0.185 1185 0.169 6859 0.154 2027 0.138 6732

+0.091 6046 0.084 9579 0.078 2860 0.071 5907 0.064 8741 0.058 1378

+0.093 5567 0.086 9170 0.080 2516 0.073 5623 0.066 8510 0.060 1196

15 16 17 18 19 20

-0.996 7974 0.998 6576 1.000 2254 1.001 5000 1.002 4806 1.003 1669

-0.996 6931 0.998 5668 1.000 1481 1.001 4362 1.002 4303 1.003 1301

+0.123 1022 0.107 4943 0.091 8545 0.076 1876 0.060 4986 0.044 7926

+0.123 1023 0.107 4944 0.091 8546 0.076 1877 0.060 4988 0.044 7928

+0.051 3841 0.044 6148 0.037 8321 0.031 0380 0.024 2348 0.017 4246

+0.053 3701 0.046 6044 0.039 8248 0.033 0332 0.026 2319 0.019 4230

21 22 23 24 25 26

-1.003 5585 1.003 6555 1.003 4580 1.002 9663 1.002 1805 1.001 1012

-1.003 5354 1.003 6460 1.003 4621 1.002 9839 1.002 2117 1.001 1460

+0.029 0744 +0.013 3491 -0.002 3787 0.018 1042 0.033 8228 0.049 5300

+0.029 0747 +0.013 3494 -0.002 3784 0.018 1038 0.033 8224 0.049 5297

+0.010 6096 +0.003 7920 -0.003 0262 0.009 8428 0.016 6558 0.023 4633

+0.012 6087 +0.005 7912 -0.001 0274 0.007 8450 0.014 6597 0.021 4693

27 28 29 30 Oct. 1

-0.999 7286 0.998 0633 0.996 1056 0.993 8561 -0.991 3152

-0.999 7870 0.998 1351 0.996 1910 0.993 9549 -0.991 4275

-0.065 2214 0.080 8926 0.096 5391 0.112 1566 -0.127 7408

-0.065 2210 0.080 8921 0.096 5386 0.112 1561 -0.127 7403

-0.030 2632 0.037 0537 0.043 8327 0.050 5985 -0.057 3491

-0.028 2721 0.035 0659 0.041 8489 0.048 6192 -0.055 3750

40

SUN, 2020 EQUATORIAL RECTANGULAR CO-ORDINATES FOR 0h TERRESTRIAL TIME MEAN EQUATOR AND EQUINOX OF J 2020.5 AND J 2000.0 Date Oct.

Nov.

X 2020.5

X 2000.0

Y 2020.5

Y 2000.0

Z 2020.5

Z 2000.0

1 2 3 4 5 6

-0.991 3152 0.988 4834 0.985 3614 0.981 9497 0.978 2489 0.974 2597

-0.991 4275 0.988 6092 0.985 5005 0.982 1022 0.978 4146 0.974 4387

-0.127 7408 0.143 2874 0.158 7919 0.174 2501 0.189 6575 0.205 0099

-0.127 7403 0.143 2868 0.158 7913 0.174 2495 0.189 6569 0.205 0092

-0.057 3491 0.064 0827 0.070 7973 0.077 4912 0.084 1624 0.090 8090

-0.055 3750 0.062 1142 0.068 8351 0.075 5358 0.082 2145 0.088 8691

7 8 9 10 11 12

-0.969 9827 0.965 4187 0.960 5686 0.955 4332 0.950 0134 0.944 3102

-0.970 1749 0.965 6241 0.960 7871 0.955 6646 0.950 2578 0.944 5675

-0.220 3027 0.235 5315 0.250 6919 0.265 7792 0.280 7889 0.295 7165

-0.220 3020 0.235 5308 0.250 6911 0.265 7784 0.280 7881 0.295 7156

-0.097 4292 0.104 0210 0.110 5826 0.117 1120 0.123 6073 0.130 0665

-0.095 4979 0.102 0988 0.108 6702 0.115 2099 0.121 7160 0.128 1866

13 14 15 16 17 18

-0.938 3248 0.932 0584 0.925 5124 0.918 6883 0.911 5880 0.904 2136

-0.938 5949 0.932 3413 0.925 8079 0.918 9964 0.911 9085 0.904 5464

-0.310 5571 0.325 3060 0.339 9584 0.354 5094 0.368 9541 0.383 2877

-0.310 5562 0.325 3051 0.339 9574 0.354 5084 0.368 9531 0.383 2866

-0.136 4875 0.142 8684 0.149 2071 0.155 5015 0.161 7494 0.167 9487

-0.134 6196 0.141 0131 0.147 3648 0.153 6728 0.159 9349 0.166 1490

19 20 21 22 23 24

-0.896 5671 0.888 6513 0.880 4685 0.872 0215 0.863 3130 0.854 3458

-0.896 9123 0.889 0085 0.880 8378 0.872 4028 0.863 7061 0.854 7506

-0.397 5054 0.411 6026 0.425 5749 0.439 4180 0.453 1275 0.466 6996

-0.397 5043 0.411 6016 0.425 5738 0.439 4168 0.453 1264 0.466 6984

-0.174 0974 0.180 1934 0.186 2348 0.192 2195 0.198 1459 0.204 0120

-0.172 3130 0.178 4248 0.184 4825 0.190 4842 0.196 4279 0.202 3120

25 26 27 28 29 30

-0.845 1226 0.835 6462 0.825 9195 0.815 9453 0.805 7263 0.795 2656

-0.845 5390 0.836 0741 0.826 3587 0.816 3957 0.806 1878 0.795 7379

-0.480 1302 0.493 4153 0.506 5513 0.519 5341 0.532 3602 0.545 0257

-0.480 1290 0.493 4141 0.506 5500 0.519 5328 0.532 3589 0.545 0244

-0.209 8162 0.215 5567 0.221 2319 0.226 8400 0.232 3796 0.237 8490

-0.208 1346 0.213 8940 0.219 5886 0.225 2167 0.230 7766 0.236 2669

31 1 2 3 4 5

-0.784 5659 0.773 6301 0.762 4613 0.751 0624 0.739 4365 0.727 5864

-0.785 0490 0.774 1239 0.762 9656 0.751 5770 0.739 9612 0.728 1212

-0.557 5270 0.569 8604 0.582 0223 0.594 0090 0.605 8170 0.617 4425

-0.557 5257 0.569 8591 0.582 0209 0.594 0076 0.605 8155 0.617 4410

-0.243 2465 0.248 5708 0.253 8201 0.258 9929 0.264 0878 0.269 1031

-0.241 6858 0.247 0319 0.252 3035 0.257 4991 0.262 6171 0.267 6561

6 7 8 9 10 11

-0.715 5155 0.703 2268 0.690 7236 0.678 0092 0.665 0870 0.651 9606

-0.716 0601 0.703 7811 0.691 2874 0.678 5824 0.665 6694 0.652 5520

-0.628 8819 0.640 1317 0.651 1881 0.662 0476 0.672 7063 0.683 1607

-0.628 8805 0.640 1302 0.651 1866 0.662 0460 0.672 7048 0.683 1591

-0.274 0374 0.278 8891 0.283 6566 0.288 3384 0.292 9330 0.297 4387

-0.272 6145 0.277 4907 0.282 2831 0.286 9903 0.291 6107 0.296 1426

12 13 14 15 16

-0.638 6337 0.625 1100 0.611 3937 0.597 4891 -0.583 4006

-0.639 2339 0.625 7189 0.612 0110 0.598 1147 -0.584 0343

-0.693 4070 0.703 4415 0.713 2606 0.722 8608 -0.732 2386

-0.693 4054 0.703 4399 0.713 2590 0.722 8592 -0.732 2370

-0.301 8541 0.306 1774 0.310 4071 0.314 5416 -0.318 5795

-0.300 5845 0.304 9348 0.309 1919 0.313 3541 -0.317 4201

41

SUN, 2020 EQUATORIAL RECTANGULAR CO-ORDINATES FOR 0h TERRESTRIAL TIME MEAN EQUATOR AND EQUINOX OF J 2020.5 AND J 2000.0 Date

X 2020.5

X 2000.0

Y 2020.5

Y 2000.0

Z 2020.5

Z 2000.0

Nov. 16 17 18 19 20 21

-0.583 4006 0.569 1328 0.554 6905 0.540 0783 0.525 3011 0.510 3637

-0.584 0343 0.569 7743 0.555 3397 0.540 7350 0.525 9651 0.511 0347

-0.732 2386 0.741 3908 0.750 3144 0.759 0065 0.767 4644 0.775 6857

-0.732 2370 0.741 3891 0.750 3127 0.759 0048 0.767 4628 0.775 6840

-0.318 5795 0.322 5193 0.326 3596 0.330 0993 0.333 7370 0.337 2716

-0.317 4201 0.321 3884 0.325 2575 0.329 0263 0.332 6934 0.336 2579

22 23 24 25 26 27

-0.495 2708 0.480 0271 0.464 6373 0.449 1062 0.433 4383 0.417 6384

-0.495 9487 0.480 7116 0.465 3283 0.449 8034 0.434 1416 0.418 3475

-0.783 6679 0.791 4087 0.798 9059 0.806 1573 0.813 1608 0.819 9143

-0.783 6662 0.791 4070 0.798 9042 0.806 1555 0.813 1590 0.819 9126

-0.340 7022 0.344 0277 0.347 2471 0.350 3596 0.353 3642 0.356 2600

-0.339 7186 0.343 0745 0.346 3246 0.349 4680 0.352 5038 0.355 4312

28 29 30 Dec. 1 2 3

-0.401 7112 0.385 6614 0.369 4935 0.353 2123 0.336 8225 0.320 3287

-0.402 4259 0.386 3814 0.370 2187 0.353 9424 0.337 5573 0.321 0680

-0.826 4161 0.832 6640 0.838 6563 0.844 3910 0.849 8666 0.855 0810

-0.826 4143 0.832 6622 0.838 6545 0.844 3893 0.849 8648 0.855 0792

-0.359 0463 0.361 7223 0.364 2871 0.366 7400 0.369 0803 0.371 3073

-0.358 2492 0.360 9571 0.363 5542 0.366 0396 0.368 4125 0.370 6724

4 5 6 7 8 9

-0.303 7357 0.287 0481 0.270 2709 0.253 4088 0.236 4668 0.219 4499

-0.304 4792 0.287 7956 0.271 0222 0.254 1636 0.237 2249 -0.220 2111

-0.860 0327 0.864 7199 0.869 1408 0.873 2938 0.877 1773 0.880 7894

-0.860 0309 0.864 7181 0.869 1390 0.873 2920 0.877 1755 0.880 7876

-0.373 4202 0.375 4183 0.377 3010 0.379 0675 0.380 7171 0.382 2492

-0.372 8183 0.374 8497 0.376 7659 0.378 5660 0.380 2494 0.381 8154

10 11 12 13 14 15

-0.202 3633 0.185 2122 0.168 0021 0.150 7386 0.133 4274 0.116 0742

-0.203 1273 0.185 9789 0.168 7712 0.151 5098 0.134 2005 0.116 8490

-0.884 1288 0.887 1937 0.889 9829 0.892 4949 0.894 7286 0.896 6832

-0.884 1270 0.887 1919 0.889 9811 0.892 4931 0.894 7268 0.896 6814

-0.383 6631 0.384 9580 0.386 1334 0.387 1887 0.388 1233 0.388 9369

-0.383 2632 0.384 5924 0.385 8021 0.386 8917 0.387 8609 0.388 7090

16 17 18 19 20 21

-0.098 6850 0.081 2654 0.063 8214 0.046 3586 0.028 8828 -0.011 3994

-0.099 4611 0.082 0428 0.064 5997 0.047 1376 0.029 6622 -0.012 1790

-0.898 3579 0.899 7521 0.900 8655 0.901 6980 0.902 2496 0.902 5202

-0.898 3561 0.899 7503 0.900 8637 0.901 6963 0.902 2478 0.902 5184

-0.389 6290 0.390 1994 0.390 6479 0.390 9745 0.391 1791 0.391 2618

-0.389 4357 0.390 0408 0.390 5241 0.390 8855 0.391 1249 0.391 2425

22 23 24 25 26 27

+0.006 0861 0.023 5681 0.041 0413 0.058 5005 0.075 9402 0.093 3553

+0.005 3065 0.022 7888 0.040 2626 0.057 7225 0.075 1632 0.092 5796

-0.902 5101 0.902 2195 0.901 6487 0.900 7981 0.899 6681 0.898 2593

-0.902 5083 0.902 2177 0.901 6469 0.900 7963 0.899 6663 0.898 2575

-0.391 2226 0.391 0617 0.390 7792 0.390 3753 0.389 8502 0.389 2043

-0.391 2381 0.391 1120 0.390 8643 0.390 4952 0.390 0048 0.389 3936

28 29 30 31 32

+0.110 7406 0.128 0910 0.145 4014 0.162 6667 +0.179 8819

+0.109 9664 0.127 3185 0.144 6309 0.161 8984 +0.179 1161

-0.896 5722 0.894 6074 0.892 3656 0.889 8476 -0.887 0539

-0.896 5704 0.894 6057 0.892 3639 0.889 8458 -0.887 0522

-0.388 4377 0.387 5508 0.386 5439 0.385 4173 -0.384 1715

-0.388 6616 0.387 8092 0.386 8368 0.385 7446 -0.384 5331

42

SUN, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date

Position Angle of Axis P

Heliographic Latitude B0

Date

Position Angle of Axis P

Longitude L0

Heliographic Latitude B0

Longitude L0

Jan. 0 1 2 3 4 5

º +2.81 2.32 1.84 1.35 0.87 +0.38

º -2.82 2.94 3.06 3.18 3.29 3.40

º 84.02 70.85 57.68 44.51 31.34 18.17

Feb. 15 16 17 18 19 20

º -17.19 17.53 17.86 18.18 18.50 18.81

º -6.80 6.84 6.89 6.92 6.96 7.00

º 198.32 185.15 171.98 158.81 145.64 132.48

6 7 8 9 10 11

-0.10 0.58 1.06 1.55 2.03 2.50

-3.52 3.63 3.74 3.85 3.96 4.07

5.00 351.83 338.66 325.49 312.33 299.16

21 22 23 24 25 26

-19.12 19.42 19.72 20.01 20.29 20.57

-7.03 7.06 7.09 7.11 7.14 7.16

119.31 106.14 92.97 79.80 66.63 53.46

12 13 14 15 16 17

-2.98 3.45 3.93 4.40 4.87 5.33

-4.17 4.28 4.38 4.48 4.58 4.68

285.99 272.82 259.65 246.48 233.32 220.15

27 28 29 Mar. 1 2 3

-20.84 21.10 21.36 21.62 21.86 22.10

-7.18 7.20 7.21 7.22 7.23 7.24

40.29 27.12 13.94 0.77 347.60 334.43

18 19 20 21 22 23

-5.80 6.26 6.71 7.17 7.62 8.07

-4.78 4.88 4.97 5.06 5.16 5.25

206.98 193.81 180.65 167.48 154.31 141.15

4 5 6 7 8 9

-22.34 22.56 22.78 23.00 23.20 23.41

-7.25 7.25 7.25 7.25 7.25 7.24

321.25 308.08 294.90 281.73 268.55 255.37

24 25 26 27 28 29

-8.51 8.95 9.39 9.83 10.25 10.68

-5.33 5.42 5.50 5.59 5.67 5.75

127.98 114.82 101.65 88.48 75.32 62.15

10 11 12 13 14 15

-23.60 23.79 23.97 24.14 24.31 24.47

-7.24 7.23 7.21 7.20 7.18 7.17

242.20 229.02 215.84 202.66 189.48 176.30

30 31 Feb. 1 2 3 4

-11.10 11.52 11.93 12.34 12.74 13.14

-5.83 5.90 5.98 6.05 6.12 6.19

48.99 35.82 22.65 9.49 356.32 343.16

16 17 18 19 20 21

-24.63 24.78 24.92 25.05 25.18 25.30

-7.15 7.12 7.10 7.07 7.04 7.01

163.12 149.94 136.76 123.58 110.39 97.21

5 6 7 8 9 10

-13.53 13.92 14.31 14.69 15.06 15.43

-6.25 6.32 6.38 6.44 6.50 6.55

329.99 316.82 303.66 290.49 277.32 264.15

22 23 24 25 26 27

-25.41 25.52 25.62 25.71 25.79 25.87

-6.98 6.94 6.90 6.86 6.82 6.78

84.02 70.84 57.65 44.47 31.28 18.09

11 12 13 14 15

-15.79 16.15 16.50 16.85 -17.19

-6.61 6.66 6.71 6.76 -6.80

250.99 237.82 224.65 211.48 198.32

28 29 30 31 Apr. 1

-25.94 26.01 26.07 26.12 -26.16

-6.73 6.69 6.64 6.58 -6.53

4.90 351.71 338.52 325.33 312.14

43

SUN, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date

Position Angle of Axis P

Date

Heliographic Latitude B0

Position Angle of Axis P

Longitude L0

Heliographic Latitude B0

Longitude L0

Apr. 1 2 3 4 5 6

º -26.16 26.19 26.22 26.24 26.26 26.26

º -6.53 6.48 6.42 6.36 6.30 6.24

º 312.14 298.95 285.75 272.56 259.36 246.17

May 17 18 19 20 21 22

º -20.28 19.99 19.69 19.38 19.07 18.75

º -2.41 2.30 2.18 2.06 1.95 -1.83

º 64.45 51.22 37.99 24.77 11.54 358.31

7 8 9 10 11 12

-26.26 26.26 26.24 26.22 26.19 26.15

-6.17 6.11 6.04 5.97 5.90 5.82

232.97 219.77 206.57 193.37 180.17 166.97

23 24 25 26 27 28

-18.43 18.10 17.77 17.42 17.08 16.73

-1.71 1.59 1.48 1.36 1.24 1.12

345.08 331.85 318.62 305.39 292.16 278.93

13 14 15 16 17 18

-26.11 26.05 26.00 25.93 25.85 25.77

-5.75 5.67 5.59 5.51 5.43 5.35

153.77 140.57 127.36 114.16 100.95 87.75

29 30 31 June 1 2 3

-16.37 16.01 15.64 15.27 14.89 14.51

-1.00 0.88 0.76 0.64 0.52 0.40

265.69 252.46 239.23 225.99 212.76 199.53

19 20 21 22 23 24

-25.68 25.59 25.49 25.37 25.26 25.13

-5.26 5.18 5.09 5.00 4.91 4.82

74.54 61.33 48.13 34.92 21.71 8.50

4 5 6 7 8 9

-14.12 13.73 13.34 12.94 12.54 12.13

-0.28 0.15 -0.03 +0.09 0.21 0.33

186.29 173.06 159.82 146.58 133.35 120.11

25 26 27 28 29 30

-25.00 24.86 24.71 24.56 24.39 24.23

-4.73 4.63 4.54 4.44 4.34 4.25

355.29 342.07 328.86 315.65 302.43 289.22

10 11 12 13 14 15

-11.72 11.31 10.89 10.47 10.04 9.62

+0.45 0.57 0.69 0.81 0.93 1.05

106.88 93.64 80.40 67.17 53.93 40.70

May 1 2 3 4 5 6

-24.05 23.87 23.68 23.48 23.27 23.06

-4.15 4.04 3.94 3.84 3.73 3.63

276.00 262.79 249.57 236.35 223.13 209.91

16 17 18 19 20 21

-9.19 8.75 8.32 7.88 7.44 7.00

+1.17 1.29 1.41 1.52 1.64 1.76

27.46 14.22 0.99 347.75 334.51 321.28

7 8 9 10 11 12

-22.84 22.62 22.38 22.14 21.90 21.64

-3.52 3.42 3.31 3.20 3.09 2.98

196.69 183.47 170.25 157.02 143.80 130.58

22 23 24 25 26 27

-6.55 6.11 5.66 5.21 4.76 4.31

+1.87 1.99 2.11 2.22 2.34 2.45

308.04 294.80 281.57 268.33 255.09 241.86

13 14 15 16 17

-21.38 21.12 20.84 20.56 -20.28

-2.87 2.75 2.64 2.53 -2.41

117.35 104.13 90.90 77.68 64.45

28 29 30 July 1 2

-3.86 3.41 2.96 2.50 -2.05

+2.56 2.67 2.79 2.90 +3.01

228.62 215.38 202.15 188.91 175.67

44

SUN, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date

Position Angle of Axis P

Heliographic Latitude B0

Date

Position Angle of Axis P

Longitude L0

Heliographic Latitude B0

Longitude L0

July 1 2 3 4 5 6

º -2.50 2.05 1.60 1.14 0.69 -0.24

º +2.90 3.01 3.12 3.22 3.33 3.44

º 188.91 175.67 162.44 149.20 135.97 122.73

Aug. 16 17 18 19 20 21

º +16.45 16.78 17.11 17.43 17.75 18.06

º +6.70 6.75 6.79 6.83 6.87 6.91

º 300.39 287.18 273.96 260.74 247.53 234.31

7 8 9 10 11 12

+0.21 0.67 1.12 1.57 2.01 2.46

+3.54 3.65 3.75 3.86 3.96 4.06

109.49 96.26 83.02 69.79 56.55 43.32

22 23 24 25 26 27

+18.37 18.67 18.96 19.26 19.54 19.82

+6.95 6.98 7.01 7.04 7.07 7.10

221.10 207.88 194.67 181.46 168.24 155.03

13 14 15 16 17 18

+2.91 3.35 3.80 4.24 4.68 5.12

+4.16 4.25 4.35 4.45 4.54 4.64

30.09 16.85 3.62 350.39 337.16 323.93

28 29 30 31 Sept. 1 2

+20.10 20.37 20.63 20.89 21.15 21.40

+7.12 7.14 7.16 7.18 7.20 7.21

141.82 128.61 115.40 102.19 88.98 75.77

19 20 21 22 23 24

+5.55 5.98 6.42 6.84 7.27 7.69

+4.73 4.82 4.91 5.00 5.08 5.17

310.69 297.46 284.23 271.00 257.77 244.54

3 4 5 6 7 8

+21.64 21.88 22.11 22.33 22.55 22.77

+7.22 7.23 7.24 7.25 7.25 7.25

62.56 49.35 36.14 22.94 9.73 356.52

25 26 27 28 29 30

+8.11 8.53 8.94 9.35 9.76 10.17

+5.25 5.34 5.42 5.50 5.58 5.65

231.32 218.09 204.86 191.63 178.40 165.18

9 10 11 12 13 14

+22.97 23.18 23.37 23.56 23.75 23.93

+7.25 7.25 7.24 7.24 7.23 7.22

343.32 330.11 316.91 303.70 290.50 277.30

31 Aug. 1 2 3 4 5

+10.57 10.97 11.36 11.75 12.14 12.52

+5.73 5.80 5.87 5.94 6.01 6.08

151.95 138.72 125.50 112.27 99.05 85.82

15 16 17 18 19 20

+24.10 24.26 24.42 24.58 24.73 24.87

+7.20 7.19 7.17 7.15 7.13 7.11

264.10 250.89 237.69 224.49 211.29 198.09

6 7 8 9 10 11

+12.90 13.27 13.64 14.01 14.37 14.73

+6.14 6.21 6.27 6.33 6.39 6.44

72.60 59.38 46.15 32.93 19.71 6.49

21 22 23 24 25 26

+25.00 25.13 25.25 25.36 25.47 25.57

+7.08 7.05 7.02 6.99 6.96 6.92

184.89 171.69 158.49 145.30 132.10 118.90

12 13 14 15 16

+15.08 15.43 15.78 16.12 +16.45

+6.50 6.55 6.60 6.65 +6.70

353.27 340.05 326.83 313.61 300.39

27 28 29 30 Oct. 1

+25.67 25.75 25.84 25.91 +25.98

+6.88 6.84 6.80 6.76 +6.71

105.70 92.50 79.31 66.11 52.92

45

SUN, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date

Position Angle of Axis P

Heliographic Latitude B0

Date

Position Angle of Axis P

Longitude L0

Heliographic Latitude B0

Longitude L0

Oct. 1 2 3 4 5 6

º +25.98 26.04 26.09 26.14 26.18 26.21

º +6.71 6.66 6.61 6.56 6.51 6.45

º 52.92 39.72 26.52 13.33 0.13 346.94

Nov. 16 17 18 19 20 21

º +21.00 20.71 20.41 20.11 19.80 19.48

º +2.70 2.59 2.47 2.35 2.23 2.10

º 166.24 153.06 139.87 126.69 113.51 100.33

7 8 9 10 11 12

+26.23 26.25 26.26 26.26 26.26 26.25

+6.39 6.33 6.27 6.20 6.14 6.07

333.75 320.55 307.36 294.17 280.97 267.78

22 23 24 25 26 27

+19.16 18.83 18.49 18.14 17.79 17.43

+1.98 1.86 1.73 1.61 1.49 1.36

87.15 73.97 60.79 47.61 34.43 21.25

13 14 15 16 17 18

+26.23 26.20 26.17 26.13 26.08 26.02

+6.00 5.93 5.86 5.78 5.71 5.63

254.59 241.40 228.21 215.02 201.83 188.64

28 29 30 Dec. 1 2 3

+17.07 16.70 16.32 15.94 15.55 15.15

+1.23 1.11 0.98 0.85 0.73 0.60

8.07 354.89 341.71 328.53 315.35 302.17

19 20 21 22 23 24

+25.96 25.88 25.80 25.72 25.62 25.52

+5.55 5.46 5.38 5.30 5.21 5.12

175.45 162.26 149.07 135.88 122.69 109.50

4 5 6 7 8 9

+14.75 14.34 13.93 13.52 13.09 12.67

+0.47 0.34 0.22 +0.09 -0.04 0.17

288.99 275.81 262.64 249.46 236.28 223.10

25 26 27 28 29 30

+25.41 25.29 25.16 25.03 24.89 24.74

+5.03 4.94 4.85 4.75 4.66 4.56

96.32 83.13 69.94 56.75 43.57 30.38

10 11 12 13 14 15

+12.24 11.80 11.36 10.92 10.47 10.02

-0.30 0.42 0.55 0.68 0.81 0.94

209.93 196.75 183.58 170.40 157.23 144.05

31 Nov. 1 2 3 4 5

+24.58 24.42 24.24 24.06 23.87 23.68

+4.46 4.36 4.26 4.15 4.05 3.94

17.19 4.00 350.82 337.63 324.45 311.26

16 17 18 19 20 21

+9.56 9.10 8.64 8.18 7.71 7.24

-1.06 1.19 1.32 1.44 1.57 1.69

130.88 117.70 104.53 91.35 78.18 65.01

6 7 8 9 10 11

+23.47 23.26 23.04 22.81 22.57 22.33

+3.84 3.73 3.62 3.51 3.40 3.28

298.07 284.89 271.70 258.52 245.34 232.15

22 23 24 25 26 27

+6.77 6.29 5.81 5.34 4.86 4.38

-1.82 1.94 2.07 2.19 2.31 2.43

51.83 38.66 25.49 12.32 359.14 345.97

12 13 14 15 16

+22.08 21.82 21.55 21.28 +21.00

+3.17 3.05 2.94 2.82 +2.70

218.97 205.79 192.60 179.42 166.24

28 29 30 31 32

+3.89 3.41 2.93 2.44 +1.96

-2.55 2.67 2.79 2.91 -3.03

332.80 319.63 306.46 293.29 280.11

46

MOON, 2020 UNIVERSAL TIME PHASES OF THE MOON Lunation

1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213

New Moon

Dec. Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

d 26 24 23 24 23 22 21 20 19 17 16 15 14

h 05 21 15 09 02 17 06 17 02 11 19 05 16

m 13 42 32 28 26 39 41 33 42 00 31 07 17

First Quarter

Jan. Feb. Mar. Apr. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

d 3 2 2 1 30 30 28 27 25 24 23 22 21

h 04 01 19 10 20 03 08 12 17 01 13 04 23

m 45 42 57 21 38 30 16 33 58 55 23 45 41

Full Moon

MOON AT PERIGEE

Dec. Jan. Feb. Mar. Apr.

d 18 13 10 10 7

h 20 20 20 07 18

May Jun. Jun. Jul. Aug.

d 6 3 30 25 21

h 03 04 02 05 11

Sep. Oct. Nov. Dec. Jan.

d 10 9 9 8 7 5 5 3 2 1 31 30 30

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Oct. Nov. Dec.

h 19 07 17 02 10 19 04 15 05 21 14 09 03

m 21 33 48 35 45 12 44 59 22 05 49 30 28

Last Quarter

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Jan.

d 17 15 16 14 14 13 12 11 10 10 8 8 6

h 12 22 09 22 14 06 23 16 09 00 13 00 09

m 58 17 34 56 03 24 29 45 26 40 46 37 37

d 6 3 30 27 24 21

h 06 17 19 00 17 13

MOON AT APOGEE d 18 16 14 12 9

h 14 24 12 21 16

Dec. Jan. Jan. Feb. Mar.

d 5 2 29 26 24

h 04 02 21 12 15

Apr. May Jun. Jul. Aug.

d 20 18 15 12 9

h 19 08 01 19 14

Sep. Oct. Oct. Nov. Dec. Jan.

47

MOON, 2020 MEAN EQUATOR, ORBIT, LONGITUDE AND ELONGATION Date

Mean Equator i

∆

Orbit Perigee

Node

Γ'

Ω

Ω'

Mean Longitude

Mean Elongation D

° 23.704 23.690 23 676 23.676 23.662 23.648 23.634

° 281.722 281.200 280 676 280.676 280.153 279.629 279.105

° 356.200 356.193 356 186 356.186 356.180 356.174 356.168

° 177 178 179 180 181 182

' 05 12 19 26 33 40

" 59.5 50.0 40 5 40.5 31.0 21.6 12.1

° 98 97 97 96 96 95

' 14 42 11 39 07 35

" 37.9 51.6 05 2 05.2 18.9 32.6 46.2

° 345 117 248 20 152 284

' 18 04 49 35 21 07

" 16.7 06.9 57 2 57.2 47.5 37.7 28.0

° 65.177 187.085 308 992 308.992 70.900 192.807 314.714

Mar.

1 11 21 31 Apr. 10 20

23.620 23.606 23.591 23.577 23.563 23.549

278.581 278.056 277.531 277.006 276.481 275.955

356.162 356.157 356.152 356.148 356.144 356.140

183 184 186 187 188 189

47 53 00 07 14 21

02.6 53.1 43.7 34.2 24.7 15.2

95 94 94 93 92 92

03 32 00 28 56 25

59.9 13.6 27.2 40.9 54.6 08.2

55 187 319 91 222 354

53 39 24 10 56 42

18.3 08.6 58.8 49.1 39.4 29.7

76.622 198.529 320.437 82.344 204.252 326.159

30 May 10 20 30 June 9 19

23.535 23.521 23.506 23.492 23.478 23.464

275.429 274.902 274.376 273.848 273.321 272.794

356.136 356.133 356.130 356.128 356.125 356.123

190 191 192 193 194 196

28 34 41 48 55 02

05.8 56.3 46.8 37.3 27.8 18.4

91 91 90 90 89 89

53 21 49 18 46 14

21.9 35.6 49.2 02.9 16.5 30.2

126 258 30 161 293 65

28 14 00 45 31 17

19.9 10.2 00.5 50.7 41.0 31.3

88.067 209.974 331.882 93.789 215.697 337.604

29 9 19 29 Aug. 8 18

23.450 23.436 23 421 23.421 23.407 23.393 23.379

272.266 271.737 271 209 271.209 270.680 270.151 269.621

356.122 356.121 356 120 356.120 356.119 356.119 356.119

197 198 199 200 201 202

09 15 22 29 36 43

08.9 59.4 49 9 49.9 40.5 31.0 21.5

88 88 87 87 86 86

42 10 39 07 35 03

43.9 57.5 11 2 11.2 24.9 38.5 52.2

197 328 100 232 4 135

03 49 35 20 06 52

21.6 11.8 02 1 02.1 52.4 42.7 32.9

99.512 221.419 343 327 343.327 105.234 227.142 349.049

28 7 17 27 Oct. 7 17

23.365 23.350 23.336 23.322 23.308 23.293

269.092 268.562 268.031 267.501 266.970 266.439

356.119 356.120 356.121 356.123 356.124 356.126

203 204 206 207 208 209

50 57 03 10 17 24

12.0 02.5 53.1 43.6 34.1 24.6

85 85 84 83 83 82

32 00 28 56 25 53

05.9 19.5 33.2 46.9 00.5 14.2

267 39 171 302 74 206

38 24 10 55 41 27

23.2 13.5 03.7 54.0 44.3 34.6

110.957 232.864 354.772 116.679 238.587 0.494

27 6 16 26 Dec. 6 16

23.279 23.265 23.251 23.236 23.222 23.208

265.907 265.375 264.843 264.311 263.778 263.245

356.129 356.132 356.135 356.138 356.142 356.146

210 211 212 213 214 216

31 38 44 51 58 05

15.2 05.7 56.2 46.7 37.3 27.8

82 81 81 80 80 79

21 49 17 46 14 42

27.9 41.5 55.2 08.9 22.5 36.2

338 109 241 13 145 277

13 59 45 30 16 02

24.8 15.1 05.4 55.7 45.9 36.2

122.402 244.309 6.217 128.124 250.032 11.939

26 36 46

23.194 23.179 23.165

262.712 356.150 262.178 356.155 261.644 356.160

48 48 26.5 180 34 16.7 312 20 07.0

133.847 255.754 17.662

Jan.

1 11 21 31 Feb. 10 20

July

Sept.

Nov.

217 12 18.3 218 19 08.8 219 25 59.3

79 10 49.9 78 39 03.5 78 07 17.2

48

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Jan.

0.0 0.5 1.0 1.5 2.0 2.5

º 334 340 346 352 358 3

' 09 09 07 04 00 56

" 53.3 41.7 43.9 30.8 35.3 31.7

º -4 4 4 5 5 5

' 22 39 53 04 11 16

" 27.7 36.2 37.5 26.3 58.6 11.1

3.0 3.5 4.0 4.5 5.0 5.5

9 15 21 27 33 40

52 50 49 50 54 02

55.1 21.3 26.0 44.6 51.4 19.2

-5 5 5 4 4 4

17 14 08 59 46 30

6.0 6.5 7.0 7.5 8.0 8.5

46 52 58 65 71 78

13 29 49 15 45 22

38.8 18.0 41.0 08.0 54.1 08.8

-4 3 3 2 2 1

9.0 9.5 10.0 10.5 11.0 11.5

85 91 98 105 112 119

03 51 43 41 43 49

55.5 10.7 44.0 18.1 28.5 44.6

12.0 12.5 13.0 13.5 14.0 14.5

126 134 141 148 155 163

59 12 26 42 59 15

15.0 15.5 16.0 16.5 17.0 17.5

170 177 184 192 199 206

18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0

(X 10 3) 2.6870 2.6942 2.6996 2.7031 2.7044 2.7036

' 14 14 14 14 14 14

" 51.54 49.14 47.35 46.22 45.78 46.05

01.5 28.0 29.6 06.4 19.2 10.2

2.7006 2.6954 2.6880 2.6786 2.6672 2.6542

14 14 14 14 14 15

47.04 48.76 51.20 54.33 58.13 02.55

10 48 22 53 22 48

43.2 04.0 20.9 45.1 31.2 57.7

2.6396 2.6238 2.6070 2.5896 2.5720 2.5544

15 15 15 15 15 15

07.53 13.00 18.87 25.04 31.40 37.82

-1 -0 +0 0 1 1

13 36 01 40 18 55

26.9 25.6 35.5 01.9 16.2 38.8

2.5372 2.5207 2.5054 2.4914 2.4791 2.4685

15 15 15 16 16 16

44.17 50.33 56.15 01.52 06.31 10.42

30.2 04.4 43.4 41.8 13.8 35.5

+2 3 3 4 4 4

31 05 35 03 26 46

29.4 08.2 57.2 21.7 51.7 02.4

2.4600 2.4535 2.4491 2.4467 2.4464 2.4478

16 16 16 16 16 16

13.80 16.37 18.13 19.07 19.22 18.63

31 45 57 06 13 16

05.4 06.5 06.1 37.1 18.0 52.4

+5 5 5 5 5 5

00 10 15 14 09 00

35.2 17.8 04.3 54.7 54.8 15.3

2.4510 2.4556 2.4615 2.4685 2.4764 2.4851

16 16 16 16 16 16

17.38 15.54 13.20 10.43 07.33 03.97

213 220 227 233 240 247

17 14 07 57 43 26

09.0 00.9 24.7 20.1 48.7 53.7

+4 4 4 3 3 2

46 28 06 40 12 42

11.2 01.2 07.2 53.4 46.0 12.6

2.4943 2.5039 2.5139 2.5241 2.5346 2.5452

16 15 15 15 15 15

00.41 56.71 52.91 49.04 45.13 41.20

254 260 267 273 280

06 43 16 46 13

39.0 08.9 27.5 38.7 46.2

+2 1 1 +0 -0

09 35 00 25 10

41.9 42.9 45.0 17.3 11.8

2.5559 2.5668 2.5778 2.5889 2.6000

15 15 15 15 15

37.24 33.27 29.30 25.32 21.35

49

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Jan.

Feb.

23.0 23.5 24.0 24.5 25.0 25.5

º 280 286 292 299 305 311

' 13 37 59 17 32 45

" 46.2 53.2 02.8 18.1 42.8 21.1

º -0 0 1 1 2 2

' 10 45 19 52 23 52

" 11.8 15.0 26.3 21.5 38.3 56.6

26.0 26.5 27.0 27.5 28.0 28.5

317 324 330 336 342 348

55 02 07 10 11 10

18.5 42.1 40.5 24.8 08.2 06.7

-3 3 4 4 4 4

19 44 06 25 40 53

29.0 29.5 30.0 30.5 31.0 31.5

354 0 5 11 17 23

07 04 59 55 51 47

38.8 05.9 51.9 23.6 09.9 42.2

-5 5 5 5 5 4

1.0 1.5 2.0 2.5 3.0 3.5

29 35 41 47 54 60

45 45 47 52 02 15

33.8 19.7 35.9 59.3 06.6 34.2

4.0 4.5 5.0 5.5 6.0 6.5

66 72 79 86 92 99

33 57 27 03 46 35

7.0 7.5 8.0 8.5 9.0 9.5

106 113 120 127 135 142

10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0

3 (X 10 )

2.6000 2.6112 2.6223 2.6334 2.6443 2.6548

' 15 15 15 15 15 15

" 21.35 17.41 13.51 09.67 05.94 02.34

58.7 29.2 15.1 05.9 53.0 30.0

2.6649 2.6744 2.6832 2.6910 2.6977 2.7031

14 14 14 14 14 14

58.91 55.72 52.80 50.21 48.00 46.22

02 08 11 11 07 59

52.2 56.5 41.2 05.6 10.4 56.8

2.7070 2.7093 2.7098 2.7085 2.7051 2.6997

14 14 14 14 14 14

44.94 44.18 44.01 44.45 45.55 47.33

-4 4 4 3 3 3

49 35 18 58 36 10

27.2 44.7 53.4 58.6 07.0 26.9

2.6922 2.6827 2.6711 2.6576 2.6423 2.6254

14 14 14 15 15 15

49.80 52.97 56.84 01.40 06.61 12.44

56.6 46.1 31.4 36.3 18.5 48.3

-2 2 1 1 -0 +0

42 11 38 03 27 09

08.8 25.8 33.9 52.8 45.9 19.3

2.6072 2.5880 2.5680 2.5476 2.5273 2.5074

15 15 15 15 15 15

18.81 25.64 32.85 40.30 47.85 55.37

32 35 44 59 19 44

07.2 06.6 27.3 38.7 59.0 36.1

+0 1 2 2 3 3

46 24 00 35 08 38

50.9 13.2 47.2 51.5 43.9 42.7

2.4884 2.4707 2.4547 2.4407 2.4290 2.4200

16 16 16 16 16 16

02.66 09.56 15.90 21.50 26.20 29.90

150 157 165 172 180 187

12 42 13 44 13 40

29.1 30.3 28.2 10.6 27.5 14.4

+4 4 4 4 5 5

05 27 45 57 05 08

09.1 28.3 12.1 59.5 37.6 02.2

2.4137 2.4102 2.4097 2.4118 2.4167 2.4239

16 16 16 16 16 16

32.48 33.90 34.14 33.24 31.26 28.31

195 202 209 216 223

03 22 36 45 49

34.4 40.3 55.3 53.4 19.1

+5 4 4 4 +4

05 57 45 28 07

17.1 33.2 07.7 23.0 44.6

2.4332 2.4444 2.4571 2.4710 2.4857

16 16 16 16 16

24.51 20.00 14.94 09.47 03.73

50

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Feb.

Mar.

15.0 15.5 16.0 16.5 17.0 17.5

º 223 230 237 244 251 257

' 49 47 39 26 07 44

" 19.1 06.5 17.8 02.1 33.7 10.7

º +4 3 3 2 2 1

' 07 43 16 47 15 43

" 44.6 40.7 40.8 15.0 53.1 04.5

18.0 18.5 19.0 19.5 20.0 20.5

264 270 277 283 289 296

16 44 08 28 45 00

13.7 04.5 05.0 36.6 59.5 32.2

+1 0 +0 -0 1 1

09 35 00 33 06 38

21.0 21.5 22.0 22.5 23.0 23.5

302 308 314 320 326 332

12 22 29 35 39 41

31.4 11.8 46.2 25.9 20.7 39.4

-2 2 3 3 3 4

24.0 24.5 25.0 25.5 26.0 26.5

338 344 350 356 2 8

42 42 40 37 34 30

30.4 02.1 23.1 43.3 13.9 07.9

27.0 27.5 28.0 28.5 29.0 29.5

14 20 26 32 38 44

25 21 16 13 10 09

1.0 1.5 2.0 2.5 3.0 3.5

50 56 62 68 74 81

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

(X 10 3) 2.4857 2.5010 2.5165 2.5321 2.5476 2.5627

' 16 15 15 15 15 15

" 03.73 57.84 51.92 46.05 40.31 34.77

17.7 00.0 37.6 24.6 43.1 55.7

2.5774 2.5915 2.6049 2.6178 2.6299 2.6413

15 15 15 15 15 15

29.45 24.39 19.61 15.10 10.89 06.95

09 38 05 30 52 11

41.7 42.1 39.3 17.5 22.9 43.5

2.6520 2.6620 2.6713 2.6798 2.6876 2.6946

15 14 14 14 14 14

03.29 59.89 56.77 53.91 51.33 49.02

-4 4 4 4 5 5

28 41 51 58 02 02

09.0 31.3 44.3 43.5 26.5 52.3

2.7007 2.7059 2.7101 2.7132 2.7152 2.7158

14 14 14 14 14 14

47.00 45.30 43.92 42.90 42.28 42.07

40.6 09.7 55.5 21.3 53.2 59.7

-5 4 4 4 4 3

00 53 44 32 16 58

01.7 56.8 40.9 18.8 56.0 39.3

2.7150 2.7128 2.7089 2.7033 2.6959 2.6868

14 14 14 14 14 14

42.32 43.06 44.33 46.15 48.57 51.59

11 15 22 33 48 09

12.4 04.7 12.1 11.5 40.3 15.7

-3 3 2 2 1 -1

37 13 47 19 49 17

36.7 57.2 51.1 30.3 08.5 01.5

2.6758 2.6631 2.6486 2.6324 2.6147 2.5958

14 14 15 15 15 15

55.24 59.54 04.46 10.01 16.16 22.85

87 94 100 107 114 121

35 08 47 33 27 29

33.6 07.3 26.1 53.4 45.1 07.6

+0 0 0 1 1 2

43 08 26 02 37 11

27.5 47.8 33.4 08.3 25.5 50.4

2.5758 2.5550 2.5337 2.5124 2.4915 2.4714

15 15 15 15 16 16

30.03 37.60 45.45 53.46 01.47 09.31

128 135 143 150 158

37 53 16 44 18

55.9 52.4 25.1 48.0 01.3

+2 3 3 4 +4

44 15 43 07 28

45.6 31.4 27.8 55.3 17.7

2.4525 2.4353 2.4202 2.4076 2.3978

16 16 16 16 16

16.77 23.67 29.81 34.98 39.03

51

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Date

Apparent Longitude

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Mar.

Apr.

9.0 9.5 10.0 10.5 11.0 11.5

º 158 165 173 181 188 196

' 18 54 34 14 53 30

" 01.3 53.1 01.8 00.3 19.4 32.7

º +4 4 4 5 5 4

' 28 44 54 00 00 55

" 17.7 03.5 48.2 15.6 18.8 01.0

12.0 12.5 13.0 13.5 14.0 14.5

204 211 218 226 233 240

04 33 57 14 25 28

20.6 33.2 13.5 38.1 17.7 56.6

+4 4 4 3 3 2

44 29 09 46 19 50

15.0 15.5 16.0 16.5 17.0 17.5

247 254 260 267 274 280

25 15 58 34 05 30

31.5 09.4 05.9 43.5 29.2 53.3

+2 1 1 0 +0 -0

18.0 18.5 19.0 19.5 20.0 20.5

286 293 299 305 311 317

51 07 20 29 35 40

27.5 44.2 15.0 30.2 58.2 05.0

21.0 21.5 22.0 22.5 23.0 23.5

323 329 335 341 347 353

42 42 42 40 37 34

24.0 24.5 25.0 25.5 26.0 26.5

359 5 11 17 23 29

27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 1.0

(X 10 3) 2.3978 2.3912 2.3877 2.3876 2.3907 2.3970

' 16 16 16 16 16 16

" 39.03 41.83 43.28 43.34 42.02 39.40

34.1 18.4 40.8 12.6 28.5 04.2

2.4062 2.4180 2.4322 2.4482 2.4657 2.4843

16 16 16 16 16 16

35.57 30.70 24.94 18.49 11.53 04.26

18 45 11 37 02 31

35.3 36.3 39.8 16.4 53.9 02.2

2.5036 2.5232 2.5427 2.5618 2.5803 2.5980

15 15 15 15 15 15

56.84 49.42 42.14 35.10 28.39 22.07

-1 1 2 2 3 3

04 36 06 35 01 26

08.6 04.4 30.6 09.9 46.7 07.1

2.6147 2.6302 2.6445 2.6575 2.6692 2.6796

15 15 15 15 14 14

16.19 10.78 05.86 01.42 57.47 54.00

14.2 46.6 00.7 12.2 35.0 21.0

-3 4 4 4 4 4

47 07 23 36 47 54

58.4 09.4 30.6 53.6 11.9 20.3

2.6886 2.6965 2.7030 2.7084 2.7126 2.7157

14 14 14 14 14 14

50.98 48.40 46.24 44.48 43.11 42.10

30 26 22 18 14 11

41.0 44.6 41.4 40.9 53.6 31.0

-4 4 4 4 4 4

58 58 56 50 41 29

15.4 55.3 20.0 31.1 31.9 27.2

2.7177 2.7185 2.7183 2.7169 2.7144 2.7107

14 14 14 14 14 14

41.47 41.19 41.26 41.71 42.52 43.71

35 41 47 53 59 65

08 06 06 07 09 14

46.3 54.7 14.1 04.5 48.8 52.6

-4 3 3 3 2 2

14 56 35 12 47 19

23.5 28.5 51.7 43.7 16.3 42.9

2.7058 2.6997 2.6922 2.6834 2.6732 2.6615

14 14 14 14 14 15

45.31 47.34 49.80 52.73 56.14 00.06

71 77 83 90 96

22 33 48 08 32

44.1 53.5 53.1 16.1 36.3

-1 1 0 -0 +0

50 19 46 13 20

18.0 17.8 59.8 43.5 10.0

2.6485 2.6341 2.6184 2.6015 2.5835

15 15 15 15 15

04.48 09.42 14.88 20.82 27.23

52

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Apr.

1.0 1.5 2.0 2.5 3.0 3.5

º 96 103 109 116 123 130

' 32 02 38 20 09 06

" 36.3 26.9 18.8 40.0 52.8 13.0

º +0 0 1 2 2 3

' 20 54 28 01 33 03

" 10.0 17.1 12.2 27.2 31.7 53.1

4.0 4.5 5.0 5.5 6.0 6.5

137 144 151 159 166 174

09 20 38 02 31 05

47.0 30.6 06.9 05.1 40.4 53.9

+3 3 4 4 4 4

31 57 18 36 49 58

7.0 7.5 8.0 8.5 9.0 9.5

181 189 197 204 212 219

43 23 03 43 20 54

34.5 21.3 47.2 22.9 41.2 21.4

+5 4 4 4 4 3

10.0 10.5 11.0 11.5 12.0 12.5

227 234 242 249 256 263

23 46 02 12 14 08

12.4 15.4 45.6 12.2 18.2 59.1

13.0 13.5 14.0 14.5 15.0 15.5

269 276 283 289 295 302

56 36 10 37 59 16

16.0 16.5 17.0 17.5 18.0 18.5

308 314 320 326 332 338

19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0

(X 10 3) 2.5835 2.5647 2.5451 2.5252 2.5052 2.4855

' 15 15 15 15 15 16

" 27.23 34.05 41.22 48.65 56.21 03.79

57.0 08.4 52.3 35.3 47.5 04.0

2.4665 2.4486 2.4322 2.4177 2.4055 2.3961

16 16 16 16 16 16

11.22 18.33 24.93 30.83 35.83 39.77

01 58 51 38 20 57

06.9 46.6 03.0 05.6 13.5 53.4

2.3896 2.3862 2.3862 2.3894 2.3960 2.4056

16 16 16 16 16 16

42.50 43.90 43.92 42.55 39.82 35.82

+3 3 2 1 1 0

31 02 30 56 20 44

39.1 08.6 02.3 01.3 45.4 52.2

2.4180 2.4329 2.4499 2.4686 2.4886 2.5094

16 16 16 16 16 15

30.71 24.63 17.79 10.38 02.60 54.64

21.6 41.2 21.1 49.6 38.9 23.5

+0 -0 1 1 2 2

08 26 01 34 05 35

56.3 31.3 03.5 16.5 49.6 25.3

2.5305 2.5516 2.5723 2.5922 2.6112 2.6289

15 15 15 15 15 15

46.67 38.85 31.30 24.13 17.42 11.24

28 37 42 44 44 42

39.0 01.3 05.2 24.3 30.2 52.4

-3 3 3 4 4 4

02 27 50 09 26 40

48.6 46.5 08.1 43.8 25.5 06.6

2.6451 2.6598 2.6729 2.6842 2.6938 2.7016

15 15 14 14 14 14

05.64 00.63 56.24 52.46 49.28 46.70

344 350 356 2 8 14

39 36 31 27 23 18

57.8 10.8 53.1 24.0 00.4 57.1

-4 4 5 5 5 4

50 58 02 03 00 55

41.4 05.4 15.6 09.8 47.6 09.8

2.7078 2.7123 2.7153 2.7168 2.7169 2.7157

14 14 14 14 14 14

44.68 43.20 42.23 41.74 41.71 42.09

20 26 32 38 44

15 12 10 10 10

27.3 42.4 53.3 10.1 42.9

-4 4 4 4 -3

46 34 19 01 40

18.9 18.9 15.7 16.7 31.5

2.7134 2.7099 2.7053 2.6997 2.6932

14 14 14 14 14

42.86 44.01 45.50 47.32 49.46

53

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Apr.

May

24.0 24.5 25.0 25.5 26.0 26.5

º 44 50 56 62 68 74

' 10 12 16 21 29 39

" 42.9 42.4 19.9 48.2 21.3 15.3

º -3 3 2 2 1 1

' 40 17 51 23 53 22

" 31.5 11.0 28.1 37.5 55.2 39.0

27.0 27.5 28.0 28.5 29.0 29.5

80 87 93 99 106 112

51 07 26 48 15 46

48.2 19.5 10.9 45.1 25.9 37.3

-0 -0 +0 0 1 1

50 16 17 51 25 58

30.0 30.5 1.0 1.5 2.0 2.5

119 126 132 139 146 153

22 04 50 43 42 46

42.6 03.3 58.1 41.0 20.1 56.3

+2 3 3 3 4 4

3.0 3.5 4.0 4.5 5.0 5.5

160 168 175 182 190 197

57 13 34 59 28 59

21.1 16.2 12.4 29.1 15.3 30.6

6.0 6.5 7.0 7.5 8.0 8.5

205 213 220 228 235 242

32 04 36 05 31 53

9.0 9.5 10.0 10.5 11.0 11.5

250 257 264 271 278 284

12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0

(X 10 3) 2.6932 2.6858 2.6775 2.6683 2.6583 2.6474

' 14 14 14 14 15 15

" 49.46 51.92 54.68 57.76 01.15 04.85

08.1 43.1 14.1 20.0 10.1 18.2

2.6357 2.6231 2.6097 2.5955 2.5806 2.5651

15 15 15 15 15 15

08.88 13.24 17.93 22.95 28.28 33.90

30 00 28 54 17 36

17.3 39.1 54.3 33.2 05.9 03.4

2.5490 2.5327 2.5161 2.4996 2.4835 2.4679

15 15 15 15 16 16

39.77 45.86 52.08 58.36 04.59 10.66

+4 5 5 5 5 4

50 01 07 07 02 53

58.1 25.0 03.3 37.5 58.6 05.3

2.4534 2.4401 2.4284 2.4187 2.4113 2.4064

16 16 16 16 16 16

16.43 21.74 26.46 30.41 33.46 35.49

07.0 52.2 31.8 53.6 49.6 19.6

+4 4 3 3 2 2

38 18 53 25 54 19

04.9 13.1 53.8 38.4 03.6 50.5

2.4042 2.4049 2.4086 2.4152 2.4245 2.4365

16 16 16 16 16 16

36.38 36.08 34.57 31.87 28.04 23.19

09 19 23 20 11 54

32.6 48.6 38.6 45.3 01.9 31.2

+1 1 +0 -0 0 1

43 06 28 09 46 22

41.9 21.0 29.4 14.2 14.7 01.3

2.4508 2.4671 2.4851 2.5043 2.5243 2.5448

16 16 16 15 15 15

17.45 10.98 03.96 56.56 48.97 41.35

291 298 304 310 317 323

31 02 26 45 00 10

24.4 00.0 41.9 58.7 21.8 24.9

-1 2 2 3 3 4

56 28 57 24 49 10

07.3 10.4 52.3 58.1 15.8 36.1

2.5652 2.5853 2.6046 2.6229 2.6399 2.6553

15 15 15 15 15 15

33.84 26.59 19.71 13.30 07.43 02.15

329 335 341 347 353

16 19 20 18 16

43.0 51.2 24.6 57.2 01.9

-4 4 4 5 -5

28 43 55 04 09

51.6 56.9 47.9 21.4 35.8

2.6691 2.6809 2.6908 2.6988 2.7047

14 14 14 14 14

57.52 53.54 50.25 47.63 45.68

54

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

May

June

17.0 17.5 18.0 18.5 19.0 19.5

º 353 359 5 11 16 22

' 16 12 07 03 59 56

" 01.9 09.9 50.3 30.3 34.7 26.2

º -5 5 5 5 4 4

' 09 11 10 05 57 45

" 35.8 29.9 03.8 18.4 16.0 59.9

20.0 20.5 21.0 21.5 22.0 22.5

28 34 40 46 53 59

54 53 54 57 02 10

24.7 48.3 52.7 51.6 57.1 19.7

-4 4 3 3 3 2

31 14 53 30 04 36

23.0 23.5 24.0 24.5 25.0 25.5

65 71 77 84 90 96

20 32 47 05 26 50

08.7 32.7 39.5 36.8 32.3 33.9

-2 1 1 -0 +0 0

26.0 26.5 27.0 27.5 28.0 28.5

103 109 116 123 129 136

17 48 22 00 42 27

49.6 28.0 37.6 27.1 04.4 36.9

29.0 29.5 30.0 30.5 31.0 31.5

143 150 157 164 171 178

17 10 08 10 15 24

1.0 1.5 2.0 2.5 3.0 3.5

185 192 200 207 214 222

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

(X 10 3) 2.7047 2.7087 2.7108 2.7110 2.7096 2.7066

' 14 14 14 14 14 14

" 45.68 44.38 43.70 43.62 44.09 45.07

34.7 06.9 44.4 37.3 57.3 58.5

2.7021 2.6964 2.6895 2.6816 2.6729 2.6635

14 14 14 14 14 14

46.53 48.42 50.69 53.30 56.21 59.38

06 35 02 27 07 42

57.1 11.1 00.9 48.5 02.3 06.3

2.6535 2.6430 2.6322 2.6210 2.6096 2.5980

15 15 15 15 15 15

02.77 06.35 10.09 13.97 17.96 22.07

+1 1 2 2 3 3

16 51 24 55 24 51

56.9 06.8 07.9 31.8 50.2 35.1

2.5862 2.5743 2.5624 2.5503 2.5383 2.5263

15 15 15 15 15 15

26.26 30.54 34.89 39.30 43.76 48.24

09.9 46.7 27.5 08.1 39.9 48.6

+4 4 4 5 5 5

15 35 52 04 12 15

19.4 37.3 04.8 20.2 05.2 05.2

2.5144 2.5028 2.4915 2.4807 2.4706 2.4613

15 15 16 16 16 16

52.72 57.15 01.49 05.67 09.63 13.27

37 52 10 29 49 09

14.0 29.6 02.5 14.3 21.5 36.6

+5 5 4 4 4 3

13 06 54 37 16 50

10.2 15.6 23.1 40.5 22.8 51.4

2.4532 2.4463 2.4410 2.4374 2.4357 2.4362

16 16 16 16 16 16

16.51 19.24 21.38 22.82 23.49 23.32

229 236 244 251 258 265

29 47 02 15 24 28

10.1 11.6 51.7 24.1 06.4 22.1

+3 2 2 1 0 +0

21 49 13 36 58 19

34.1 04.0 58.6 58.1 44.1 58.1

2.4388 2.4436 2.4507 2.4600 2.4714 2.4846

16 16 16 16 16 16

22.27 20.31 17.47 13.77 09.30 04.14

272 279 286 292 299

27 21 10 52 29

41.1 40.8 05.7 48.1 47.4

-0 0 1 2 -2

18 56 33 07 40

40.0 33.1 07.5 53.8 26.8

2.4995 2.5157 2.5329 2.5508 2.5690

15 15 15 15 15

58.41 52.24 45.76 39.12 32.46

55

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Date

Apparent Longitude

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

June

July

9.0 9.5 10.0 10.5 11.0 11.5

º 299 306 312 318 325 331

' 29 01 27 47 03 15

" 47.4 09.5 06.5 56.0 59.7 43.5

º -2 3 3 4 4 4

' 40 10 37 01 22 40

" 26.8 26.0 34.8 40.2 32.9 06.1

12.0 12.5 13.0 13.5 14.0 14.5

337 343 349 355 1 7

23 28 29 29 27 24

36.0 08.4 53.3 24.6 16.4 03.1

-4 5 5 5 5 5

54 04 12 16 16 13

15.0 15.5 16.0 16.5 17.0 17.5

13 19 25 31 37 43

20 16 13 11 10 12

18.6 35.8 26.7 21.4 48.4 13.9

-5 4 4 4 4 3

18.0 18.5 19.0 19.5 20.0 20.5

49 55 61 67 74 80

16 22 32 44 01 21

01.9 33.6 07.4 58.8 20.4 21.2

21.0 21.5 22.0 22.5 23.0 23.5

86 93 99 106 112 119

45 12 44 19 58 40

24.0 24.5 25.0 25.5 26.0 26.5

126 133 140 147 154 161

27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 1.0 1.5 2.0

(X 10 3) 2.5690 2.5872 2.6050 2.6221 2.6381 2.6529

' 15 15 15 15 15 15

" 32.46 25.91 19.59 13.60 08.05 03.00

15.5 58.6 14.4 03.3 26.5 26.0

2.6660 2.6775 2.6870 2.6946 2.7000 2.7033

14 14 14 14 14 14

58.53 54.69 51.51 49.02 47.23 46.14

07 57 44 28 09 47

04.9 26.7 36.1 38.6 41.1 51.8

2.7045 2.7037 2.7009 2.6962 2.6898 2.6818

14 14 14 14 14 14

45.74 46.02 46.95 48.49 50.61 53.24

-3 2 2 1 1 -0

23 56 27 55 22 48

20.5 19.1 01.3 43.5 44.1 24.4

2.6725 2.6621 2.6508 2.6387 2.6262 2.6134

14 14 15 15 15 15

56.35 59.86 03.71 07.83 12.16 16.63

07.7 43.0 07.4 18.5 11.3 38.7

-0 +0 0 1 2 2

13 22 58 33 08 41

07.8 39.8 30.5 54.8 22.3 21.6

2.6006 2.5878 2.5753 2.5633 2.5518 2.5408

15 15 15 15 15 15

21.16 25.70 30.18 34.55 38.77 42.81

26 15 07 02 00 00

31.5 39.2 49.5 49.4 24.7 20.6

+3 3 4 4 4 5

12 40 06 28 46 01

21.8 52.6 25.1 32.6 51.3 00.6

2.5306 2.5211 2.5123 2.5042 2.4969 2.4903

15 15 15 15 15 16

46.63 50.21 53.54 56.61 59.41 01.95

168 175 182 189 196 203

02 06 11 18 25 33

21.7 11.8 34.2 11.5 45.2 56.0

+5 5 5 5 5 4

10 15 16 11 02 48

43.7 48.0 05.7 33.8 14.2 14.2

2.4844 2.4793 2.4750 2.4715 2.4688 2.4671

16 16 16 16 16 16

04.21 06.20 07.89 09.27 10.31 10.99

210 217 224 232 239

42 50 58 05 11

23.6 46.2 41.2 44.7 32.1

+4 4 3 3 +2

29 07 40 10 38

46.0 07.2 39.9 50.6 10.0

2.4664 2.4667 2.4682 2.4710 2.4752

16 16 16 16 16

11.28 11.14 10.54 09.44 07.81

56

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

July

1.0 1.5 2.0 2.5 3.0 3.5

º 224 232 239 246 253 260

' 58 05 11 15 17 17

" 41.2 44.7 32.1 38.2 37.6 05.3

º +3 3 2 2 1 0

' 40 10 38 03 26 48

" 39.9 50.6 10.0 11.5 31.1 46.0

4.0 4.5 5.0 5.5 6.0 6.5

267 274 280 287 294 301

13 06 56 42 23 00

37.2 50.7 25.6 04.3 32.6 40.1

+0 -0 1 1 2 2

10 27 04 40 15 47

7.0 7.5 8.0 8.5 9.0 9.5

307 314 320 326 333 339

33 01 25 44 00 11

20.5 32.1 17.5 44.0 03.1 30.6

-3 3 4 4 4 4

10.0 10.5 11.0 11.5 12.0 12.5

345 351 357 3 9 15

19 24 26 26 24 21

26.0 12.6 16.6 06.8 14.5 12.6

13.0 13.5 14.0 14.5 15.0 15.5

21 27 33 39 45 51

17 13 10 09 09 11

16.0 16.5 17.0 17.5 18.0 18.5

57 63 69 75 82 88

19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0

(X 10 3) 2.4682 2.4710 2.4752 2.4807 2.4877 2.4961

' 16 16 16 16 16 15

" 10.54 09.44 07.81 05.65 02.94 59.70

33.7 28.9 46.7 47.0 00.1 00.1

2.5059 2.5170 2.5293 2.5426 2.5568 2.5715

15 15 15 15 15 15

55.95 51.74 47.12 42.15 36.93 31.55

16 42 06 26 43 56

25.0 56.5 20.6 26.5 06.9 17.2

2.5867 2.6019 2.6170 2.6315 2.6454 2.6582

15 15 15 15 15 15

26.10 20.68 15.38 10.31 05.56 01.19

-5 5 5 5 5 5

05 12 14 13 09 01

55.5 01.7 37.4 45.4 29.9 55.5

2.6697 2.6798 2.6881 2.6946 2.6991 2.7015

14 14 14 14 14 14

57.30 53.93 51.16 49.01 47.53 46.74

35.5 58.4 57.0 06.9 03.2 20.1

-4 4 4 4 3 3

51 37 20 00 37 12

07.7 12.8 17.8 30.4 59.3 54.6

2.7018 2.6999 2.6958 2.6898 2.6818 2.6719

14 14 14 14 14 14

46.66 47.28 48.60 50.61 53.27 56.55

16 25 37 54 15 41

29.9 03.2 27.5 07.2 22.5 29.2

-2 2 1 1 0 -0

45 15 44 11 36 01

27.6 51.7 22.2 16.6 55.3 41.1

2.6605 2.6477 2.6337 2.6189 2.6034 2.5877

15 15 15 15 15 15

00.40 04.76 09.56 14.72 20.14 25.74

95 101 108 115 122 129

12 48 30 16 07 03

37.9 53.3 14.3 33.3 36.6 04.2

+0 1 1 2 2 3

34 09 44 18 51 21

00.1 40.2 48.3 52.2 18.0 32.0

2.5719 2.5565 2.5416 2.5275 2.5145 2.5028

15 15 15 15 15 15

31.41 37.04 42.53 47.77 52.67 57.15

136 143 150 157 164

02 05 11 19 29

30.6 25.7 15.3 22.8 10.1

+3 4 4 4 +5

49 13 33 50 01

01.1 14.1 42.6 02.4 53.8

2.4924 2.4835 2.4762 2.4705 2.4663

16 16 16 16 16

01.13 04.56 07.41 09.65 11.29

57

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

24.0 24.5 25.0 25.5 26.0 26.5

º 164 171 178 186 193 200

' 29 39 51 02 12 22

" 10.1 59.6 14.5 20.9 48.0 08.8

º +5 5 5 5 5 4

' 01 09 11 08 01 49

" 53.8 02.7 20.9 45.9 21.3 16.2

27.0 27.5 28.0 28.5 29.0 29.5

207 214 221 228 235 242

30 36 40 41 41 38

00.9 05.5 08.2 57.7 25.6 25.8

+4 4 3 3 2 2

32 12 47 19 49 16

30.0 30.5 31.0 31.5 Aug. 1.0 1.5

249 256 263 270 276 283

32 24 13 00 44 24

53.4 44.5 55.3 22.1 00.4 45.7

+1 1 +0 -0 0 1

2.0 2.5 3.0 3.5 4.0 4.5

290 296 303 309 316 322

02 37 08 37 02 23

32.6 15.7 49.6 09.5 11.6 53.6

5.0 5.5 6.0 6.5 7.0 7.5

328 334 341 347 353 359

42 57 09 17 23 26

8.0 8.5 9.0 9.5 10.0 10.5

5 11 17 23 29 35

11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0

July

(X 10 3) 2.4663 2.4637 2.4625 2.4626 2.4639 2.4663

' 16 16 16 16 16 16

" 11.29 12.33 12.82 12.78 12.26 11.31

44.8 05.6 41.5 58.4 24.8 31.4

2.4697 2.4740 2.4791 2.4850 2.4915 2.4987

16 16 16 16 16 15

09.97 08.28 06.28 04.00 01.46 58.69

41 05 29 07 43 19

50.3 54.5 17.2 28.8 51.3 19.8

2.5066 2.5150 2.5241 2.5338 2.5440 2.5547

15 15 15 15 15 15

55.69 52.48 49.06 45.45 41.65 37.68

-1 2 2 3 3 4

53 25 55 23 47 09

25.3 41.6 45.0 14.7 53.2 26.5

2.5660 2.5777 2.5898 2.6020 2.6144 2.6268

15 15 15 15 15 15

33.56 29.32 25.00 20.63 16.27 11.97

15.1 18.4 08.5 53.4 44.8 57.5

-4 4 4 5 5 5

27 42 54 01 06 07

43.6 36.7 01.0 54.2 16.5 10.1

2.6388 2.6505 2.6616 2.6718 2.6810 2.6890

15 15 15 14 14 14

07.79 03.79 00.04 56.59 53.51 50.86

27 26 24 20 15 11

49.9 43.8 04.2 19.1 59.2 37.6

-5 4 4 4 4 4

04 58 49 37 22 04

38.8 47.8 43.6 33.2 24.9 27.2

2.6955 2.7005 2.7037 2.7050 2.7043 2.7015

14 14 14 14 14 14

48.70 47.07 46.03 45.61 45.84 46.74

41 47 53 59 65 71

07 05 04 06 10 19

49.7 12.0 22.7 00.1 42.8 08.6

-3 3 2 2 1 1

43 20 55 27 58 27

49.6 42.0 15.5 41.8 14.3 07.5

2.6966 2.6897 2.6807 2.6697 2.6569 2.6425

14 14 14 14 15 15

48.34 50.64 53.63 57.30 01.62 06.55

77 83 90 96 103

31 49 12 41 16

53.5 31.4 32.5 22.5 21.2

-0 -0 +0 0 +1

54 21 13 47 22

38.2 04.9 11.0 45.9 13.1

2.6266 2.6096 2.5916 2.5731 2.5545

15 15 15 15 15

12.03 17.98 24.33 30.97 37.78

58

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Aug. 16.0 16.5 17.0 17.5 18.0 18.5

º 103 109 116 123 130 137

' 16 57 45 39 39 45

" 21.2 41.6 28.5 37.3 54.0 53.9

º +1 1 2 2 3 3

' 22 56 28 59 28 54

" 13.1 03.4 45.0 44.5 27.0 18.1

19.0 19.5 20.0 20.5 21.0 21.5

144 152 159 166 174 181

57 12 31 53 16 40

02.7 36.6 43.7 26.5 43.5 32.6

+4 4 4 4 5 5

16 35 49 58 03 02

22.0 22.5 23.0 23.5 24.0 24.5

189 196 203 211 218 225

03 25 45 02 15 24

53.3 49.3 30.9 15.7 30.4 50.4

+4 4 4 4 3 3

25.0 25.5 26.0 26.5 27.0 27.5

232 239 246 253 260 266

29 30 27 19 07 51

59.7 49.8 19.3 31.7 35.0 39.6

28.0 28.5 29.0 29.5 30.0 30.5

273 280 286 293 299 306

31 08 42 12 39 03

31.0 31.5 Sept. 1.0 1.5 2.0 2.5

312 318 325 331 337 343

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

(X 10 3) 2.5545 2.5359 2.5179 2.5009 2.4850 2.4707

' 15 15 15 15 16 16

" 37.78 44.63 51.38 57.88 03.99 09.56

44.2 14.8 23.5 49.3 18.1 42.9

2.4583 2.4480 2.4399 2.4342 2.4309 2.4299

16 16 16 16 16 16

14.45 18.56 21.80 24.10 25.45 25.84

57 46 31 11 48 21

04.6 31.4 18.2 46.0 20.5 31.1

2.4313 2.4347 2.4401 2.4471 2.4557 2.4655

16 16 16 16 16 16

25.31 23.92 21.75 18.91 15.50 11.62

+2 2 1 1 +0 -0

51 19 46 11 35 00

49.4 48.7 02.6 04.3 26.5 19.5

2.4763 2.4878 2.4999 2.5123 2.5250 2.5377

16 16 15 15 15 15

07.39 02.91 58.25 53.51 48.73 43.97

57.8 42.3 05.4 18.6 32.1 54.5

-0 1 1 2 2 3

35 10 43 15 44 12

44.0 18.8 37.8 17.1 54.7 11.2

2.5504 2.5630 2.5754 2.5877 2.5996 2.6113

15 15 15 15 15 15

39.27 34.65 30.14 25.75 21.49 17.36

25 44 00 14 26 35

32.8 32.4 57.8 52.4 19.6 22.7

-3 3 4 4 4 4

36 58 17 32 44 53

49.5 35.1 15.9 42.5 48.2 28.8

2.6227 2.6338 2.6444 2.6546 2.6643 2.6735

15 15 15 15 14 14

13.38 09.55 05.88 02.40 59.11 56.04

349 355 1 7 13 19

42 46 48 49 48 45

06.1 35.3 57.7 22.8 02.9 13.1

-4 5 4 4 4 4

58 00 58 53 45 34

42.4 29.5 52.7 56.3 46.5 30.8

2.6819 2.6895 2.6962 2.7018 2.7063 2.7094

14 14 14 14 14 14

53.23 50.70 48.48 46.63 45.17 44.15

25 31 37 43 49

41 36 31 25 21

11.4 19.4 01.4 45.0 00.8

-4 4 3 3 -2

20 03 43 21 57

17.9 17.4 39.9 36.6 19.5

2.7111 2.7111 2.7095 2.7060 2.7007

14 14 14 14 14

43.61 43.59 44.12 45.25 47.00

59

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Date

Apparent Longitude

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Sept.

Oct.

8.0 8.5 9.0 9.5 10.0 10.5

º 49 55 61 67 73 79

' 21 17 15 15 19 26

" 00.8 22.1 24.6 45.9 05.3 02.7

º -2 2 2 1 1 -0

' 57 31 02 33 02 30

" 19.5 01.2 55.1 15.5 17.5 17.8

11.0 11.5 12.0 12.5 13.0 13.5

85 91 98 104 111 117

37 53 15 43 17 59

18.3 31.4 19.3 16.4 52.2 30.0

+0 0 1 1 2 2

02 35 08 41 13 44

14.0 14.5 15.0 15.5 16.0 16.5

124 131 138 145 153 160

48 44 48 58 15 38

25.0 43.1 18.6 53.4 56.4 43.2

+3 3 4 4 4 4

17.0 17.5 18.0 18.5 19.0 19.5

168 175 183 190 198 205

06 37 11 45 20 53

16.9 30.4 08.3 51.2 18.7 13.5

20.0 20.5 21.0 21.5 22.0 22.5

213 220 228 235 242 249

23 49 11 28 39 44

23.0 23.5 24.0 24.5 25.0 25.5

256 263 270 277 283 290

26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 1.0

(X 10 3) 2.7007 2.6935 2.6843 2.6731 2.6601 2.6454

' 14 14 14 14 15 15

" 47.00 49.39 52.43 56.15 00.53 05.55

25.7 33.0 42.4 29.6 28.3 09.5

2.6290 2.6112 2.5922 2.5723 2.5519 2.5312

15 15 15 15 15 15

11.19 17.40 24.12 31.27 38.73 46.39

13 39 03 23 39 51

02.3 34.3 12.1 22.7 34.7 20.3

2.5108 2.4909 2.4721 2.4547 2.4392 2.4260

15 16 16 16 16 16

54.11 01.71 09.03 15.88 22.08 27.45

+4 5 4 4 4 4

58 00 56 48 34 15

16.4 06.9 43.3 06.1 24.7 57.0

2.4153 2.4073 2.4023 2.4003 2.4014 2.4053

16 16 16 16 16 16

31.83 35.10 37.17 37.99 37.56 35.92

24.8 51.1 42.1 19.3 16.6 19.3

+3 3 2 2 1 1

53 26 56 24 49 14

08.6 31.1 40.4 15.0 54.4 17.5

2.4120 2.4212 2.4326 2.4458 2.4605 2.4764

16 16 16 16 16 16

33.16 29.39 24.77 19.44 13.58 07.35

43 36 23 05 42 14

23.1 32.1 57.7 56.6 48.9 57.1

+0 +0 -0 1 1 2

38 01 34 09 42 14

01.5 41.6 10.3 04.9 36.4 21.7

2.4930 2.5101 2.5274 2.5445 2.5614 2.5776

16 15 15 15 15 15

00.89 54.34 47.82 41.43 35.26 29.35

296 303 309 315 321 328

42 06 26 43 58 09

44.8 35.4 51.4 53.9 02.1 33.4

-2 3 3 3 4 4

44 11 35 57 16 31

00.6 15.5 51.4 35.6 17.4 48.5

2.5933 2.6081 2.6220 2.6351 2.6472 2.6583

15 15 15 15 15 15

23.75 18.50 13.61 09.09 04.94 01.16

334 340 346 352 358

18 25 30 34 35

42.9 43.7 47.3 03.8 42.1

-4 4 4 5 -4

44 52 58 00 59

02.4 54.7 23.0 26.9 07.8

2.6684 2.6776 2.6859 2.6932 2.6995

14 14 14 14 14

57.73 54.65 51.90 49.49 47.40

60

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Oct.

1.0 1.5 2.0 2.5 3.0 3.5

º 358 4 10 16 22 28

' 35 35 34 32 28 24

" 42.1 50.8 38.4 13.8 47.0 29.2

º -4 4 4 4 4 4

' 59 54 46 35 21 04

" 07.8 29.1 35.8 34.7 34.1 43.7

4.0 4.5 5.0 5.5 6.0 6.5

34 40 46 52 57 63

19 14 08 03 59 56

33.9 16.3 54.4 48.7 22.7 02.5

-3 3 2 2 2 1

45 23 59 33 05 35

7.0 7.5 8.0 8.5 9.0 9.5

69 75 81 88 94 100

54 54 57 03 14 28

17.1 38.0 39.1 56.1 06.0 46.5

-1 0 -0 +0 1 1

10.0 10.5 11.0 11.5 12.0 12.5

106 113 119 126 133 140

48 14 45 24 10 03

35.0 07.7 57.8 34.7 21.7 34.3

13.0 13.5 14.0 14.5 15.0 15.5

147 154 161 168 176 183

04 12 27 49 17 50

16.0 16.5 17.0 17.5 18.0 18.5

191 199 206 214 222 229

19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0

(X 10 3) 2.6995 2.7048 2.7092 2.7126 2.7148 2.7160

' 14 14 14 14 14 14

" 47.40 45.64 44.21 43.12 42.38 42.02

14.6 18.8 09.5 00.6 06.8 43.6

2.7159 2.7146 2.7119 2.7077 2.7021 2.6949

14 14 14 14 14 14

42.04 42.47 43.35 44.70 46.55 48.92

05 33 01 31 03 35

07.2 34.6 23.4 07.5 38.2 47.7

2.6861 2.6756 2.6635 2.6497 2.6344 2.6177

14 14 14 15 15 15

51.84 55.33 59.41 04.07 09.32 15.14

+2 2 3 3 3 4

07 37 06 32 57 18

13.4 31.2 15.2 58.2 11.5 25.8

2.5996 2.5804 2.5604 2.5398 2.5189 2.4982

15 15 15 15 15 15

21.50 28.34 35.61 43.20 51.01 58.90

18.5 28.9 47.4 41.8 26.3 01.6

+4 4 4 5 5 4

36 49 59 03 03 57

11.2 59.1 22.8 59.3 31.1 47.6

2.4780 2.4588 2.4410 2.4251 2.4115 2.4004

16 16 16 16 16 16

06.71 14.26 21.35 27.80 33.39 37.96

26 04 44 23 00 34

16.9 52.8 24.3 25.2 32.0 27.7

+4 4 4 3 3 2

46 30 09 43 14 41

46.2 34.0 27.2 51.4 19.8 32.0

2.3923 2.3874 2.3858 2.3875 2.3925 2.4007

16 16 16 16 16 16

41.33 43.40 44.07 43.35 41.25 37.86

237 244 251 258 266 273

04 28 46 58 03 02

04.5 26.7 51.2 47.8 59.3 19.6

+2 1 0 +0 -0 1

06 29 50 12 25 02

11.8 04.6 55.9 29.1 35.7 42.3

2.4117 2.4252 2.4409 2.4584 2.4773 2.4970

16 16 16 16 16 15

33.31 27.76 21.39 14.41 07.00 59.36

279 286 293 299 306

53 38 17 50 17

52.5 50.1 31.1 18.8 39.7

-1 2 2 3 -3

38 11 43 12 37

19.2 59.6 21.0 05.0 57.0

2.5172 2.5375 2.5576 2.5771 2.5957

15 15 15 15 15

51.66 44.04 36.64 29.55 22.87

61

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

24.0 24.5 25.0 25.5 26.0 26.5

º 306 312 318 325 331 337

' 17 40 57 11 22 29

" 39.7 02.7 57.1 52.5 17.6 39.7

º -3 4 4 4 4 4

' 37 00 20 36 49 58

" 57.0 45.3 21.1 37.9 31.2 58.2

27.0 27.5 28.0 28.5 29.0 29.5

343 349 355 1 7 13

34 36 37 36 34 31

24.7 56.2 36.1 44.1 38.1 34.2

-5 5 5 5 4 4

04 07 06 02 54 44

30.0 30.5 31.0 31.5 Nov. 1.0 1.5

19 25 31 37 43 49

27 23 18 14 09 05

47.0 30.1 56.3 17.7 46.9 36.6

-4 4 3 3 3 2

2.0 2.5 3.0 3.5 4.0 4.5

55 60 66 72 78 85

02 59 57 57 58 02

00.4 13.1 31.0 12.0 36.0 04.8

5.0 5.5 6.0 6.5 7.0 7.5

91 97 103 109 116 122

08 16 29 45 05 30

8.0 8.5 9.0 9.5 10.0 10.5

129 135 142 149 156 163

11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0

Oct.

(X 10 3) 2.5957 2.6133 2.6297 2.6448 2.6584 2.6705

' 15 15 15 15 15 14

" 22.87 16.65 10.94 05.76 01.12 57.03

57.9 30.5 37.9 23.2 51.1 07.4

2.6812 2.6903 2.6980 2.7043 2.7092 2.7128

14 14 14 14 14 14

53.47 50.43 47.89 45.83 44.22 43.04

30 13 54 32 07 41

19.8 37.0 09.4 08.7 47.9 21.5

2.7152 2.7164 2.7165 2.7155 2.7134 2.7102

14 14 14 14 14 14

42.27 41.88 41.85 42.18 42.86 43.88

-2 1 1 0 -0 +0

13 43 12 40 07 25

04.8 14.6 08.4 04.6 22.5 38.0

2.7061 2.7008 2.6945 2.6871 2.6785 2.6689

14 14 14 14 14 14

45.25 46.96 49.04 51.49 54.34 57.59

02.2 53.8 06.7 09.5 31.0 40.3

+0 1 2 2 3 3

58 31 03 33 02 30

36.2 10.9 00.1 41.2 51.1 05.7

2.6580 2.6459 2.6327 2.6183 2.6028 2.5863

15 15 15 15 15 15

01.26 05.37 09.92 14.92 20.36 26.22

01 37 19 07 02 04

05.2 11.6 22.0 54.2 59.8 42.4

+3 4 4 4 5 5

55 17 36 51 03 10

00.8 11.5 12.9 40.2 09.6 19.2

2.5690 2.5510 2.5325 2.5137 2.4951 2.4769

15 15 15 15 16 16

32.47 39.06 45.93 52.97 00.09 07.14

170 177 184 192 199 207

12 27 47 13 42 15

56.4 25.6 42.5 08.0 51.5 52.4

+5 5 5 4 4 4

12 10 02 50 32 10

49.6 25.4 56.4 18.9 37.0 03.0

2.4595 2.4433 2.4287 2.4160 2.4058 2.3982

16 16 16 16 16 16

13.99 20.45 26.35 31.51 35.74 38.89

214 222 230 237 245

51 27 02 36 08

02.1 06.1 47.4 50.1 01.7

+3 3 2 2 +1

42 11 37 00 21

58.1 51.9 21.6 10.2 04.7

2.3935 2.3920 2.3937 2.3986 2.4066

16 16 16 16 16

40.84 41.48 40.77 38.72 35.39

62

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Apparent Longitude

Date

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Nov. 16.0 16.5 17.0 17.5 18.0 18.5

º 245 252 259 267 274 281

' 08 35 57 14 24 28

" 01.7 16.8 38.7 21.4 49.9 40.9

º +1 0 +0 -0 1 1

' 21 40 00 39 18 55

" 04.7 53.9 26.0 33.0 21.5 22.6

19.0 19.5 20.0 20.5 21.0 21.5

288 295 301 308 315 321

25 15 59 36 06 31

41.7 49.8 11.7 01.0 38.0 27.3

-2 3 3 3 4 4

30 02 30 56 18 37

22.0 22.5 23.0 23.5 24.0 24.5

327 334 340 346 352 358

50 05 16 22 26 27

57.3 38.9 04.5 46.8 18.7 12.6

-4 5 5 5 5 5

25.0 25.5 26.0 26.5 27.0 27.5

4 10 16 22 28 34

25 23 19 14 09 04

59.5 09.2 09.7 27.2 26.1 28.6

28.0 28.5 29.0 29.5 30.0 30.5

39 45 51 57 63 69

59 56 53 51 51 53

1.0 1.5 2.0 2.5 3.0 3.5

75 82 88 94 100 106

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

Dec.

(X 10 3) 2.4066 2.4176 2.4312 2.4471 2.4650 2.4843

' 16 16 16 16 16 16

" 35.39 30.88 25.33 18.91 11.82 04.26

05.4 04.4 59.8 36.9 45.3 18.3

2.5047 2.5257 2.5468 2.5678 2.5881 2.6074

15 15 15 15 15 15

56.41 48.46 40.59 32.93 25.61 18.73

52 03 11 14 15 12

12.3 26.1 00.7 58.3 22.6 18.4

2.6256 2.6424 2.6575 2.6709 2.6824 2.6921

15 15 15 14 14 14

12.37 06.59 01.43 56.91 53.05 49.85

-5 4 4 4 4 3

05 56 43 27 08 47

51.1 07.5 14.8 21.6 37.3 12.5

2.6999 2.7058 2.7100 2.7124 2.7132 2.7126

14 14 14 14 14 14

47.28 45.33 43.97 43.18 42.90 43.12

55.2 04.4 13.2 37.0 29.8 05.0

-3 2 2 1 1 0

23 57 29 59 27 55

19.0 10.1 00.3 05.6 43.5 12.7

2.7105 2.7072 2.7028 2.6973 2.6910 2.6838

14 14 14 14 14 14

43.79 44.86 46.32 48.10 50.20 52.58

56 02 10 20 33 49

34.7 11.1 05.7 30.4 37.1 38.3

-0 +0 0 1 1 2

21 11 45 19 52 24

53.2 53.6 45.7 19.9 12.8 00.2

2.6759 2.6674 2.6582 2.6484 2.6380 2.6272

14 14 15 15 15 15

55.21 58.09 01.20 04.52 08.07 11.83

113 119 125 132 139 145

08 31 57 27 01 39

46.6 15.6 18.6 09.7 02.1 08.9

+2 3 3 4 4 4

54 22 48 12 32 49

18.1 42.3 49.0 15.0 37.7 35.7

2.6157 2.6038 2.5913 2.5783 2.5649 2.5511

15 15 15 15 15 15

15.82 20.02 24.45 29.10 33.96 39.01

152 159 166 172 179

21 08 00 57 58

41.4 49.3 39.2 14.0 32.0

+5 5 5 5 +5

02 11 16 17 12

48.9 58.9 49.8 08.4 44.9

2.5370 2.5228 2.5085 2.4943 2.4806

15 15 15 16 16

44.23 49.57 54.98 00.39 05.70

63

MOON, 2020 h h FOR 0 AND 12 TERRESTRIAL TIME Date

Apparent Longitude

Apparent Latitude

True Geocentric Distance (A. U.)

Semi Diameter

-

Dec.

9.0 9.5 10.0 10.5 11.0 11.5

º 179 187 194 201 208 216

' 58 04 14 29 46 07

" 32.0 26.0 42.5 00.9 53.6 45.5

º +5 5 4 4 4 3

' 12 03 49 30 07 40

" 44.9 33.8 34.6 52.4 38.6 11.3

12.0 12.5 13.0 13.5 14.0 14.5

223 230 238 245 253 260

30 55 20 45 09 30

54.9 33.9 49.9 46.8 27.5 55.5

+3 2 1 1 +0 -0

08 34 57 18 37 03

15.0 15.5 16.0 16.5 17.0 17.5

267 275 282 289 296 303

49 03 13 17 16 09

16.7 41.8 27.4 57.7 44.7 29.4

-0 1 2 2 3 3

18.0 18.5 19.0 19.5 20.0 20.5

309 316 323 329 336 342

56 36 10 38 01 18

01.3 18.2 25.5 35.7 07.4 24.2

21.0 21.5 22.0 22.5 23.0 23.5

348 354 0 6 12 18

30 39 43 45 43 40

24.0 24.5 25.0 25.5 26.0 26.5

24 30 36 42 48 54

27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0

3 (X 10 )

2.4806 2.4675 2.4554 2.4445 2.4351 2.4276

' 16 16 16 16 16 16

" 05.70 10.82 15.62 19.97 23.75 26.81

55.5 22.7 10.2 00.2 37.8 10.3

2.4221 2.4190 2.4184 2.4205 2.4252 2.4327

16 16 16 16 16 16

29.03 30.30 30.54 29.70 27.76 24.74

43 23 00 35 08 37

37.8 00.8 38.9 56.7 24.5 38.6

2.4427 2.4550 2.4695 2.4859 2.5037 2.5225

16 16 16 16 15 15

20.71 15.76 10.03 03.66 56.81 49.66

-4 4 4 4 5 5

03 25 43 57 07 14

21.1 19.7 26.7 39.1 57.0 23.2

2.5420 2.5618 2.5814 2.6006 2.6188 2.6359

15 15 15 15 15 15

42.37 35.09 27.98 21.16 14.74 08.81

53.8 07.3 38.1 01.1 52.1 47.4

-5 5 5 5 4 4

17 16 11 03 52 38

02.9 02.6 29.8 33.2 21.7 05.0

2.6515 2.6654 2.6775 2.6876 2.6957 2.7016

15 14 14 14 14 14

03.46 58.73 54.67 51.31 48.65 46.70

36 31 25 20 16 14

22.9 13.7 53.8 55.7 50.1 05.3

-4 4 3 3 2 2

20 00 38 13 46 17

53.2 56.8 27.0 36.0 36.7 43.3

2.7054 2.7072 2.7070 2.7049 2.7010 2.6956

14 14 14 14 14 14

45.45 44.87 44.95 45.64 46.90 48.69

60 66 72 78 84 90

13 14 18 24 34 47

07.4 20.0 03.6 36.0 11.9 03.0

-1 1 0 -0 +0 0

47 15 42 08 25 59

11.2 17.3 20.0 39.5 22.7 23.3

2.6887 2.6807 2.6716 2.6617 2.6511 2.6401

14 14 14 15 15 15

50.95 53.63 56.67 00.01 03.59 07.35

97 103 109 116 122

03 23 46 13 43

17.8 02.1 18.8 08.3 28.7

+1 2 2 3 +3

32 05 37 06 34

58.0 41.2 06.7 48.1 19.1

2.6288 2.6174 2.6060 2.5946 2.5834

15 15 15 15 15

11.25 15.23 19.25 23.27 27.26

64

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Jan.

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

0.0 0.5 1.0 1.5 2.0 2.5

h 22 22 23 23 0 0

m 30 53 16 38 00 22

s 44.46 55.73 38.29 57.59 59.58 50.52

º -14 12 9 7 5 -3

' 03 04 58 48 33 16

" 06.46 04.59 41.62 10.67 39.54 11.78

' 54 54 54 54 54 54

" 33.04 24.23 17.67 13.51 11.88 12.87

3.0 3.5 4.0 4.5 5.0 5.5

0 1 1 1 2 2

44 06 28 50 13 36

36.93 25.48 22.95 36.19 12.00 17.09

-0 +1 3 6 8 10

56 23 43 02 19 32

48.34 30.80 44.65 49.28 35.81 48.50

54 54 54 54 54 55

16.51 22.83 31.78 43.29 57.25 13.47

6.0 6.5 7.0 7.5 8.0 8.5

2 3 3 4 4 5

59 24 49 15 42 10

57.84 20.16 29.12 28.62 20.88 06.03

+12 14 16 18 19 21

41 42 36 19 50 07

03.07 45.44 11.08 25.47 25.85 04.70

55 55 56 56 56 57

31.76 51.84 13.39 36.04 59.38 22.95

9.0 9.5 10.0 10.5 11.0 11.5

5 6 6 7 7 8

38 08 38 08 39 09

41.63 02.45 00.46 25.20 04.56 45.83

+22 22 23 23 22 22

07 48 10 10 48 04

15.15 58.17 31.07 36.29 29.10 02.92

57 58 58 58 59 59

46.29 08.89 30.27 49.96 07.55 22.67

12.0 12.5 13.0 13.5 14.0 14.5

8 9 9 10 10 11

40 10 40 09 37 05

16.88 27.22 08.82 16.51 48.03 43.77

+20 19 17 15 13 10

57 31 45 43 26 58

51.09 04.98 28.82 12.40 42.94 37.35

59 59 59 59 59 59

35.05 44.51 50.95 54.40 54.96 52.82

15.0 15.5 16.0 16.5 17.0 17.5

11 12 12 12 13 13

33 00 26 52 18 44

06.35 00.07 30.50 43.93 47.04 46.50

+8 5 2 +0 -2 5

21 38 51 02 44 28

35.76 16.57 13.30 52.84 25.11 27.83

59 59 59 59 59 58

48.22 41.46 32.84 22.70 11.31 58.97

18.0 18.5 19.0 19.5 20.0 20.5

14 14 15 15 15 16

10 36 03 30 57 24

48.72 59.49 23.77 05.32 06.49 27.93

-8 10 13 15 17 18

07 38 00 11 09 52

08.94 27.73 28.78 22.02 23.60 57.50

58 58 58 58 57 57

45.90 32.32 18.37 04.17 49.82 35.36

21.0 21.5 22.0 22.5 23.0

16 17 17 18 18

52 20 48 16 44

08.46 04.97 12.53 24.69 33.95

-20 21 22 22 -23

20 31 23 57 12

37.96 12.51 45.21 39.71 41.45

57 57 56 56 56

20.83 06.26 51.67 37.07 22.51

65

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Jan.

Feb.

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

23.0 23.5 24.0 24.5 25.0 25.5

h 18 19 19 20 20 21

m 44 12 40 07 34 00

s 33.95 32.32 12.01 26.03 08.68 15.88

º -23 23 22 22 21 20

' 12 08 47 07 12 01

" 41.45 58.72 02.08 42.36 07.30 37.47

' 56 56 55 55 55 55

" 22.51 08.03 53.70 39.62 25.90 12.68

26.0 26.5 27.0 27.5 28.0 28.5

21 21 22 22 23 23

25 50 14 38 01 24

45.27 36.22 49.66 27.85 34.18 12.89

-18 17 15 13 11 9

37 01 15 20 18 10

41.90 53.92 47.57 54.91 44.02 37.97

55 54 54 54 54 54

00.12 48.38 37.66 28.15 20.04 13.52

29.0 29.5 30.0 30.5 31.0 31.5

23 0 0 0 1 1

46 08 30 51 13 35

28.90 27.64 14.91 56.80 39.59 29.74

-6 4 -2 +0 2 4

57 41 23 03 16 35

54.44 45.92 20.45 42.66 04.88 00.04

54 54 54 54 54 54

08.80 06.03 05.40 07.03 11.06 17.57

1.0 1.5 2.0 2.5 3.0 3.5

1 2 2 3 3 3

57 19 42 06 30 55

33.82 58.42 50.09 15.18 19.69 08.97

+6 9 11 13 15 17

51 05 15 19 17 05

59.49 56.84 40.85 53.71 09.53 53.32

54 54 54 55 55 55

26.64 38.29 52.51 09.25 28.39 49.77

4.0 4.5 5.0 5.5 6.0 6.5

4 4 5 5 6 6

20 47 14 42 12 41

47.41 17.99 41.87 57.92 02.42 48.87

+18 20 21 22 22 23

44 10 22 18 56 14

20.77 38.96 48.72 48.62 40.92 39.18

56 56 57 57 57 58

13.16 38.26 04.70 32.06 59.80 27.38

7.0 7.5 8.0 8.5 9.0 9.5

7 7 8 8 9 9

12 42 13 44 15 45

08.28 49.66 40.97 30.16 06.32 20.57

+23 22 21 20 19 17

11 45 57 46 14 22

16.91 36.19 14.81 30.79 23.41 30.55

58 59 59 60 60 60

54.16 19.51 42.77 03.32 20.61 34.16

10.0 10.5 11.0 11.5 12.0 12.5

10 10 11 11 12 12

15 44 13 41 08 36

06.60 20.94 02.76 13.55 56.64 16.70

+15 12 10 7 4 +1

13 48 12 26 35 40

03.12 37.37 06.56 32.88 00.33 29.22

60 60 60 60 60 60

43.64 48.85 49.74 46.42 39.16 28.33

13.0 13.5 14.0 14.5 15.0

13 13 13 14 14

03 30 56 23 50

19.23 10.10 55.23 40.16 29.79

-1 4 6 9 -12

14 06 53 32 02

07.93 08.88 03.06 32.02 29.40

60 59 59 59 58

14.38 57.84 39.26 19.17 58.08

66

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Feb.

Mar.

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

15.0 15.5 16.0 16.5 17.0 17.5

h 14 15 15 16 16 17

m 50 17 44 12 39 07

s 29.79 28.09 37.84 00.42 35.63 21.67

º -12 14 16 18 19 21

' 02 21 26 17 51 09

" 29.40 00.71 23.23 06.31 52.04 36.46

' 58 58 58 57 57 57

" 58.08 36.46 14.71 53.17 32.12 11.75

18.0 18.5 19.0 19.5 20.0 20.5

17 18 18 18 19 19

35 03 31 58 26 53

15.15 11.31 04.35 47.89 15.45 20.97

-22 22 23 23 23 22

09 51 14 18 04 33

31.02 04.04 01.98 29.99 51.67 47.86

56 56 56 55 55 55

52.23 33.66 16.09 59.56 44.07 29.61

21.0 21.5 22.0 22.5 23.0 23.5

20 20 21 21 22 22

19 46 11 36 01 24

59.27 06.33 39.53 37.64 00.82 50.46

-21 20 19 17 16 14

46 43 26 56 15 25

14.58 20.25 22.68 45.87 57.23 25.06

55 55 54 54 54 54

16.17 03.72 52.25 41.76 32.27 23.79

24.0 24.5 25.0 25.5 26.0 26.5

22 23 23 23 0 0

48 10 33 55 17 39

08.97 59.67 26.53 34.09 27.28 11.33

-12 10 8 5 3 -1

26 20 09 54 36 16

36.71 57.15 48.18 28.02 11.39 09.82

54 54 54 54 53 53

16.39 10.12 05.07 01.34 59.03 58.27

27.0 27.5 28.0 28.5 29.0 29.5

1 1 1 2 2 2

00 22 44 06 28 51

51.73 34.11 24.26 28.01 51.20 39.60

+1 3 5 7 10 12

04 24 43 58 10 17

27.67 33.75 01.68 44.17 32.10 13.19

53 54 54 54 54 54

59.19 01.91 06.56 13.26 22.12 33.23

1.0 1.5 2.0 2.5 3.0 3.5

3 3 4 4 4 5

14 38 03 28 54 21

58.77 53.91 29.64 49.71 56.71 51.66

+14 16 17 19 20 21

17 10 53 25 45 51

30.80 02.81 20.93 50.48 51.02 37.98

54 55 55 55 56 56

46.64 02.40 20.49 40.87 03.43 28.00

4.0 4.5 5.0 5.5 6.0 6.5

5 6 6 7 7 8

49 18 47 16 46 16

33.79 00.18 05.76 43.44 44.50 59.29

+22 23 23 23 22 21

41 13 26 18 49 58

25.63 31.39 21.41 37.16 22.24 08.57

56 57 57 58 58 59

54.34 22.14 50.98 20.40 49.80 18.57

7.0 7.5 8.0 8.5 9.0

8 9 9 10 10

47 17 47 17 46

18.03 31.67 32.65 15.42 36.65

+20 19 17 15 +12

45 10 16 04 36

01.30 41.35 25.72 05.18 00.12

59 60 60 60 61

45.98 11.31 33.83 52.83 07.71

67

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Mar.

Apr.

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

9.0 9.5 10.0 10.5 11.0 11.5

h 10 11 11 12 12 13

m 46 15 44 12 40 08

s 36.65 35.25 12.16 29.92 32.29 23.77

º +12 9 7 4 +1 -1

' 36 54 03 06 04 56

" 00.12 54.83 51.14 01.69 43.56 47.57

' 61 61 61 61 61 61

" 07.71 17.98 23.30 23.52 18.69 09.06

12.0 12.5 13.0 13.5 14.0 14.5

13 14 14 14 15 15

36 03 31 59 27 55

09.18 53.24 40.15 33.32 35.01 46.13

-4 7 10 13 15 17

55 48 32 04 24 28

22.43 02.19 01.68 51.64 20.50 35.60

60 60 60 59 59 59

55.01 37.10 15.96 52.27 26.73 00.03

15.0 15.5 16.0 16.5 17.0 17.5

16 16 17 17 18 18

24 52 21 49 17 45

06.06 32.61 02.12 29.68 49.51 55.40

-19 20 21 22 23 23

16 45 56 47 19 32

04.17 34.10 14.53 35.99 30.20 09.05

58 58 57 57 56 56

32.78 05.55 38.81 12.96 48.32 25.13

18.0 18.5 19.0 19.5 20.0 20.5

19 19 20 20 20 21

13 41 07 34 59 24

41.23 01.42 51.36 07.64 48.20 52.35

-23 23 22 21 20 18

26 01 20 24 12 48

03.00 58.71 56.23 05.91 45.31 16.44

56 55 55 55 54 54

03.55 43.69 25.62 09.33 54.83 42.07

21.0 21.5 22.0 22.5 23.0 23.5

21 22 22 22 23 23

49 13 36 59 22 44

20.65 14.79 37.39 31.84 02.11 12.59

-17 15 13 11 9 7

12 25 30 26 17 03

03.41 30.58 01.25 56.92 36.84 17.93

54 54 54 54 54 53

30.98 21.51 13.57 07.12 02.08 58.40

24.0 24.5 25.0 25.5 26.0 26.5

0 0 0 1 1 1

06 27 49 11 33 54

08.03 53.39 33.79 14.43 00.60 57.56

-4 2 -0 +2 4 6

45 24 02 19 40 58

15.02 41.16 48.14 12.95 11.04 54.40

53 53 53 53 53 54

56.06 55.03 55.32 56.93 59.92 04.31

27.0 27.5 28.0 28.5 29.0 29.5

2 2 3 3 3 4

17 39 02 26 50 15

10.52 44.56 44.54 14.96 19.79 02.30

+9 11 13 15 17 18

14 24 29 26 14 52

09.93 42.44 14.03 23.60 46.50 54.69

54 54 54 54 54 55

10.19 17.61 26.66 37.41 49.94 04.31

30.0 30.5 31.0 31.5 1.0

4 5 5 6 6

40 06 33 00 28

24.79 28.36 12.73 35.99 34.58

+20 21 22 23 +23

19 32 30 12 36

17.22 21.42 34.88 28.14 38.25

55 55 55 56 56

20.56 38.70 58.72 20.56 44.09

68

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Apr.

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

1.0 1.5 2.0 2.5 3.0 3.5

h 6 6 7 7 8 8

m 28 57 25 55 24 53

s 34.58 03.41 56.04 05.20 23.32 43.15

º +23 23 23 22 21 20

' 36 41 27 52 56 39

" 38.25 52.87 14.66 05.54 10.37 39.63

' 56 57 57 58 58 58

" 44.09 09.14 35.45 02.71 30.50 58.32

4.0 4.5 5.0 5.5 6.0 6.5

9 9 10 10 11 11

22 52 20 49 18 46

58.38 04.11 57.12 36.06 01.29 14.75

+19 17 14 12 9 6

03 07 55 27 45 54

10.96 49.48 06.99 00.33 48.93 11.84

59 59 60 60 60 61

25.60 51.70 15.93 37.59 55.97 10.43

7.0 7.5 8.0 8.5 9.0 9.5

12 12 13 13 14 14

14 42 10 38 06 35

19.62 19.94 20.29 25.28 39.19 05.54

+3 +0 -2 5 8 11

55 51 13 15 12 01

04.29 33.67 04.88 33.26 35.48 02.83

61 61 61 61 61 60

20.44 25.60 25.66 20.61 10.58 55.93

10.0 10.5 11.0 11.5 12.0 12.5

15 15 16 16 17 17

03 32 01 31 00 30

46.68 43.46 54.91 18.20 48.59 19.74

-13 16 18 19 21 22

37 00 07 54 23 30

58.95 44.63 02.23 59.39 11.88 45.31

60 60 59 59 58 58

37.14 14.84 49.72 22.51 53.94 24.72

13.0 13.5 14.0 14.5 15.0 15.5

17 18 18 19 19 20

59 28 57 25 53 20

44.15 53.77 40.69 57.80 39.26 40.89

-23 23 23 23 23 22

17 42 47 33 00 10

15.45 46.94 50.56 19.22 23.09 24.52

57 57 56 56 56 55

55.46 26.73 59.01 32.68 08.06 45.38

16.0 16.5 17.0 17.5 18.0 18.5

20 21 21 22 22 22

47 12 37 01 25 48

00.27 36.71 31.10 45.63 23.56 28.97

-21 19 18 16 14 12

04 45 13 30 38 37

53.20 21.98 23.69 28.81 04.17 32.41

55 55 54 54 54 54

24.80 06.42 50.29 36.41 24.76 15.26

19.0 19.5 20.0 20.5 21.0 21.5

23 23 23 0 0 1

11 33 55 17 38 00

06.49 21.17 18.33 03.41 41.95 19.50

-10 8 6 3 -1 +1

30 17 00 39 17 06

12.01 17.81 01.71 33.69 02.71 22.20

54 54 53 53 53 53

07.85 02.42 58.87 57.08 56.94 58.34

22.0 22.5 23.0 23.5 24.0

1 1 2 2 2

22 43 06 28 51

01.55 53.54 00.74 28.21 20.72

+3 5 8 10 +12

29 51 10 25 34

31.05 11.99 10.56 09.10 46.31

54 54 54 54 54

01.19 05.38 10.86 17.55 25.42

69

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Apr.

May

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

24.0 24.5 25.0 25.5 26.0 26.5

h 2 3 3 4 4 4

m 51 14 38 03 28 54

s 20.72 42.55 37.42 08.21 16.82 03.91

º +12 14 16 18 19 21

' 34 37 32 17 50 11

" 46.31 37.17 13.05 02.37 31.64 07.22

' 54 54 54 54 55 55

" 25.42 34.43 44.58 55.87 08.31 21.92

27.0 27.5 28.0 28.5 29.0 29.5

5 5 6 6 7 7

20 47 15 42 11 39

28.70 28.90 00.63 58.64 16.51 47.19

+22 23 23 23 23 23

17 07 40 55 51 27

17.56 36.11 44.69 36.98 21.99 26.97

55 55 56 56 56 57

36.72 52.73 09.95 28.37 47.93 08.56

30.0 30.5 1.0 1.5 2.0 2.5

8 8 9 9 10 10

08 36 05 33 01 29

23.50 58.73 27.16 44.53 48.22 37.40

+22 21 20 18 16 14

43 40 17 36 38 24

39.53 08.74 25.31 20.80 06.40 11.47

57 57 58 58 59 59

30.13 52.47 15.31 38.37 01.26 23.54

3.0 3.5 4.0 4.5 5.0 5.5

10 11 11 12 12 13

57 24 51 19 46 13

12.94 37.27 54.07 08.03 24.48 49.03

+11 9 6 3 +0 -2

56 16 27 30 30 32

22.14 40.07 21.43 55.94 05.74 16.13

59 60 60 60 60 60

44.71 04.23 21.54 36.05 47.26 54.68

6.0 6.5 7.0 7.5 8.0 8.5

13 14 14 15 15 16

41 09 37 06 35 05

27.22 24.07 43.64 28.57 39.64 15.40

-5 8 11 13 16 18

33 29 17 55 19 26

08.01 22.68 51.52 29.61 21.77 49.18

60 60 60 60 60 60

57.97 56.88 51.34 41.42 27.36 09.54

9.0 9.5 10.0 10.5 11.0 11.5

16 17 17 18 18 19

35 05 35 05 35 05

11.93 22.86 39.71 52.47 50.48 23.40

-20 21 22 23 23 23

15 43 50 35 57 57

36.08 55.94 36.22 01.06 11.28 41.58

59 59 58 58 58 57

48.47 24.72 58.94 31.78 03.90 35.90

12.0 12.5 13.0 13.5 14.0 14.5

19 20 20 20 21 21

34 02 30 56 22 47

22.07 39.20 09.79 51.22 43.11 47.00

-23 22 22 20 19 17

37 58 01 48 22 44

35.41 18.19 29.93 58.33 32.86 00.39

57 56 56 55 55 55

08.35 41.74 16.48 52.93 31.37 12.01

15.0 15.5 16.0 16.5 17.0

22 22 22 23 23

12 35 58 21 43

05.98 44.35 47.23 20.30 29.60

-15 13 11 9 -7

55 57 51 40 24

02.29 12.94 59.34 41.55 33.68

54 54 54 54 54

54.99 40.40 28.31 18.69 11.53

70

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Apparent Right Ascension

Date

May

June

Apparent Declination

Horizontal Parallax

17.0 17.5 18.0 18.5 19.0 19.5

h 23 0 0 0 1 1

m 43 05 27 48 10 31

s 29.60 21.36 01.85 37.40 14.24 58.52

º -7 5 2 -0 +2 4

' 24 04 42 18 05 29

" 33.68 45.29 22.84 31.36 44.01 16.52

' 54 54 54 54 54 54

" 11.53 06.75 04.26 03.95 05.68 09.30

20.0 20.5 21.0 21.5 22.0 22.5

1 2 2 3 3 3

53 16 38 02 25 50

56.21 13.06 54.51 05.51 50.41 12.69

+6 9 11 13 15 17

50 09 23 31 32 24

56.43 29.84 37.83 55.90 53.82 56.22

54 54 54 54 54 55

14.66 21.59 29.93 39.52 50.21 01.84

23.0 23.5 24.0 24.5 25.0 25.5

4 4 5 5 6 6

15 40 07 34 01 29

14.73 57.56 20.57 21.40 55.80 57.84

+19 20 21 22 23 23

06 35 50 50 33 57

23.67 34.76 48.92 30.10 11.04 37.81

55 55 55 55 56 56

14.28 27.42 41.15 55.38 10.06 25.12

26.0 26.5 27.0 27.5 28.0 28.5

6 7 7 8 8 9

58 26 55 24 52 20

20.16 54.52 32.48 06.05 28.36 34.21

+24 23 23 22 21 19

02 48 13 19 06 34

54.10 24.75 57.90 45.73 23.53 47.58

56 56 57 57 57 58

40.53 56.23 12.21 28.41 44.78 01.23

29.0 29.5 30.0 30.5 31.0 31.5

9 10 10 11 11 12

48 15 42 09 36 02

20.27 45.30 49.97 36.74 09.53 33.44

+17 15 13 10 8 5

46 42 24 54 14 26

12.22 06.76 12.63 21.13 31.99 52.56

58 58 58 59 59 59

17.67 33.94 49.87 05.23 19.75 33.12

1.0 1.5 2.0 2.5 3.0 3.5

12 12 13 13 14 14

28 55 21 48 15 43

54.41 18.90 53.60 45.01 59.14 41.00

+2 -0 3 6 9 11

33 22 20 15 05 49

37.70 50.17 00.89 16.79 53.59 02.27

59 59 60 60 60 60

45.00 55.05 02.89 08.20 10.66 10.03

4.0 4.5 5.0 5.5 6.0 6.5

15 15 16 16 17 17

11 40 09 39 09 40

54.19 40.37 58.81 46.06 55.82 19.21

-14 16 18 20 21 23

21 41 45 31 57 01

52.34 36.36 36.07 29.45 18.25 35.08

60 59 59 59 59 58

06.16 58.98 48.53 34.97 18.54 59.59

7.0 7.5 8.0 8.5 9.0

18 18 19 19 20

10 41 10 40 09

45.30 02.10 57.57 20.79 02.83

-23 24 23 23 -22

43 02 59 35 52

28.70 46.64 54.44 51.62 04.91

58 58 57 57 57

38.55 15.89 52.12 27.75 03.30

71

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

June

July

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

9.0 9.5 10.0 10.5 11.0 11.5

h 20 20 21 21 21 22

m 09 36 04 30 55 20

s 02.83 57.28 00.46 11.31 31.05 02.73

º -22 21 20 19 17 15

' 52 50 32 00 16 22

" 04.91 20.24 34.41 47.81 58.64 58.95

' 57 56 56 55 55 55

" 03.30 39.24 16.02 54.04 33.64 15.12

12.0 12.5 13.0 13.5 14.0 14.5

22 23 23 23 0 0

43 07 29 51 13 35

50.81 00.72 38.58 50.89 44.40 25.94

-13 11 8 6 4 -1

20 11 56 37 15 51

32.36 13.24 26.97 30.92 35.98 48.31

54 54 54 54 54 54

58.71 44.60 32.93 23.78 17.20 13.20

15.0 15.5 16.0 16.5 17.0 17.5

0 1 1 2 2 2

57 18 40 02 24 47

02.35 40.45 26.94 28.40 51.14 41.17

+0 2 5 7 9 12

32 57 20 41 58 10

48.76 12.73 20.06 04.34 14.66 34.26

54 54 54 54 54 54

11.75 12.78 16.19 21.85 29.62 39.30

18.0 18.5 19.0 19.5 20.0 20.5

3 3 3 4 4 5

11 35 59 25 51 18

03.98 04.37 46.15 11.88 22.46 16.89

+14 16 18 19 21 22

16 14 03 41 06 16

39.49 59.39 55.96 45.32 40.03 52.61

54 55 55 55 55 56

50.70 03.58 17.72 32.87 48.76 05.16

21.0 21.5 22.0 22.5 23.0 23.5

5 6 6 7 7 8

45 14 42 11 40 09

52.00 02.42 40.76 38.01 44.30 49.66

+23 23 24 23 23 22

10 46 03 59 35 50

40.22 30.30 06.47 34.20 25.19 39.84

56 56 56 57 57 57

21.80 38.45 54.90 10.96 26.47 41.28

24.0 24.5 25.0 25.5 26.0 26.5

8 9 9 10 10 10

38 07 35 03 30 57

44.95 22.54 36.89 24.81 45.41 39.98

+21 20 18 16 14 12

45 21 39 41 29 04

47.54 44.61 50.68 43.96 16.47 29.58

57 58 58 58 58 58

55.30 08.44 20.67 31.94 42.25 51.56

27.0 27.5 28.0 28.5 29.0 29.5

11 11 12 12 13 13

24 50 16 42 08 34

11.68 25.12 26.09 21.10 17.14 21.32

+9 6 3 +1 -1 4

29 46 57 05 48 40

30.62 30.46 42.17 20.55 17.71 53.51

58 59 59 59 59 59

59.87 07.15 13.35 18.41 22.25 24.76

30.0 30.5 1.0 1.5 2.0

14 14 14 15 15

00 27 54 22 50

40.55 21.21 28.71 07.13 18.69

-7 10 12 15 -17

30 13 48 12 24

04.89 26.92 32.21 52.58 01.90

59 59 59 59 59

25.83 25.31 23.09 19.05 13.08

72

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

July

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

1.0 1.5 2.0 2.5 3.0 3.5

h 14 15 15 16 16 17

m 54 22 50 19 48 17

s 28.71 07.13 18.69 03.36 18.48 58.61

º -12 15 17 19 20 22

' 48 12 24 19 57 16

" 32.21 52.58 01.90 40.42 40.39 12.65

' 59 59 59 59 58 58

" 23.09 19.05 13.08 05.14 55.20 43.30

4.0 4.5 5.0 5.5 6.0 6.5

17 18 18 19 19 20

47 17 47 17 46 15

55.71 59.55 58.61 41.03 55.74 33.36

-23 23 24 23 23 22

13 49 03 55 27 38

53.26 49.32 42.72 51.08 05.49 45.44

58 58 57 57 57 56

29.54 14.07 57.09 38.87 19.71 59.94

7.0 7.5 8.0 8.5 9.0 9.5

20 21 21 22 22 22

43 10 36 02 26 50

26.86 31.81 46.39 11.13 48.47 42.39

-21 20 18 16 14 12

32 10 34 46 47 41

31.86 19.41 09.14 02.27 55.63 38.61

56 56 56 55 55 55

39.93 20.02 00.59 41.97 24.50 08.48

10.0 10.5 11.0 11.5 12.0 12.5

23 23 23 0 0 1

13 36 58 20 42 04

57.95 41.01 57.91 55.31 40.03 18.97

-10 8 5 3 -1 +1

28 11 49 26 01 23

51.65 05.93 43.91 00.48 04.62 58.88

54 54 54 54 54 54

54.18 41.83 31.64 23.76 18.33 15.43

13.0 13.5 14.0 14.5 15.0 15.5

1 1 2 2 2 3

25 47 09 32 55 18

59.04 47.13 49.99 14.24 06.20 31.73

+3 6 8 10 12 14

48 10 29 44 54 56

07.37 18.42 27.83 27.75 05.01 59.76

54 54 54 54 54 54

15.11 17.39 22.25 29.61 39.39 51.44

16.0 16.5 17.0 17.5 18.0 18.5

3 4 4 4 5 5

42 07 32 59 26 54

36.08 23.53 57.10 18.14 26.02 17.79

+16 18 20 21 22 23

51 36 10 30 35 24

44.53 44.07 16.05 32.98 45.54 07.35

55 55 55 55 56 56

05.57 21.58 39.20 58.14 18.06 38.62

19.0 19.5 20.0 20.5 21.0 21.5

6 6 7 7 8 8

22 51 21 50 20 49

48.12 49.38 12.13 45.83 19.70 43.76

+23 24 23 23 22 21

54 04 53 21 27 13

01.01 04.91 20.00 15.46 52.45 45.27

56 57 57 57 58 58

59.43 20.10 40.25 59.50 17.49 33.93

22.0 22.5 23.0 23.5 24.0

9 9 10 10 11

18 47 15 43 10

49.59 31.01 44.30 28.26 43.98

+19 17 15 13 +10

39 48 40 18 44

59.72 09.28 09.77 13.35 42.88

58 59 59 59 59

48.55 01.15 11.60 19.83 25.84

73

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

24.0 24.5 25.0 25.5 26.0 26.5

h 11 11 12 12 12 13

m 10 37 04 30 56 22

s 43.98 34.50 04.39 19.37 25.89 30.77

º +10 8 5 +2 -0 3

' 44 02 12 19 35 29

" 42.88 06.96 56.21 40.63 11.89 16.22

' 59 59 59 59 59 59

" 25.84 29.68 31.47 31.33 29.42 25.92

27.0 27.5 28.0 28.5 29.0 29.5

13 14 14 15 15 16

48 15 41 08 36 04

40.88 02.82 42.55 45.06 13.96 11.11

-6 9 11 14 16 18

20 05 43 10 26 27

10.06 33.79 10.28 45.18 07.93 13.62

59 59 59 58 58 58

21.00 14.79 07.45 59.08 49.77 39.59

30.0 30.5 31.0 31.5 Aug. 1.0 1.5

16 17 17 18 18 18

32 01 30 00 29 58

36.26 26.78 37.66 01.61 29.57 51.43

-20 21 22 23 23 24

12 39 46 33 59 04

06.04 01.69 34.55 40.92 43.69 35.10

58 58 58 57 57 57

28.58 16.79 04.24 50.96 37.01 22.43

2.0 2.5 3.0 3.5 4.0 4.5

19 19 20 20 21 21

27 56 24 52 18 44

56.86 36.25 41.44 06.28 46.86 41.52

-23 23 22 21 19 17

48 12 18 06 39 58

37.40 41.16 01.43 12.33 01.02 21.66

57 56 56 56 56 55

07.31 51.75 35.88 19.86 03.85 48.07

5.0 5.5 6.0 6.5 7.0 7.5

22 22 22 23 23 0

09 34 58 21 43 06

50.63 16.32 02.08 12.44 52.70 08.66

-16 14 11 9 7 4

06 04 54 38 18 54

10.20 20.25 40.18 51.34 27.35 54.17

55 55 55 54 54 54

32.72 18.03 04.24 51.59 40.28 30.56

8.0 8.5 9.0 9.5 10.0 10.5

0 0 1 1 1 2

28 49 11 33 55 17

06.46 52.46 33.11 14.94 04.46 08.14

-2 -0 +2 4 7 9

29 03 21 45 07 24

30.72 30.00 59.48 52.19 03.79 29.46

54 54 54 54 54 54

22.62 16.65 12.81 11.26 12.10 15.43

11.0 11.5 12.0 12.5 13.0 13.5

2 3 3 3 4 4

39 02 25 49 14 39

32.31 23.07 46.13 46.65 28.93 56.15

+11 13 15 17 19 20

37 43 42 33 13 41

02.11 30.82 39.40 05.39 19.53 46.09

54 54 54 54 55 55

21.31 29.74 40.73 54.20 10.06 28.15

14.0 14.5 15.0 15.5 16.0

5 5 6 6 6

06 33 00 29 58

09.98 10.28 54.77 18.93 16.06

+21 22 23 24 +24

56 56 39 03 08

44.21 30.48 22.94 46.38 18.65

55 56 56 56 57

48.26 10.13 33.44 57.82 22.82

July

74

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

Aug. 16.0 16.5 17.0 17.5 18.0 18.5

h 6 7 7 8 8 9

m 58 27 57 26 56 25

s 16.06 37.62 13.87 54.69 30.43 52.81

º +24 23 23 22 20 19

' 08 51 14 14 54 13

" 18.65 57.28 05.66 37.79 00.88 15.52

' 57 57 58 58 58 59

" 22.82 47.98 12.76 36.63 59.05 19.48

19.0 19.5 20.0 20.5 21.0 21.5

9 10 10 11 11 12

54 23 51 19 47 14

55.48 34.41 47.95 36.65 03.03 11.07

+17 14 12 9 6 3

13 57 27 45 54 57

53.43 53.28 35.46 36.19 41.98 44.55

59 59 60 60 60 60

37.45 52.54 04.43 12.90 17.83 19.26

22.0 22.5 23.0 23.5 24.0 24.5

12 13 13 14 14 14

41 07 34 01 28 55

05.92 53.39 39.59 30.59 32.02 48.73

+0 -2 5 7 10 13

57 02 00 53 39 14

36.68 51.10 52.86 48.97 07.26 23.91

60 60 60 59 59 59

17.31 12.21 04.26 53.82 41.29 27.07

25.0 25.5 26.0 26.5 27.0 27.5

15 15 16 16 17 17

23 51 19 48 17 46

24.43 21.34 39.87 18.45 13.39 19.02

-15 17 19 21 22 23

37 46 38 13 28 24

24.45 05.04 34.26 15.45 49.58 18.21

59 58 58 58 58 57

11.55 55.08 37.99 20.56 03.02 45.54

28.0 28.5 29.0 29.5 30.0 30.5

18 18 19 19 20 20

15 44 13 41 09 37

28.05 32.07 22.27 50.17 48.28 10.66

-23 24 24 23 22 21

59 13 06 39 54 51

06.14 03.24 24.93 51.09 23.43 21.66

57 57 56 56 56 56

28.28 11.34 54.77 38.65 23.00 07.85

31.0 31.5 Sept. 1.0 1.5 2.0 2.5

21 21 21 22 22 23

03 29 55 19 43 07

53.18 53.63 11.62 48.39 46.51 09.61

-20 18 17 15 13 10

32 58 13 16 10 57

18.97 57.37 03.39 24.45 46.08 49.92

55 55 55 55 55 54

53.22 39.16 25.70 12.90 00.83 49.57

3.0 3.5 4.0 4.5 5.0 5.5

23 23 0 0 0 1

30 52 14 36 58 19

02.13 29.05 35.78 27.94 11.34 51.85

-8 6 3 -1 +1 3

39 16 50 23 03 29

12.57 25.06 52.84 56.16 09.19 11.01

54 54 54 54 54 54

39.24 29.94 21.82 15.00 09.65 05.90

6.0 6.5 7.0 7.5 8.0

1 2 2 2 3

41 03 25 48 10

35.37 27.75 34.78 02.07 54.97

+5 8 10 12 +14

52 13 29 39 43

59.54 26.32 22.92 39.71 04.66

54 54 54 54 54

03.92 03.84 05.81 09.95 16.36

75

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Sept.

Oct.

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

8.0 8.5 9.0 9.5 10.0 10.5

h 3 3 3 4 4 5

m 10 34 58 22 48 14

s 54.97 18.45 16.88 53.86 11.95 12.38

º +14 16 18 19 21 22

' 43 38 24 59 21 30

" 04.66 22.38 13.34 13.64 55.27 47.28

' 54 54 54 54 55 55

" 16.36 25.13 36.33 49.96 06.04 24.48

11.0 11.5 12.0 12.5 13.0 13.5

5 6 6 7 7 8

40 08 36 04 33 02

54.80 17.12 15.39 43.96 35.73 42.70

+23 24 24 24 23 23

24 00 19 18 56 14

17.80 57.13 21.78 19.31 53.43 29.03

55 56 56 56 57 57

45.19 08.00 32.67 58.90 26.30 54.43

14.0 14.5 15.0 15.5 16.0 16.5

8 9 9 9 10 10

31 01 30 59 27 56

56.59 09.57 14.90 07.47 44.06 03.45

+22 20 19 16 14 12

10 46 02 58 38 03

56.28 33.59 08.92 59.54 50.29 50.80

58 58 59 59 60 60

22.75 50.67 17.55 42.70 05.45 25.17

17.0 17.5 18.0 18.5 19.0 19.5

11 11 12 12 13 13

24 51 19 47 14 42

06.33 55.06 33.33 05.77 37.58 14.09

+9 6 3 +0 -2 6

16 19 16 09 57 01

31.79 40.95 18.51 32.73 24.57 22.23

60 60 61 61 61 60

41.26 53.28 00.88 03.89 02.30 56.28

20.0 20.5 21.0 21.5 22.0 22.5

14 14 15 15 16 16

10 38 06 34 03 33

00.39 00.87 18.85 56.18 52.93 07.13

-8 11 14 16 18 20

59 48 24 47 53 41

13.75 00.99 57.58 32.14 31.37 03.04

60 60 60 59 59 59

46.14 32.32 15.34 55.79 34.27 11.38

23.0 23.5 24.0 24.5 25.0 25.5

17 17 18 18 19 19

02 32 01 31 00 29

34.77 09.87 44.92 11.43 20.64 04.28

-22 23 24 24 24 24

08 15 00 23 25 07

38.78 16.36 21.29 47.18 54.68 28.98

58 58 57 57 57 56

47.66 23.62 59.69 36.23 13.55 51.85

26.0 26.5 27.0 27.5 28.0 28.5

19 20 20 21 21 22

57 24 51 17 43 07

15.20 47.84 38.53 45.46 08.64 49.60

-23 22 21 19 18 16

29 33 21 53 13 21

36.08 38.19 08.95 48.87 21.43 29.98

56 56 55 55 55 55

31.31 12.03 54.08 37.49 22.25 08.35

29.0 29.5 30.0 30.5 1.0

22 22 23 23 0

31 55 18 40 02

51.13 17.01 11.71 40.22 47.81

-14 12 9 7 -5

19 10 54 32 07

55.63 15.91 04.03 48.83 54.95

54 54 54 54 54

55.76 44.45 34.37 25.51 17.85

76

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Oct.

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

1.0 1.5 2.0 2.5 3.0 3.5

h 0 0 0 1 1 1

m 02 24 46 08 29 51

s 47.81 39.98 22.27 00.29 39.57 25.58

º -5 2 -0 +2 4 7

' 07 40 12 15 41 05

" 54.95 43.28 31.66 24.49 51.33 35.90

' 54 54 54 54 53 53

" 17.85 11.39 06.14 02.14 59.43 58.07

4.0 4.5 5.0 5.5 6.0 6.5

2 2 2 3 3 4

13 35 58 21 44 09

23.62 38.81 15.97 19.51 53.32 00.56

+9 11 13 15 17 19

25 40 48 49 40 21

25.29 05.99 23.20 00.35 38.80 57.84

53 53 54 54 54 54

58.15 59.75 02.98 07.93 14.71 23.41

7.0 7.5 8.0 8.5 9.0 9.5

4 4 5 5 6 6

33 59 25 51 18 46

43.53 03.39 00.06 32.04 36.36 08.70

+20 22 23 23 24 24

51 08 10 56 25 36

35.07 07.31 12.05 29.53 45.39 53.78

54 54 55 55 55 55

34.14 46.96 01.92 19.05 38.33 59.70

10.0 10.5 11.0 11.5 12.0 12.5

7 7 8 8 9 9

14 42 10 38 07 35

03.56 14.67 35.43 59.49 21.25 36.31

+24 24 23 22 20 18

29 01 13 06 38 52

00.68 27.09 51.94 14.25 54.63 36.01

56 56 57 57 58 58

23.04 48.17 14.84 42.73 11.40 40.36

13.0 13.5 14.0 14.5 15.0 15.5

10 10 10 11 11 12

03 31 59 26 54 21

41.76 36.38 20.62 56.48 27.29 57.44

+16 14 11 9 6 3

48 27 52 04 06 01

23.67 44.87 28.18 42.47 55.70 53.25

59 59 60 60 60 61

09.03 36.74 02.80 26.46 47.01 03.76

16.0 16.5 17.0 17.5 18.0 18.5

12 13 13 14 14 15

49 17 45 13 42 11

32.06 16.59 16.44 36.46 20.55 31.05

+0 -3 6 9 12 15

07 17 25 28 21 01

24.26 43.95 44.46 00.58 08.77 53.26

61 61 61 61 61 61

16.15 23.73 26.22 23.55 15.84 03.40

19.0 19.5 20.0 20.5 21.0 21.5

15 16 16 17 17 18

41 11 41 12 42 13

08.35 10.48 32.86 08.44 48.04 21.07

-17 19 21 22 23 24

27 34 21 46 48 26

12.70 26.78 22.73 20.67 17.55 48.68

60 60 60 59 59 58

46.69 26.31 02.94 37.30 10.11 42.06

22.0 22.5 23.0 23.5 24.0

18 19 19 20 20

43 13 42 10 38

36.47 23.71 33.68 59.36 36.14

-24 24 24 23 -22

42 34 06 18 12

06.73 58.00 36.61 37.41 48.53

58 57 57 56 56

13.77 45.80 18.62 52.61 28.07

77

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

24.0 24.5 25.0 25.5 26.0 26.5

h 20 21 21 21 22 22

m 38 05 31 56 20 44

s 36.14 21.85 16.55 22.21 42.23 21.14

º -22 20 19 17 15 13

' 12 51 15 27 29 22

" 48.53 04.71 21.72 32.43 24.25 37.93

' 56 56 55 55 55 54

" 28.07 05.24 44.27 25.24 08.22 53.19

27.0 27.5 28.0 28.5 29.0 29.5

23 23 23 0 0 0

07 29 52 13 35 57

24.19 57.10 05.88 56.60 35.36 08.20

-11 8 6 3 -1 +0

08 49 25 58 30 58

47.29 19.75 37.20 57.15 34.01 19.74

54 54 54 54 54 54

40.12 28.97 19.65 12.08 06.18 01.84

30.0 30.5 31.0 31.5 Nov. 1.0 1.5

1 1 2 2 2 3

18 40 02 24 46 09

41.01 19.52 09.24 15.39 42.82 35.90

+3 5 8 10 12 14

26 52 16 34 48 54

32.31 51.62 04.38 55.41 07.15 19.41

53 53 53 53 54 54

59.00 57.56 57.47 58.69 01.17 04.92

2.0 2.5 3.0 3.5 4.0 4.5

3 3 4 4 5 5

32 56 21 46 12 38

58.37 53.20 22.38 26.72 05.76 17.57

+16 18 20 21 22 23

52 40 17 41 51 46

09.49 12.65 03.02 14.98 25.09 14.48

54 54 54 54 54 54

09.94 16.24 23.87 32.87 43.31 55.24

5.0 5.5 6.0 6.5 7.0 7.5

6 6 6 7 7 8

04 32 59 27 54 22

58.82 04.84 29.94 07.74 51.71 35.68

+24 24 24 24 23 23

24 45 47 31 55 00

31.56 14.94 36.13 01.91 15.98 19.81

55 55 55 55 56 56

08.73 23.81 40.53 58.89 18.86 40.38

8.0 8.5 9.0 9.5 10.0 10.5

8 9 9 10 10 11

50 17 45 12 38 05

14.33 43.60 00.97 05.60 58.31 41.48

+21 20 18 16 13 11

46 14 25 19 58 25

32.66 30.96 07.30 29.42 59.36 13.06

57 57 57 58 58 59

03.33 27.53 52.72 18.59 44.72 10.63

11.0 11.5 12.0 12.5 13.0 13.5

11 11 12 12 13 13

32 58 25 52 19 47

18.87 55.40 36.84 29.59 40.26 15.34

+8 5 +2 -0 3 6

40 45 43 22 30 36

00.36 25.48 47.60 18.72 03.55 22.58

59 59 60 60 60 61

35.75 59.48 21.14 40.07 55.62 07.20

14.0 14.5 15.0 15.5 16.0

14 14 15 15 16

15 44 13 43 13

20.71 01.10 19.49 16.50 49.75

-9 12 15 17 -19

37 31 13 40 49

59.43 29.51 25.91 26.98 25.59

61 61 61 61 60

14.33 16.69 14.09 06.57 54.34

Oct.

78

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

Nov. 16.0 16.5 17.0 17.5 18.0 18.5

h 16 16 17 17 18 18

m 13 44 16 47 19 50

s 49.75 53.60 19.07 54.34 25.66 38.68

º -19 21 23 24 24 24

' 49 37 02 04 40 51

" 25.59 39.20 59.71 01.53 06.51 24.52

' 60 60 60 59 59 59

" 54.34 37.77 17.39 53.83 27.80 00.02

19.0 19.5 20.0 20.5 21.0 21.5

19 19 20 20 21 21

21 51 20 48 15 41

19.87 17.73 23.67 32.36 41.68 52.29

-24 24 23 21 20 18

38 03 08 54 25 41

49.48 51.58 27.16 48.09 12.13 55.32

58 58 57 57 56 56

31.21 02.04 33.12 04.99 38.11 12.86

22.0 22.5 23.0 23.5 24.0 24.5

22 22 22 23 23 0

07 31 55 18 40 02

07.13 30.80 09.05 08.37 35.60 37.79

-16 14 12 10 7 5

47 42 30 12 49 23

06.76 45.63 40.03 27.24 34.85 22.36

55 55 55 54 54 54

49.51 28.29 09.35 52.78 38.60 26.82

25.0 25.5 26.0 26.5 27.0 27.5

0 0 1 1 1 2

24 45 07 28 50 12

21.96 55.04 23.82 54.87 34.50 28.74

-2 -0 +2 4 6 9

55 25 03 31 56 18

03.16 46.49 20.67 11.80 39.20 32.70

54 54 54 54 54 54

17.39 10.23 05.25 02.33 01.34 02.14

28.0 28.5 29.0 29.5 30.0 30.5

2 2 3 3 4 4

34 57 20 44 08 33

43.21 23.04 32.74 15.96 35.34 32.23

+11 13 15 17 19 21

35 46 50 44 28 01

38.55 38.72 10.62 47.34 58.57 12.16

54 54 54 54 54 54

04.58 08.54 13.86 20.43 28.13 36.86

1.0 1.5 2.0 2.5 3.0 3.5

4 5 5 6 6 7

59 25 51 19 46 14

06.48 16.28 58.10 06.77 35.74 17.50

+22 23 24 24 24 24

19 23 11 41 52 45

56.48 43.50 12.40 13.47 51.89 30.83

54 54 55 55 55 55

46.53 57.10 08.50 20.71 33.73 47.55

4.0 4.5 5.0 5.5 6.0 6.5

7 8 8 9 9 9

42 09 37 04 31 58

04.21 48.30 23.09 43.31 45.46 27.92

+24 23 22 21 19 17

18 33 28 05 26 30

53.60 04.44 27.87 47.04 01.17 22.81

56 56 56 56 57 57

02.17 17.61 33.87 50.94 08.78 27.33

7.0 7.5 8.0 8.5 9.0

10 10 11 11 12

24 50 16 42 08

51.00 56.79 48.95 32.45 13.35

+15 12 10 7 +4

20 57 22 38 47

15.28 10.71 48.76 56.35 27.99

57 58 58 58 59

46.49 06.10 25.96 45.81 05.32

Dec.

79

MOON, 2020 FOR 0h AND 12h TERRESTRIAL TIME Date

Dec.

Apparent Right Ascension

Apparent Declination

Horizontal Parallax

9.0 9.5 10.0 10.5 11.0 11.5

h 12 12 12 13 13 14

m 08 33 59 26 52 20

s 13.35 58.50 55.26 11.27 54.04 10.58

º +4 +1 -1 4 7 10

' 47 50 09 11 10 05

" 27.99 26.86 53.89 09.76 43.88 46.87

' 59 59 59 59 60 60

" 05.32 24.11 41.73 57.72 11.59 22.82

12.0 12.5 13.0 13.5 14.0 14.5

14 15 15 16 16 17

48 16 46 16 47 18

06.88 47.28 13.82 25.51 17.78 42.26

-12 15 17 19 21 23

53 30 53 59 45 09

18.08 08.58 06.56 05.08 12.07 01.71

60 60 60 60 60 60

30.98 35.65 36.54 33.44 26.31 15.22

15.0 15.5 16.0 16.5 17.0 17.5

17 18 18 19 19 20

50 22 53 25 55 25

27.00 17.34 57.26 10.97 44.54 27.03

-24 24 24 24 23 22

08 43 52 37 58 58

45.48 21.18 37.60 13.93 33.81 35.30

60 59 59 58 58 58

00.42 42.26 21.21 57.82 32.69 06.43

18.0 18.5 19.0 19.5 20.0 20.5

20 21 21 22 22 23

54 21 48 14 38 02

11.15 53.33 33.29 13.53 58.57 54.34

-21 20 18 16 14 11

39 04 14 14 04 46

38.89 15.76 57.83 10.40 07.65 50.46

57 57 56 56 55 55

39.65 12.94 46.83 21.78 58.22 36.47

21.0 21.5 22.0 22.5 23.0 23.5

23 23 0 0 0 1

26 48 10 32 54 15

07.68 45.93 56.63 47.37 25.66 58.84

-9 6 4 -1 +0 3

24 57 28 58 32 01

06.12 29.29 23.78 04.70 19.16 42.97

55 54 54 54 54 54

16.81 59.45 44.55 32.20 22.44 15.28

24.0 24.5 25.0 25.5 26.0 26.5

1 1 2 2 3 3

37 59 21 43 06 29

34.06 18.19 17.83 39.16 27.85 48.90

+5 7 10 12 14 16

29 53 13 27 36 36

03.62 17.62 19.24 58.91 02.04 08.31

54 54 54 54 54 54

10.68 08.57 08.85 11.38 16.02 22.58

27.0 27.5 28.0 28.5 29.0 29.5

3 4 4 5 5 6

53 18 43 09 36 03

46.40 23.25 40.94 39.21 15.86 26.67

+18 20 21 22 23 24

26 06 34 47 44 25

51.58 40.55 00.41 15.53 53.08 27.66

54 54 54 55 55 55

30.89 40.72 51.87 04.13 17.27 31.10

30.0 30.5 31.0 31.5 32.0

6 6 7 7 8

31 59 27 55 23

05.47 04.51 14.98 27.71 33.98

+24 24 24 23 +23

47 50 34 57 01

46.27 53.29 14.71 40.87 27.48

55 56 56 56 56

45.41 00.02 14.78 29.54 44.20

80

MOON, 2020 AT EPHEMERIS TRANSIT Date

Age ( at 0h ) d

Ephemeris Transit

Geocentric Declination

Date

Age ( at 0h )

d 31 1 1 2 2 3

h 16 04 17 05 17 06

m 23.1 44.3 05.1 25.6 46.0 06.4

° -11 9 6 4 -2 +0

' 18.9 07.7 51.6 31.8 09.4 14.6

U L U L U L

3 4 4 5 5 6

18 06 19 07 19 08

26.9 47.6 08.6 30.1 52.3 15.2

+2 5 7 9 11 14

38.9 02.7 24.6 43.4 57.6 05.6

27 27 28 28 29 29

6 U 7 11.78 L 7 U 8 12.78 L 8 U 9 13.78 L

6 7 7 8 8 9

20 09 21 09 22 10

38.8 +16 03.4 17 29.0 19 55.6 20 23.0 22 51.4 22

05.4 55.1 32.5 54.9 00.2 45.8

30 30 31 31 Feb. 1 1

9 U 10 14.78 L 11 15.78 U 11 L 12 16.78 U 12 L

9 10 11 11 12 12

23 11 00 12 01 13

20.5 +23 50.1 23 20.0 22 49.9 22 19.6 20 48.8 19

13 17.78 U 13 L 14 18.78 U 14 L 15 19.78 U 15 L

13 13 14 14 15 15

02 14 03 15 04 16

16 20.78 U 16 L 17 21.78 U 17 L 18 22.78 U 18 L

16 16 17 17 18 18

19 23.78 U 19 L 20 24.78 U 20 L 21 25.78 U 21 L 22 26.78 U 22 L 23 27.78 U 23 L

Jan. 0 1 1 2 2 3

U 5.78 L U 6.78 L U 7.78 L

3 4 8.78 4 5 9.78 5 6 10.78

d Jan. 23 L 24 28.78 U 25 0.10 L 25 U 26 1.10 L 26 U

Ephemeris Transit

Geocentric Declination

d 23 24 25 25 26 26

h 23 11 00 12 01 13

m 27.8 54.0 19.7 44.6 08.9 32.5

° -22 22 21 19 18 16

' 48.4 08.1 10.4 56.8 29.0 48.8

2.10 L U 3.10 L U 4.10 L U

27 27 28 28 29 29

01 14 02 15 03 15

55.4 17.6 39.3 00.5 21.3 41.8

-14 12 10 8 6 3

57.9 58.1 50.9 37.7 20.1 59.3

5.10 L U 6.10 L U 7.10 L U

30 30 31 31 1 1

04 16 04 17 05 17

02.1 22.4 42.7 03.3 24.1 45.3

-1 +0 3 5 7 10

36.5 47.3 10.8 33.0 52.7 08.8

09.9 10.7 47.6 00.2 49.3 16.3

2 8.10 L 2 U 3 9.10 L 3 U 4 10.10 L 4 U

2 2 3 3 4 4

06 18 06 19 07 20

07.1 +12 29.6 14 52.8 16 16.9 18 42.0 19 08.0 21

19.8 24.3 20.6 07.0 41.2 01.2

17.6 +17 45.7 15 13.1 12 39.8 10 06.0 7 31.7 4

23.3 13.0 48.0 11.5 26.4 35.6

5 11.10 L 5 U 6 12.10 L 6 U 7 13.10 L 7 U

5 5 6 6 7 7

08 21 09 22 10 23

35.0 +22 02.9 22 31.7 23 01.1 23 30.9 22 01.0 22

04.6 49.1 12.6 13.3 50.0 02.1

04 17 05 18 06 19

57.0 22.0 46.8 11.7 36.7 01.8

+1 -1 4 6 9 12

41.8 12.2 04.0 51.2 31.5 02.9

8 9 9 10 10 11

14.10 L 15.10 U L 16.10 U L 17.10 U

8 9 9 10 10 11

11 00 12 00 13 01

31.1 +20 00.9 19 30.3 17 59.2 15 27.5 12 55.2 9

49.8 14.3 17.4 01.7 30.2 46.2

19 19 20 20 21 21

07 19 08 20 09 21

27.3 53.1 19.3 45.9 12.7 39.8

-14 16 18 19 21 22

23.2 30.5 22.8 58.6 16.4 15.0

11 L 12 18.10 U 12 L 13 19.10 U 13 L 14 20.10 U

11 12 12 13 13 14

14 02 15 03 16 04

22.3 48.9 15.1 41.0 06.7 32.4

+6 3 +0 -2 5 7

53.1 54.2 53.1 07.3 04.0 54.4

22 22 23 23

10 22 11 23

07.0 34.2 01.2 27.8

-22 23 23 -22

53.6 11.9 10.0 48.4

14 L 15 21.10 U 15 L 16 22.10 U

14 15 15 16

16 05 17 06

58.1 23.8 49.8 16.0

-10 13 15 -17

35.9 06.3 23.7 26.1

81

MOON, 2020 AT EPHEMERIS TRANSIT Date

Age ( at 0h )

Ephemeris Transit

Geocentric Declination

Date

Age ( at 0h )

Ephemeris Transit

Geocentric Declination

d Feb. 16 22.10 U 16 L 17 23.10 U 17 L 18 24.10 U 18 L

d 16 16 17 17 18 18

h 06 18 07 19 08 20

m 16.0 42.5 09.2 36.0 02.9 29.8

° -17 19 20 21 22 23

' 26.1 12.1 40.3 49.7 39.4 09.2

d Mar. 10 L 11 16.35 U 11 L 12 17.35 U 12 L 13 18.35 U

d 10 11 11 12 12 13

h 13 01 13 02 14 03

m 00.2 27.2 54.1 20.8 47.5 14.3

° +3 -0 2 5 8 11

' 51.0 42.7 25.3 29.7 27.0 14.5

19 25.10 U 19 L 20 26.10 U 20 L 21 27.10 U 21 L

19 19 20 20 21 21

08 21 09 22 10 23

56.6 23.1 49.2 14.8 39.9 04.3

-23 23 22 21 20 19

19.1 09.3 40.7 54.2 51.1 32.8

13 L 14 19.35 U 14 L 15 20.35 U 15 L 16 21.35 U

13 14 14 15 15 16

15 04 16 05 17 05

41.3 08.3 35.6 03.0 30.5 58.0

-13 16 18 19 21 22

49.2 09.0 11.8 56.0 20.4 24.2

22 28.10 U 22 L 23 29.10 U 24 0.35 L 24 U 25 1.35 L

22 22 23 24 24 25

11 23 12 00 12 01

28.2 51.3 13.9 35.8 57.3 18.4

-18 16 14 12 10 7

01.0 17.2 23.2 20.5 10.7 55.3

16 L 17 22.35 U 17 L 18 23.35 U 18 L 19 24.35 U

16 17 17 18 18 19

18 06 19 07 20 08

25.5 52.7 19.6 46.1 12.0 37.4

-23 23 23 23 22 21

07.1 29.1 30.6 12.5 35.7 41.6

25 26 26 27 27 28

U 2.35 L U 3.35 L U 4.35 L

25 26 26 27 27 28

13 01 14 02 15 03

39.1 59.5 19.8 40.1 00.4 20.9

-5 3 -0 +1 3 6

35.6 13.0 48.9 35.7 59.5 21.2

19 L 20 25.35 U 20 L 21 26.35 U 21 L 22 27.35 U

19 20 20 21 21 22

21 09 21 10 22 10

02.0 26.1 49.4 12.2 34.3 55.9

-20 19 17 15 13 11

31.7 07.4 30.3 42.1 44.2 38.2

28 29 29 Mar. 1 1 2

U 5.35 L U 6.35 L U 7.35 L

28 29 29 30 1 2

15 04 16 04 17 05

41.7 02.8 24.4 46.7 09.6 33.3

+8 10 13 15 16 18

39.8 53.9 02.2 03.3 55.7 37.6

22 L 23 28.35 U 23 L 24 29.35 U 25 0.61 L 25 U

22 23 23 24 25 25

23 11 23 12 00 12

17.1 37.9 58.4 18.8 39.0 59.3

-9 7 4 -2 +0 2

25.5 07.5 45.6 21.0 04.9 30.9

U L U L U L

2 3 3 4 4 5

17 06 18 07 19 08

57.8 +20 23.2 21 49.5 22 16.7 23 44.6 23 13.2 23

07.3 22.7 22.0 03.1 24.1 23.3

26 26 27 27 28 28

1.61 L U 2.61 L U 3.61 L U

26 26 27 27 28 28

01 13 02 14 02 15

19.7 40.2 01.1 22.4 44.2 06.5

+4 7 9 11 13 15

55.7 18.0 36.5 49.9 56.6 55.4

5 U 6 11.35 L 6 U 7 12.35 L 7 U 8 13.35 L

5 6 6 7 7 8

20 09 21 10 22 11

42.2 +22 11.6 22 41.1 21 10.6 19 39.8 17 08.7 15

59.6 12.1 00.8 26.4 30.1 14.1

29 29 30 30 31 31

4.61 L U 5.61 L U 6.61 L U

29 29 30 30 31 31

03 15 04 16 05 17

29.5 +17 53.2 19 17.6 20 42.8 21 08.7 22 35.4 23

44.5 22.2 47.0 57.1 50.6 26.0

8 U 9 14.35 L 10 15.35 U 10 L

8 9 10 10

23 12 00 13

37.2 +12 05.2 9 32.9 6 00.2 +3

40.9 53.7 55.9 51.0

Apr. 1 1 2 2

7.61 L U 8.61 L U

1 1 2 2

06 18 06 19

02.6 +23 30.3 23 58.5 23 26.8 +22

41.7 36.4 09.3 19.8

2 3 8.35 3 4 9.35 4 5 10.35

82

MOON, 2020 AT EPHEMERIS TRANSIT Date

Age ( at 0h )

Ephemeris Transit

d 7.61 L U 8.61 L U 9.61 L U

d 1 1 2 2 3 3

h 06 18 06 19 07 20

m ° 02.6 +23 30.3 23 58.5 23 26.8 22 55.3 21 23.7 19

' 41.7 36.4 09.3 19.8 07.9 34.2

Apr. 24 25 25 26 26 27

U 1.90 L U 2.90 L U 3.90 L

d 24 25 25 26 26 27

h 13 01 13 02 14 03

m ° 04.8 +14 27.5 16 50.9 18 14.9 20 39.7 21 05.1 22

' 48.3 45.5 32.2 06.7 27.1 31.8

4 10.61 L 4 U 5 11.61 L 5 U 6 12.61 L 6 U

4 4 5 5 6 6

08 21 09 22 10 23

51.9 +17 20.0 15 47.7 12 15.2 10 42.5 7 09.6 4

39.7 26.0 55.3 10.0 13.1 07.8

27 28 28 29 29 30

U 4.90 L U 5.90 L U 6.90 U

27 28 28 29 29 30

15 03 16 04 17 18

31.2 +23 57.8 23 24.9 23 52.3 23 20.0 23 15.2 20

19.1 47.7 56.3 44.0 10.4 59.4

13.61 L 14.61 U L 15.61 U L 16.61 U

7 8 8 9 9 10

11 00 12 00 13 01

36.6 03.6 30.7 58.0 25.5 53.3

+0 -2 5 8 11 14

57.6 14.0 23.2 26.5 20.3 01.4

May 1 1 2 2 3 3

7.90 L U 8.90 L U 9.90 L U

1 1 2 2 3 3

06 19 07 20 08 20

42.6 +19 09.8 17 36.7 15 03.4 12 29.8 10 56.1 7

23.1 27.7 14.9 46.4 04.4 11.4

10 L 11 17.61 U 11 L 12 18.61 U 12 L 13 19.61 U

10 11 11 12 12 13

14 02 15 03 16 04

21.4 49.7 18.2 46.9 15.5 43.9

-16 18 20 21 22 23

26.9 34.2 21.3 46.7 49.7 29.8

4 10.90 L 4 U 5 11.90 L 5 U 6 12.90 L 6 U

4 4 5 5 6 6

09 21 10 22 11 23

22.3 48.5 14.8 41.4 08.3 35.7

+4 +1 -2 5 8 11

10.1 03.3 05.6 13.6 16.9 12.3

13 L 14 20.61 U 14 L 15 21.61 U 15 L 16 22.61 U

13 14 14 15 15 16

17 05 18 06 18 07

12.0 39.6 06.6 32.9 58.5 23.2

-23 23 23 22 21 20

47.5 43.4 18.8 35.1 34.1 17.5

7 8 8 9 9 10

13.90 L 14.90 U L 15.90 U L 16.90 U

7 8 8 9 9 10

12 00 13 01 13 02

03.5 31.8 00.5 29.6 59.0 28.5

-13 16 18 20 21 23

56.2 25.3 36.7 27.7 56.5 01.6

16 L 17 23.61 U 17 L 18 24.61 U 18 L 19 25.61 U

16 17 17 18 18 19

19 08 20 08 21 09

47.2 10.4 33.0 54.9 16.3 37.2

-18 17 15 13 10 8

47.0 04.4 11.3 09.2 59.7 44.0

10 L 11 17.90 U 11 L 12 18.90 U 12 L 13 19.90 U

10 11 11 12 12 13

14 03 15 04 16 05

57.8 26.8 55.3 23.1 50.1 16.3

-23 23 23 23 22 21

42.6 59.5 53.4 25.4 37.5 31.5

19 L 20 26.61 U 20 L 21 27.61 U 21 L 22 28.61 U

19 20 20 21 21 22

21 10 22 10 23 11

57.8 18.2 38.4 58.6 18.9 39.4

-6 3 -1 +0 3 5

23.6 59.6 33.3 54.1 21.4 47.2

13 L 14 20.90 U 14 L 15 21.90 U 15 L 16 22.90 U

13 14 14 15 15 16

17 06 18 06 19 07

41.5 05.8 29.2 51.9 13.8 35.2

-20 18 16 14 12 10

09.6 33.9 46.3 48.6 42.6 29.6

23 29.61 L 23 U 24 0.90 L 24 U

23 23 24 24

00 12 00 13

00.1 +8 21.2 10 42.7 12 04.8 +14

10.2 29.0 42.3 48.3

16 L 17 23.90 U 17 L 18 24.90 U

16 17 17 18

19 08 20 08

56.1 16.7 37.0 57.2

-8 5 3 -0

11.1 48.4 22.7 55.1

Apr. 1 1 2 2 3 3

7 8 8 9 9 10

Geocentric Declination

Date

Age ( at 0h ) d

Ephemeris Transit

Geocentric Declination

83

MOON, 2020 AT EPHEMERIS TRANSIT Date

Age ( at 0h )

Ephemeris Transit

Geocentric Declination

Date

Age ( at 0h )

Ephemeris Transit

Geocentric Declination

d May 18 24.90 U 18 L 19 25.90 U 19 L 20 26.90 U 20 L

d 18 18 19 19 20 20

h 08 21 09 21 10 22

m 57.2 17.4 37.6 58.2 19.0 40.3

° -0 +1 4 6 8 11

' 55.1 33.2 01.0 27.2 50.3 09.0

d June 10 L 11 19.26 U 11 L 12 20.26 U 12 L 13 21.26 U

d 10 11 11 12 12 13

h 16 04 17 05 17 06

m 21.6 45.4 08.3 30.6 52.1 13.2

° -18 16 14 12 10 7

' 24.4 32.9 31.5 21.9 05.9 44.9

21 27.90 U 21 L 22 28.90 U 23 0.26 L 23 U 24 1.26 L

21 21 22 23 23 24

11 23 11 00 12 01

02.1 +13 24.5 15 47.6 17 11.4 19 35.9 20 01.3 21

21.9 27.1 23.1 07.9 39.7 56.5

13 L 14 22.26 U 14 L 15 23.26 U 15 L 16 24.26 U

13 14 14 15 15 16

18 06 19 07 19 08

33.8 54.1 14.4 34.5 54.8 15.4

-5 2 -0 +2 4 6

20.2 53.0 24.6 04.1 31.8 57.5

24 25 25 26 26 27

U 2.26 L U 3.26 L U 4.26 L

24 25 25 26 26 27

13 01 14 02 15 03

27.2 +22 53.9 23 20.9 24 48.4 24 16.0 23 43.7 22

56.6 38.3 00.2 01.3 41.0 59.2

16 L 17 25.26 U 17 L 18 26.26 U 18 L 19 27.26 U

16 17 17 18 18 19

20 08 21 09 22 10

36.3 57.6 19.5 42.1 05.4 29.6

+9 11 13 15 17 19

19.9 37.6 49.2 53.0 47.3 30.1

27 28 28 29 29 30

U 5.26 L U 6.26 L U 7.26 L

27 28 28 29 29 30

16 04 17 05 17 06

11.3 +21 38.6 20 05.6 18 32.2 16 58.4 14 24.3 12

56.3 33.1 50.7 50.8 35.1 05.6

19 L 20 28.26 U 20 L 21 29.26 U 22 0.72 L 22 U

19 20 20 21 22 22

22 11 23 12 00 13

54.5 +20 20.3 22 46.8 23 13.9 23 41.6 24 09.7 23

59.5 13.4 09.8 47.0 03.5 58.1

U L U L U L

30 31 31 1 1 2

18 07 19 08 20 08

49.8 15.2 40.4 05.7 31.1 56.8

+9 6 3 +0 -2 5

24.5 34.0 36.6 34.8 28.7 31.0

23 23 24 24 25 25

1.72 L U 2.72 L U 3.72 L U

23 23 24 24 25 25

01 14 02 15 03 15

37.9 +23 06.0 22 34.0 21 01.6 19 28.7 18 55.4 15

30.5 40.7 29.4 57.7 07.2 59.9

2 U 3 11.26 L 3 U 4 12.26 L 4 U 5 13.26 L

2 3 3 4 4 5

21 09 22 10 23 11

22.8 49.4 16.5 44.3 12.7 41.6

-8 11 14 16 18 20

29.2 20.1 00.6 27.6 38.0 29.0

26 26 27 27 28 28

4.72 L U 5.72 L U 6.72 L U

26 26 27 27 28 28

04 16 05 17 06 18

21.5 +13 47.2 11 12.5 8 37.5 5 02.3 +2 27.1 -0

38.0 03.8 19.6 28.0 31.3 28.0

6 14.26 U 6 L 7 15.26 U 7 L 8 16.26 U 8 L

6 6 7 7 8 8

00 12 01 13 02 14

10.9 40.5 10.1 39.5 08.5 36.9

-21 23 23 24 23 23

58.4 04.5 46.4 03.7 57.1 28.0

29 29 30 30 July 1 1

7.72 L U 8.72 L U 9.72 L U

29 29 30 30 1 1

06 19 07 20 08 21

52.0 17.0 42.5 08.3 34.8 01.8

-3 6 9 11 14 16

27.3 24.1 15.8 59.7 33.0 52.9

9 17.26 U 9 L 10 18.26 U 10 L

9 9 10 10

03 15 03 16

04.5 31.1 56.8 21.6

-22 21 20 -18

37.9 29.2 03.8 24.4

2 10.72 L 2 U 3 11.72 L 3 U

2 2 3 3

09 21 10 22

29.5 57.7 26.5 55.6

-18 20 22 -23

56.9 42.3 07.1 09.6

30 31 8.26 31 June 1 9.26 1 2 10.26

84

MOON, 2020 AT EPHEMERIS TRANSIT Date

Age ( at 0h )

d July 1 9.72 L 1 U 2 10.72 L 2 U 3 11.72 L 3 U

Ephemeris Transit

Geocentric Declination

Date

Age ( at 0h )

Geocentric Declination

d 1 1 2 2 3 3

h 08 21 09 21 10 22

m 34.8 01.8 29.5 57.7 26.5 55.6

° -14 16 18 20 22 23

' 33.0 52.9 56.9 42.3 07.1 09.6

July 24 25 25 26 26 27

U 4.27 L U 5.27 L U 6.27 L

d 24 25 25 26 26 27

h 15 03 16 04 17 05

m 34.3 59.6 24.6 49.6 14.6 39.7

° +7 4 +1 -1 4 7

' 12.4 15.6 15.5 45.4 44.5 39.0

12.72 L U 13.72 L 14.72 U L 15.72 U

4 4 5 6 6 7

11 23 12 00 13 01

24.8 53.9 22.8 51.1 18.7 45.5

-23 24 23 23 22 21

48.6 03.7 55.3 24.3 32.4 21.4

27 28 28 29 29 30

U 7.27 L U 8.27 L U 9.27 L

27 28 28 29 29 30

18 06 18 07 19 08

05.1 30.8 57.1 23.8 51.1 18.8

-10 13 15 17 19 21

26.6 04.7 30.8 42.6 37.8 14.3

7 L 8 16.72 U 8 L 9 17.72 U 9 L 10 18.72 U

7 8 8 9 9 10

14 02 15 03 15 04

11.4 36.3 00.3 23.5 45.9 07.7

-19 18 16 14 12 9

53.8 11.6 17.3 13.0 00.6 42.0

30 U 31 10.27 L 31 U Aug. 1 11.27 L 1 U 2 12.27 L

30 31 31 1 1 2

20 09 21 10 22 11

47.0 15.5 44.0 12.5 40.8 08.5

-22 23 23 24 23 23

30.4 24.7 56.4 05.2 51.4 15.9

10 L 11 19.72 U 11 L 12 20.72 U 12 L 13 21.72 U

10 11 11 12 12 13

16 04 17 05 17 06

28.9 49.6 10.1 30.3 50.6 10.9

-7 4 -2 +0 2 5

18.7 52.1 23.7 05.5 34.4 01.7

2 U 3 13.27 L 4 14.27 U 4 L 5 15.27 U 5 L

2 3 4 4 5 5

23 12 00 12 01 13

35.7 02.1 27.6 52.3 16.2 39.3

-22 21 19 17 15 13

20.2 06.0 35.4 50.6 53.7 46.9

13 L 14 22.72 U 14 L 15 23.72 U 15 L 16 24.72 U

13 14 14 15 15 16

18 06 19 07 19 08

31.4 52.2 13.6 35.4 58.0 21.3

+7 9 12 14 16 18

26.4 47.4 03.2 12.7 14.2 06.0

6 16.27 U 6 L 7 17.27 U 7 L 8 18.27 U 8 L

6 6 7 7 8 8

02 14 02 15 03 15

01.7 23.4 44.7 05.5 26.0 46.3

-11 9 6 4 -1 +0

32.1 11.2 45.9 17.6 47.8 42.3

16 L 17 25.72 U 17 L 18 26.72 U 18 L 19 27.72 U

16 17 17 18 18 19

20 09 21 10 22 10

45.4 +19 10.4 21 36.3 22 03.0 23 30.5 23 58.5 24

46.2 12.9 24.0 17.4 51.3 04.0

9 19.27 U 9 L 10 20.27 U 10 L 11 21.27 U 11 L

9 9 10 10 11 11

04 16 04 17 05 17

06.5 26.9 47.4 08.2 29.4 51.2

+3 5 8 10 12 14

11.5 38.6 02.4 21.9 35.7 42.6

19 L 20 28.72 U 21 0.27 L 21 U 22 1.27 L 22 U

19 20 21 21 22 22

23 11 00 12 01 13

26.9 +23 55.6 23 24.3 22 52.8 21 21.0 19 48.7 17

54.3 21.5 25.7 07.5 28.3 29.9

12 22.27 U 12 L 13 23.27 U 13 L 14 24.27 U 14 L

12 12 13 13 14 14

06 18 07 19 07 20

13.5 +16 36.7 18 00.6 20 25.4 21 51.0 22 17.4 23

41.1 29.7 06.5 29.8 37.6 28.0

23 23 24 24

23 23 24 24

02 14 03 15

15.8 +15 42.5 12 08.6 10 34.3 +7

14.4 44.5 02.9 12.4

15 25.27 U 15 L 16 26.27 U 16 L

15 15 16 16

08 21 09 22

44.6 +23 12.5 24 40.9 23 09.6 +23

59.0 09.1 56.7 21.3

4 4 5 6 6 7

2.27 L U 3.27 L U

d

Ephemeris Transit

85

MOON, 2020 AT EPHEMERIS TRANSIT Date

Age ( at 0h )

d Aug. 16 L 17 27.27 U 17 L 18 28.27 U 19 29.27 L 19 U

Ephemeris Transit

Geocentric Declination

Date

Age ( at 0h )

Ephemeris Transit

Geocentric Declination

d 16 17 17 18 19 19

h 22 10 23 11 00 12

m ° 09.6 +23 38.4 22 07.1 21 35.7 19 03.8 17 31.5 14

' 21.3 22.4 00.6 17.0 13.2 51.6

d Sept. 9 20.89 U 9 L 10 21.89 U 10 L 11 22.89 U 11 L

d 9 9 10 10 11 11

h 04 17 05 18 06 18

m ° 53.4 +19 17.1 20 41.6 21 06.8 23 32.8 23 59.5 24

' 04.3 37.3 56.4 00.0 46.5 14.0

20 20 21 21 22 22

0.89 L U 1.89 L U 2.89 L U

20 20 21 21 22 22

00 13 01 14 02 15

58.8 +12 25.5 9 51.9 6 17.9 3 43.8 +0 09.5 -2

14.8 25.7 27.5 23.4 16.5 50.0

12 23.89 U 12 L 13 24.89 U 13 L 14 25.89 U 14 L

12 12 13 13 14 14

07 19 08 20 09 21

26.8 +24 54.6 24 22.7 23 51.0 22 19.3 21 47.6 19

21.0 06.5 29.5 29.6 07.2 22.8

23 23 24 24 25 25

3.89 L U 4.89 L U 5.89 L U

23 23 24 24 25 25

03 16 04 16 05 17

35.2 01.0 27.0 53.4 20.1 47.2

-5 8 11 14 16 18

53.2 50.1 38.0 14.3 36.5 42.4

15 26.89 U 15 L 16 27.89 U 16 L 17 28.89 U 18 0.54 L

15 15 16 16 17 18

10 22 11 23 12 00

15.6 +17 43.3 14 10.7 12 37.8 9 04.6 6 31.2 +3

18.0 54.5 14.9 21.9 18.6 08.3

26 26 27 27 28 28

6.89 L U 7.89 L U 8.89 L U

26 26 27 27 28 28

06 18 07 19 08 20

14.7 42.5 10.7 38.9 07.1 35.1

-20 21 23 23 24 24

30.1 57.9 04.5 48.9 10.8 10.4

18 19 19 20 20 21

U 1.54 L U 2.54 L U 3.54 L

18 19 19 20 20 21

12 01 13 02 14 03

57.7 24.2 50.8 17.6 44.7 12.1

-0 3 6 9 12 15

05.5 19.1 29.2 32.3 25.0 04.5

29 9.89 L 29 U 30 10.89 L 30 U 31 11.89 L 31 U

29 29 30 30 31 31

09 21 09 22 10 23

02.7 29.8 56.3 22.0 47.0 11.2

-23 23 22 20 19 17

48.2 05.4 03.4 44.0 09.0 20.6

21 22 22 23 23 24

U 4.54 L U 5.54 L U 6.54 L

21 22 22 23 23 24

15 04 16 05 17 06

39.9 08.0 36.4 05.0 33.7 02.4

-17 19 21 22 23 24

27.8 32.7 17.1 39.5 38.9 14.9

12.89 L U 13.89 L 14.89 U L 15.89 U

1 1 2 3 3 4

11 23 12 00 13 01

34.6 57.3 19.3 40.9 01.9 22.6

-15 13 10 8 6 3

20.7 11.3 54.2 31.2 04.0 34.1

24 25 25 26 26 27

U 7.54 L U 8.54 L U 9.54 L

24 25 25 26 26 27

18 06 19 07 20 08

30.8 58.8 26.3 53.1 19.1 44.3

-24 24 23 22 21 20

27.6 17.6 46.2 54.8 45.1 18.9

4 L 5 16.89 U 5 L 6 17.89 U 6 L 7 18.89 U

4 5 5 6 6 7

13 02 14 02 15 03

43.0 03.3 23.6 43.9 04.5 25.3

-1 +1 3 6 8 11

02.9 28.3 58.1 25.3 48.8 07.2

27 U 28 10.54 L 28 U 29 11.54 L 29 U 30 12.54 L

27 28 28 29 29 30

21 09 21 10 22 11

08.7 32.3 55.2 17.4 39.1 00.2

-18 16 14 12 10 7

38.4 45.3 41.6 29.2 09.7 44.7

7 L 8 19.89 U 8 L 9 20.89 U

7 8 8 9

15 04 16 04

46.5 +13 08.2 15 30.5 17 53.4 +19

19.3 23.8 19.3 04.3

30 U Oct. 1 13.54 L 2 14.54 U 2 L

30 1 2 2

23 11 00 12

21.0 41.4 01.7 22.0

-5 2 -0 +2

15.8 44.5 12.2 19.9

Sept. 1 1 2 3 3 4

86

MOON, 2020 AT EPHEMERIS TRANSIT Date

Age ( at 0h )

Ephemeris Transit

Geocentric Declination

d 13.54 L 14.54 U L 15.54 U L 16.54 U

d 1 2 2 3 3 4

h 11 00 12 00 13 01

m 41.4 01.7 22.0 42.2 02.6 23.2

° -2 -0 +2 4 7 9

' 44.5 12.2 19.9 50.4 17.9 41.3

4 L 5 17.54 U 5 L 6 18.54 U 6 L 7 19.54 U

4 5 5 6 6 7

13 02 14 02 15 03

44.1 +11 05.4 14 27.2 16 49.6 18 12.6 19 36.3 21

7 L 8 20.54 U 8 L 9 21.54 U 9 L 10 22.54 U

7 8 8 9 9 10

16 04 16 05 17 06

10 L 11 23.54 U 11 L 12 24.54 U 12 L 13 25.54 U

10 11 11 12 12 13

13 L 14 26.54 U 14 L 15 27.54 U 15 L 16 28.54 U 17 17 18 18 19 19

Date

Age ( at 0h )

Geocentric Declination

U L U L U L

d 24 25 25 26 26 27

h 19 07 19 08 20 08

m 06.2 30.5 53.8 16.4 38.3 59.6

° -19 18 16 14 11 9

' 56.0 09.2 10.9 02.8 46.9 24.7

59.1 10.0 12.6 05.5 47.1 16.0

27 U 28 11.19 L 28 U 29 12.19 L 29 U 30 13.19 L

27 28 28 29 29 30

21 09 22 10 22 11

20.5 41.0 01.2 21.4 41.5 01.7

-6 4 -1 +0 3 5

57.8 27.4 55.1 38.0 10.4 41.1

00.6 +22 25.7 23 51.3 24 17.5 24 44.2 24 11.3 24

30.5 29.2 10.4 32.9 35.5 17.3

30 U 31 14.19 L Nov. 1 15.19 U 1 L 2 16.19 U 2 L

30 31 1 1 2 2

23 11 00 12 00 13

22.1 42.8 03.9 25.4 47.5 10.2

+8 10 12 14 16 18

08.6 31.7 48.8 58.6 59.6 50.2

18 07 19 08 20 08

38.6 +23 06.0 22 33.4 21 00.8 19 27.9 17 54.9 15

37.6 36.3 13.5 30.0 26.8 05.4

3 17.19 U 3 L 4 18.19 U 4 L 5 19.19 U 5 L

3 3 4 4 5 5

01 13 02 14 03 15

33.5 +20 57.5 21 22.0 23 47.2 23 12.9 24 39.1 24

28.7 53.7 03.5 56.6 31.8 47.9

13 14 14 15 15 16

21 09 22 10 23 11

21.7 +12 48.3 9 14.8 6 41.3 3 07.8 +0 34.6 -3

27.8 36.2 33.4 22.4 06.4 11.0

6 20.19 U 6 L 7 21.19 U 7 L 8 22.19 U 8 L

6 6 7 7 8 8

04 16 04 17 05 18

05.5 +24 32.2 24 58.9 23 25.6 22 52.2 21 18.5 19

44.1 19.8 34.8 29.3 03.8 19.1

0.19 L U 1.19 L U 2.19 L U

17 17 18 18 19 19

00 12 00 13 01 14

01.6 28.9 56.8 25.0 53.9 23.1

-6 9 12 15 17 19

26.1 35.1 34.3 19.9 48.6 57.3

9 23.19 U 9 L 10 24.19 U 10 L 11 25.19 U 11 L

9 9 10 10 11 11

06 19 07 20 08 20

44.7 +17 10.5 14 36.2 12 01.8 9 27.3 6 52.9 3

16.4 57.2 23.0 35.8 37.8 31.5

20 20 21 21 22 22

3.19 L U 4.19 L U 5.19 L U

20 20 21 21 22 22

02 15 03 16 04 17

52.7 22.5 52.4 22.0 51.3 20.0

-21 23 24 24 24 24

43.8 06.1 03.3 35.1 41.9 24.9

12 26.19 U 12 L 13 27.19 U 13 L 14 28.19 U 14 L

12 12 13 13 14 14

09 21 10 22 11 23

18.6 44.7 11.2 38.2 05.8 34.2

+0 -2 6 9 12 15

19.6 54.8 08.4 17.7 18.8 07.9

23 23 24 24

6.19 L U 7.19 L U

23 23 24 24

05 18 06 19

47.9 15.0 41.1 06.2

-23 22 21 -19

45.8 46.5 29.1 56.0

15 29.19 U 16 0.79 L 16 U 17 1.79 L

15 16 16 17

12 00 13 01

03.3 33.1 03.3 34.1

-17 19 21 -23

41.0 54.9 46.1 12.4

Oct. 1 2 2 3 3 4

d Oct. 24 25 8.19 25 26 9.19 26 27 10.19

Ephemeris Transit

87

MOON, 2020 AT EPHEMERIS TRANSIT Date

Age ( at 0h )

Ephemeris Transit

Geocentric Declination

Date

Age ( at 0h )

Ephemeris Transit

Geocentric Declination

Nov. 17 17 18 18 19 19

d 1.79 L U 2.79 L U 3.79 L U

d 17 17 18 18 19 19

h 01 14 02 15 03 16

m 34.1 04.9 35.7 06.0 35.7 04.6

° -23 24 24 24 24 23

' 12.4 12.1 44.6 50.4 30.6 47.3

d Dec. 10 24.79 U 10 L 11 25.79 U 11 L 12 26.79 U 12 L

d 10 10 11 11 12 12

h 07 20 08 21 09 22

m 59.4 24.9 50.9 17.7 45.2 13.6

° -3 6 9 12 15 17

' 10.6 17.4 20.4 16.3 01.7 33.0

20 20 21 21 22 22

4.79 L U 5.79 L U 6.79 L U

20 20 21 21 22 22

04 16 05 17 06 18

32.5 59.3 24.9 49.5 13.1 35.8

-22 21 19 17 15 13

42.6 19.4 40.2 47.5 43.7 31.0

13 27.79 U 13 L 14 28.79 U 15 0.32 L 15 U 16 1.32 L

13 13 14 15 15 16

10 23 11 00 12 01

42.8 12.9 43.5 14.5 45.6 16.6

-19 21 23 24 24 24

46.4 38.9 07.3 09.7 44.7 52.2

23 23 24 24 25 25

7.79 L U 8.79 L U 9.79 L U

23 23 24 24 25 25

06 19 07 20 08 20

57.8 19.1 39.8 00.3 20.4 40.5

-11 8 6 3 -1 +1

11.1 45.8 16.5 44.6 11.3 22.1

16 17 17 18 18 19

U 2.32 L U 3.32 L U 4.32 L

16 17 17 18 18 19

13 02 14 03 15 04

47.0 16.6 45.3 12.8 39.3 04.5

-24 23 22 21 19 17

33.0 48.8 42.1 15.6 32.4 35.1

26 10.79 L 26 U 27 11.79 L 27 U 28 12.79 L 28 U

26 26 27 27 28 28

09 21 09 22 10 22

00.6 20.8 41.2 02.0 23.2 45.0

+3 6 8 11 13 15

54.5 24.8 51.5 13.6 29.4 37.7

19 20 20 21 21 22

U 5.32 L U 6.32 L U 7.32 L

19 20 20 21 21 22

16 04 17 05 17 06

28.7 51.9 14.2 35.8 56.8 17.4

-15 13 10 8 5 3

26.6 09.2 45.1 16.1 43.8 09.7

13.79 L U 14.79 L 15.79 U L 16.79 U

29 29 30 1 1 2

11 23 11 00 12 01

07.3 +17 30.4 19 54.1 21 18.5 22 43.6 23 09.2 24

36.7 24.9 00.5 21.8 27.0 14.9

22 23 8.32 23 24 9.32 24 25 10.32

U L U L U L

22 23 23 24 24 25

18 06 19 07 19 08

37.7 57.9 18.0 38.2 58.7 19.6

-0 +1 4 7 9 11

34.9 59.2 31.7 01.3 26.9 47.4

2 L 3 17.79 U 3 L 4 18.79 U 4 L 5 19.79 U

2 3 3 4 4 5

13 02 14 02 15 03

35.3 +24 01.8 24 28.5 24 55.3 24 21.9 23 48.4 22

43.8 53.0 41.6 09.5 16.8 04.2

25 U 26 11.32 L 26 U 27 12.32 L 27 U 28 13.32 L

25 26 26 27 27 28

20 09 21 09 22 10

40.9 +14 02.8 16 25.3 18 48.5 19 12.5 21 37.2 22

01.4 07.4 03.9 49.3 21.8 39.6

5 L 6 20.79 U 6 L 7 21.79 U 7 L 8 22.79 U

5 6 6 7 7 8

16 04 17 05 17 06

14.6 +20 40.5 18 05.9 16 31.1 14 55.9 11 20.6 8

32.4 42.8 36.8 16.0 42.2 57.3

28 U 29 14.32 L 29 U 30 15.32 L 31 16.32 U 31 L

28 29 29 30 31 31

23 11 23 12 00 13

02.6 +23 28.7 24 55.4 24 22.3 24 49.5 24 16.7 23

40.9 24.0 47.7 50.7 32.4 52.6

8 L 9 23.79 U 9 L 10 24.79 U

8 9 9 10

18 07 19 07

45.1 09.7 34.4 59.4

03.3 02.4 03.1 10.6

32 17.32 U 32 L 33 18.32 U 33 L

32 32 33 33

01 14 02 15

43.8 +22 10.6 21 37.1 19 03.1 +17

51.8 30.7 50.5 52.9

29 29 30 Dec. 1 1 2

+6 +3 -0 -3

88

MOON, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date 0h TT

Jan.

The Earth's Selenographic Long. Lat. ° °

The Sun's Selenographic Colong. Lat. ° °

Position Angle of Fraction Axis Bright Illuminated Limb ° °

0 1 2 3 4 5

+1.968 +0.773 -0.495 1.767 2.970 4.031

+5.711 6.382 6.777 6.884 6.697 6.215

323.26 335.43 347.61 359.77 11.93 24.08

-0.04 0.06 0.07 0.09 0.10 0.12

337 336 336 337 339 341

251 249 248 247 247 249

0.216 0.299 0.389 0.483 0.577 0.670

6 7 8 9 10 11

-4.879 5.455 5.709 5.614 5.164 4 383 4.383

5.444 4.398 3.106 +1.615 -0.002 1 654 1.654

36.22 48.36 60.50 72.63 84.75 96 88 96.88

-0.14 0.16 0.19 0.22 0.25 0 29 0.29

345 349 354 359 5 11

251 254 259 265 274 72

0.759 0.839 0.908 0.960 0.992 0 999 0.999

12 13 14 15 16 17

-3.320 2.055 -0.680 +0.701 1.997 3.131

-3.230 4.617 5.711 6.434 6.740 6.621

109.00 121.13 133.26 145.40 157.54 169.69

-0.32 0.36 0.40 0.44 0.48 0.51

16 20 23 24 23 22

96 103 107 110 111 111

0.981 0.936 0.867 0.778 0.674 0.563

18 19 20 21 22 23

+4.050 4.728 5.156 5.341 5.297 5.039

-6.101 5.229 4.072 2.706 -1.215 +0.316

181.84 194.01 206.18 218.36 230.54 242.72

-0.55 0.59 0.62 0.65 0.69 0.72

19 15 10 5 360 354

110 108 104 99 93 85

0.449 0.341 0.241 0.155 0.087 0.037

24 25 26 27 28 29

+4.582 3.940 3.126 2.157 +1.052 -0 157 -0.157

+1.810 3.194 4.407 5.402 6.145 6 614 6.614

254.91 267.10 279.30 291.49 303.67 315 86 315.86

-0.74 0.77 0.79 0.81 0.82 0 84 0.84

349 344 341 338 337 336

73 321 267 258 254 251

0.008 0.001 0.013 0.043 0.091 0 152 0.152

30 31 Feb. 1 2 3 4

-1.433 2.723 3.966 5.091 6.021 6.677

+6.797 6.692 6.300 5.630 4.697 3.524

328.04 340.21 352.38 04.55 16.71 28.86

-0.85 0.86 0.87 0.89 0.90 0.91

337 338 340 343 347 352

250 250 251 252 255 259

0.226 0.309 0.399 0.495 0.592 0.688

5 6 7 8 9 10

-6.985 6.882 6 332 6.332 5.335 3.937 2.236

+2.143 +0.609 -1.005 1 005 2.603 4.069 5.285

41.01 53.15 65 28 65.28 77.41 89.54 101.67

-0.93 0.95 0 97 0.97 0.99 1.02 1.04

357 3 9 14 19 22

264 271 278 289 323 88

0.779 0.861 0 928 0.928 0.976 0.998 0.992

11 12 13 14 15

-0.374 +1.487 3.187 4.601 +5.650

-6.144 6.577 6.558 6.110 -5.288

113.81 125.94 138.08 150.22 162.38

-1.07 1.10 1.13 1.15 -1.18

24 24 22 20 16

102 107 109 108 106

0.957 0.895 0.812 0.713 0.604

89

MOON, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date 0h TT

The Earth's Selenographic Long. Lat. ° °

The Sun's Selenographic Colong. Lat. ° °

Position Angle of Fraction Axis Bright Illuminated Limb ° °

Feb. 15 16 17 18 19 20

+5.650 6.308 6.586 6.524 6.177 5.598

-5.288 4.172 2.847 -1.399 +0.092 1.552

162.38 174.54 186.71 198.88 211.06 223.25

-1.18 1.21 1.23 1.26 1.28 1.31

16 12 6 1 355 350

106 103 98 93 87 80

0.604 0.493 0.386 0.286 0.197 0.123

21 22 23 24 25 26

+4.836 3.932 2.913 1.801 +0.612 -0.638 0 638

+2.917 4.128 5.139 5.911 6.417 6 643 6.643

235.45 247.64 259.84 272.04 284.24 296 44 296.44

-1.33 1.35 1.37 1.38 1.39 1 40 1.40

345 342 339 337 336 336

73 64 41 297 264 257

0.066 0.026 0.005 0.003 0.019 0 052 0.052

27 28 29 Mar. 1 2 3

-1.926 3.221 4.480 5.645 6.646 7.401

+6.584 6.243 5.633 4.772 3.684 2.404

308.64 320.83 333.02 345.21 357.39 9.56

-1.40 1.41 1.41 1.41 1.41 1.41

338 340 342 346 350 355

254 253 254 256 259 264

0.101 0.164 0.239 0.325 0.419 0.518

4 5 6 7 8 9

-7.827 7.841 7.378 6.407 4.947 3.081

+0.973 -0.551 2.092 3.555 4.830 5.803

21.73 33.89 46.05 58.20 70.34 82.48

-1.41 1.42 1.42 1.43 1.44 1.44

0 6 12 17 21 23

269 275 282 289 298 315

0.620 0.720 0.813 0.893 0.954 0.990

10 11 12 13 14 15

-0.957 +1.231 3.276 5.005 6.301 7 115 7.115

-6.376 6.491 6.142 5.376 4.278 2 948 2.948

94.63 106.77 118.91 131.06 143.22 155 38 155.38

-1.45 1.46 1.47 1.48 1.49 1 50 1.50

24 23 21 17 13 8

61 98 104 104 102 99

0.997 0.974 0.922 0.846 0.754 0 651 0.651

16 17 18 19 20 21

+7.453 7.365 6.921 6.197 5.266 4.191

-1.489 +0.010 1.470 2.828 4.033 5.039

167.56 179.73 191.92 204.11 216.31 228.52

-1.52 1.53 1.54 1.55 1.57 1.58

2 357 351 346 342 339

94 88 82 77 71 65

0.544 0.438 0.338 0.247 0.168 0.103

22 23 24 25 26 27

+3.022 1.793 +0 530 +0.530 -0.749 2.028 3.287

+5.814 6.331 6 572 6.572 6.530 6.207 5.615

240.73 252.94 265 15 265.15 277.37 289.59 301.80

-1.58 1.59 1 59 1.59 1.59 1.59 1.58

337 336 336 337 339 342

59 50 17 284 263 259

0.053 0.019 0 003 0.003 0.005 0.025 0.062

28 29 30 31 Apr. 1

-4.499 5.622 6.602 7.372 -7.854

4.775 3.716 2.475 +1.096 -0.367

314.01 326.22 338.42 350.62 2.82

-1.57 1.56 1.55 1.54 -1.53

345 349 354 359 4

258 260 263 268 273

0.115 0.183 0.264 0.356 0.456

90

MOON, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date 0h TT

Apr.

May

The Earth's Selenographic Long. Lat. ° °

The Sun's Selenographic Colong. Lat. ° °

Position Angle of Fraction Axis Bright Illuminated Limb ° °

1 2 3 4 5 6

-7.854 7 968 7.968 7.643 6.830 5.524 3.779

-0.367 1 850 1.850 3.275 4.551 5.578 6.257

2.82 15.00 15 00 27.18 39.36 51.52 63.69

-1.53 1 51 1.51 1.50 1.49 1.48 1.47

4 10 15 19 22 24

273 279 284 290 296 301

0.456 0 562 0.562 0.668 0.769 0.859 0.931

7 8 9 10 11 12

-1.717 +0.485 2.621 4.498 5.971 6 961 6.961

-6.509 6.294 5.627 4.572 3.234 1 728 1.728

75.85 88.00 100.16 112.32 124.49 136 66 136.66

-1.45 1.44 1.44 1.43 1.42 1 41 1.41

24 22 19 15 10 4

311 5 91 99 98 95

0.979 0.998 0.986 0.946 0.880 0 797 0.797

13 14 15 16 17 18

+7.450 7.472 7.088 6.377 5.421 4.295

-0.166 +1.358 2.769 4.012 5.046 5.842

148.84 161.02 173.21 185.41 197.62 209.83

-1.41 1.41 1.40 1.40 1.40 1.40

358 353 348 343 340 338

90 85 79 74 69 66

0.701 0.599 0.497 0.397 0.304 0.220

19 20 21 22 23 24

+3.065 1.783 +0.490 -0.784 2.017 3.187

+6.376 6.634 6.609 6.300 5.717 4.880

222.05 234.27 246.50 258.73 270.96 283.19

-1.40 1.40 1.39 1.38 1.37 1.36

337 336 337 339 341 344

62 59 55 47 355 273

0.147 0.087 0.042 0.013 0.002 0.009

25 26 27 28 29 30

-4.276 5.253 6.084 6.722 7.111 7 192 7.192

3.818 2.572 +1.189 -0.272 1.748 3 164 3.164

295.42 307.65 319.88 332.10 344.32 356 53 356.53

-1.34 1.32 1.30 1.27 1.25 1 22 1.22

348 352 358 3 8 14

264 264 267 271 276 282

0.034 0.078 0.139 0.216 0.307 0 408 0.408

1 2 3 4 5 6

-6.910 6.224 5.126 3.650 -1.883 +0.040

-4.442 5.496 6.241 6.600 6.521 5.990

8.74 20.93 33.13 45.31 57.49 69.67

-1.20 1.17 1.15 1.12 1.09 1.07

18 21 23 24 23 21

287 291 295 298 300 303

0.517 0.627 0.734 0.831 0.911 0.967

7 8 9 10 11 12

+1.956 3.699 5 130 5.130 6.154 6.729 6.860

-5.040 3.749 2 230 2.230 -0.603 +1.014 2.529

81.84 94.02 106 20 106.20 118.37 130.56 142.75

-1.04 1.01 0 99 0.99 0.97 0.95 0.93

17 12 7 1 355 349

320 83 94 92 87 82

0.996 0.995 0 966 0.966 0.912 0.839 0.752

13 14 15 16 17

+6.585 5.964 5.069 3.975 +2.755

+3.870 4.988 5.852 6.443 +6.749

154.95 167.15 179.36 191.58 203.80

-0.92 0.90 0.89 0.88 -0.87

345 341 338 337 336

77 72 69 66 64

0.657 0.559 0.461 0.366 0.277

91

MOON, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date 0h TT

The Earth's Selenographic Long. Lat. ° °

The Sun's Selenographic Colong. Lat. ° °

Position Angle of Fraction Axis Bright Illuminated Limb ° °

May 17 18 19 20 21 22

+2.755 1 474 1.474 +0.190 -1.050 2.207 3.252

+6.749 6 766 6.766 6.495 5.945 5.131 4.081

203.80 216 03 216.03 228.26 240.50 252.74 264.99

-0.87 0 86 0.86 0.85 0.84 0.82 0.80

336 337 338 340 343 347

64 63 62 62 61 55

0.277 0 197 0.197 0.127 0.071 0.030 0.006

23 24 25 26 27 28

-4.158 4.904 5.468 5.824 5.948 5 815 5.815

+2.830 +1.429 -0.061 1.572 3.025 4 340 4.340

277.23 289.48 301.72 313.96 326.20 338 43 338.43

-0.78 0.76 0.73 0.70 0.67 0 64 0.64

351 356 2 7 12 17

295 269 270 274 279 284

0.001 0.016 0.052 0.107 0.181 0 271 0.271

29 30 31 June 1 2 3

-5.403 4.704 3.725 2.500 -1.092 +0.412

-5.435 6.235 6.674 6.703 6.303 5.486

350.66 2.88 15.09 27.30 39.49 51.69

-0.61 0.57 0.54 0.50 0.47 0.43

20 23 24 23 21 18

288 292 294 296 296 295

0.374 0.485 0.598 0.709 0.809 0.893

4 5 6 7 8 9

+1.904 3.273 4.420 5.265 5.759 5.886

-4.306 2.850 -1.229 +0.439 2.045 3.498

63.88 76.07 88.25 100.44 112.63 124.83

-0.39 0.36 0.32 0.29 0.26 0.23

14 9 3 357 352 346

293 292 75 90 86 81

0.955 0.991 0.999 0.981 0.939 0.878

10 11 12 13 14 15

+5.654 5.098 4.268 3.225 2.038 +0 778 +0.778

+4.732 5.705 6.391 6.782 6.874 6 673 6.673

137.02 149.23 161.44 173.65 185.88 198 10 198.10

-0.21 0.19 0.17 0.16 0.14 0 13 0.13

342 339 337 336 337 338

76 72 69 67 66 65

0.802 0.715 0.623 0.527 0.432 0 339 0.339

16 17 18 19 20 21

-0.488 1.694 2.782 3.704 4.419 4.900

+6.188 5.435 4.435 3.220 1.834 +0.334

210.34 222.58 234.82 247.07 259.32 271.57

-0.12 0.10 0.09 0.07 0.05 -0.03

340 342 346 350 355 0

66 68 70 74 78 85

0.252 0.174 0.107 0.054 0.017 0.001

22 23 24 25 26 27

-5.129 5.101 4 823 4.823 4.311 3.593 2.703

-1.210 2.715 4 094 4.094 5.260 6.131 6.644

283.82 296.07 308 32 308.32 320.57 332.81 345.04

0.00 +0.03 0 06 0.06 0.09 0.12 0.16

6 11 16 20 22 24

268 274 280 285 289 292

0.006 0.034 0 084 0.084 0.156 0.245 0.349

28 29 30 July 1 2

-1.685 -0.586 +0.542 1.647 +2.674

-6.757 6.455 5.750 4.687 -3.336

357.27 9.49 21.70 33.91 46.11

+0.19 0.23 0.27 0.31 +0.35

23 22 19 16 11

293 293 292 289 285

0.462 0.577 0.688 0.790 0.875

92

MOON, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date 0h TT

July

Aug.

The Earth's Selenographic Long. Lat. ° °

The Sun's Selenographic Colong. Lat. ° °

Position Angle of Fraction Axis Bright Illuminated Limb ° °

1 2 3 4 5 6

+1.647 2.674 3.572 4.293 4.793 5.039

-4.687 3.336 1.789 -0.151 +1.473 2.986

33.91 46.11 58.31 70.50 82.70 94.89

+0.31 0.35 0.39 0.42 0.46 0.49

16 11 6 360 354 348

289 285 280 272 242 92

0.790 0.875 0.941 0.982 0.999 0.992

7 8 9 10 11 12

+5.010 4.701 4.119 3.293 2.263 +1 086 +1.086

+4.309 5.383 6.173 6.661 6.844 6 727 6.727

107.08 119.28 131.48 143.68 155.89 168 11 168.11

+0.52 0.55 0.57 0.59 0.61 0 62 0.62

344 340 338 337 336 337

83 77 73 70 69 68

0.962 0.913 0.848 0.771 0.685 0 594 0.594

13 14 15 16 17 18

-0.174 1.444 2.647 3.709 4.558 5.135

+6.324 5.652 4.732 3.593 2.270 +0.812

180.33 192.55 204.78 217.02 229.26 241.51

+0.63 0.64 0.65 0.66 0.67 0.69

339 341 344 348 353 358

68 69 72 75 80 86

0.499 0.405 0.313 0.226 0.149 0.084

19 20 21 22 23 24

-5.393 5.308 4.883 4.149 3.164 2.011

-0.720 2.248 3.682 4.925 5.885 6.487

253.76 266.01 278.26 290.51 302.76 315.01

+0.70 0.72 0.74 0.76 0.79 0.81

4 9 15 19 22 23

94 109 244 275 283 288

0.035 0.007 0.002 0.022 0.067 0.136

25 26 27 28 29 30

-0.779 +0.443 1.583 2.587 3.426 4 083 4.083

-6.682 6.455 5.826 4.841 3.573 2 105 2.105

327.25 339.48 351.71 3.93 16.15 28 35 28.35

+0.84 0.87 0.91 0.94 0.97 1 01 1.01

23 22 20 17 12 7

290 291 290 288 285 280

0.225 0.329 0.441 0.556 0.667 0 768 0.768

31 1 2 3 4 5

+4.557 4.845 4.947 4.856 4.566 4.069

-0.532 +1.051 2.555 3.901 5.025 5.882

40.55 52.75 64.94 77.13 89.32 101.51

+1.04 1.08 1.11 1.14 1.17 1.19

1 356 350 345 341 339

273 266 256 236 116 85

0.854 0.922 0.969 0.995 0.998 0.980

6 7 8 9 10 11

+3.365 2.463 1 388 1.388 +0.177 -1.115 2.420

+6.445 6.703 6 659 6.659 6.326 5.725 4.880

113.70 125.90 138 09 138.09 150.30 162.50 174.71

+1.21 1.22 1 23 1.23 1.24 1.25 1.25

337 336 337 338 340 343

77 73 71 70 71 73

0.944 0.891 0 824 0.824 0.746 0.660 0.568

12 13 14 15 16

-3.660 4.750 5.603 6.136 -6.282

+3.820 2.578 +1.195 -0.278 -1.775

186.93 199.15 211.38 223.61 235.85

+1.25 1.25 1.25 1.26 +1.26

347 351 356 2 7

75 79 84 90 97

0.472 0.376 0.283 0.196 0.119

93

MOON, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date 0h TT

The Earth's Selenographic Long. Lat. ° °

The Sun's Selenographic Colong. Lat. ° °

Position Angle of Fraction Axis Bright Illuminated Limb ° °

Aug. 16 17 18 19 20 21

-6.282 5.998 5.276 4.158 2.728 -1.116

-1.775 3.217 4.510 5.553 6.256 6.549

235.85 248.09 260.33 272.58 284.82 297.07

+1.26 1.27 1.27 1.28 1.30 1.31

7 13 17 21 23 24

97 106 119 180 271 283

0.119 0.058 0.018 0.002 0.013 0.052

22 23 24 25 26 27

+0.535 2.084 3.423 4.483 5.240 5 702 5.702

-6.404 5.834 4.891 3.655 2.220 -0.682 0 682

309.30 321.54 333.77 345.99 358.20 10 41 10.41

+1.33 1.34 1.36 1.39 1.41 1 43 1.43

23 21 17 13 8 3

287 288 287 284 280 274

0.117 0.204 0.306 0.417 0.529 0 639 0.639

28 29 30 31 Sept. 1 2

+5.896 5.857 5.618 5.203 4.626 3.894

+0.867 2.343 3.674 4.801 5.678 6.274

22.61 34.80 46.99 59.17 71.35 83.53

+1.46 1.48 1.51 1.53 1.54 1.56

357 351 346 342 339 337

268 261 254 246 233 186

0.739 0.826 0.897 0.950 0.984 0.998

3 4 5 6 7 8

+3.010 1.980 +0.817 -0.453 1.791 3.139

+6.572 6.571 6.281 5.721 4.919 3.906

95.71 107.89 120.08 132.26 144.45 156.64

+1.57 1.57 1.58 1.57 1.57 1.56

337 337 338 340 342 346

96 80 75 74 74 76

0.992 0.969 0.928 0.872 0.803 0.723

9 10 11 12 13 14

-4.426 5.568 6.474 7.050 7.210 6 892 6.892

+2.719 +1.397 -0.013 1.456 2.867 4 165 4.165

168.83 181.03 193.24 205.45 217.67 229 89 229.89

+1.55 1.54 1.53 1.52 1.51 1 50 1.50

350 354 360 5 10 15

79 83 88 94 100 107

0.635 0.540 0.441 0.342 0.246 0 159 0.159

15 16 17 18 19 20

-6.066 4.760 3.060 -1.114 +0.898 2.793

-5.258 6.051 6.458 6.423 5.935 5.034

242.12 254.35 266.58 278.81 291.04 303.27

+1.49 1.49 1.48 1.48 1.48 1.49

19 22 23 23 22 19

114 124 151 261 281 284

0.086 0.033 0.005 0.006 0.038 0.096

21 22 23 24 25 26

+4.420 5.683 6 543 6.543 7.006 7.112 6.913

-3.802 2.346 -0.780 0 780 +0.793 2.284 3.622

315.49 327.71 339 92 339.92 352.12 4.32 16.50

+1.49 1.50 1 50 1.50 1.51 1.52 1.53

15 10 4 358 353 347

283 280 276 270 264 258

0.178 0.276 0 383 0.383 0.493 0.599 0.699

27 28 29 30 Oct. 1

+6.465 5.816 5.005 4.058 +2.996

+4.754 5.637 6.244 6.560 +6.579

28.69 40.86 53.04 65.20 77.37

+1.54 1.55 1.56 1.56 +1.56

343 340 338 337 337

252 246 241 234 219

0.788 0.863 0.923 0.966 0.991

94

MOON, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date 0h TT

Oct.

Nov.

The Earth's Selenographic Long. Lat. ° °

The Sun's Selenographic Colong. Lat. ° °

Position Angle of Fraction Axis Bright Illuminated Limb ° °

1 2 3 4 5 6

+2.996 1 830 1.830 +0.577 -0.743 2.101 3.453

+6.579 6 308 6.308 5.765 4.976 3.975 2.800

77.37 89 54 89.54 101.70 113.87 126.03 138.20

+1.56 1 55 1.55 1.55 1.53 1.52 1.50

337 337 339 342 345 349

219 141 88 79 78 79

0.991 0 998 0.998 0.987 0.959 0.915 0.855

7 8 9 10 11 12

-4.741 5.894 6.830 7.460 7.697 7 468 7.468

+1.496 +0.111 -1.304 2.688 3.975 5 088 5.088

150.38 162.55 174.73 186.92 199.11 211 31 211.31

+1.48 1.46 1.43 1.41 1.38 1 36 1.36

353 358 3 9 14 18

82 87 92 97 103 109

0.782 0.698 0.604 0.504 0.400 0 298 0.298

13 14 15 16 17 18

-6.729 5.481 3.789 -1.778 +0.374 2.471

-5.943 6.455 6.552 6.195 5.391 4.198

223.52 235.73 247.94 260.15 272.37 284.59

+1.34 1.32 1.30 1.28 1.26 1.25

21 23 23 22 20 16

114 119 124 135 234 277

0.201 0.117 0.052 0.012 0.002 0.023

19 20 21 22 23 24

+4.338 5.842 6.913 7.534 7.728 7.545

-2.722 -1.091 1.091 +0.569 2.148 3.563 4.752

296.80 309.01 321.21 333.41 345.60 357.78

+1.24 1.23 1.22 1.21 1.21 1.20

12 6 0 354 349 344

280 277 272 266 260 255

0.072 0.145 0.236 0.337 0.443 0.547

25 26 27 28 29 30

+7.046 6.295 5.350 4.258 3.062 1 794 1.794

+5.679 6.319 6.661 6.704 6.455 5 929 5.929

9.96 22.13 34.29 46.45 58.61 70 76 70.76

+1.20 1.19 1.19 1.18 1.17 1 15 1.15

341 338 337 337 337 339

250 246 243 240 238 234

0.646 0.738 0.818 0.885 0.938 0 975 0.975

31 1 2 3 4 5

+0.481 -0.851 2.173 3.450 4.642 5.696

+5.150 4.149 2.968 1.651 +0.251 -1.177

82.91 95.06 107.21 119.35 131.51 143.66

+1.14 1.11 1.09 1.06 1.03 1.00

341 344 348 352 357 2

220 110 84 83 85 90

0.995 0.998 0.983 0.950 0.900 0.834

6 7 8 9 10 11

-6.551 7.141 7 396 7.396 7.255 6.676 5.648

-2.572 3.871 5 005 5.005 5.903 6.494 6.711

155.82 167.98 180 15 180.15 192.32 204.50 216.69

+0.97 0.93 0 90 0.90 0.86 0.83 0.80

7 12 17 20 22 23

95 100 105 110 114 117

0.755 0.663 0 562 0.562 0.455 0.347 0.243

12 13 14 15 16

-4.204 2.429 -0.456 +1.555 +3.438

-6.505 5.856 4.788 3.375 -1.731

228.88 241.08 253.28 265.48 277.68

+0.77 0.74 0.71 0.68 +0.65

23 21 18 14 9

118 119 121 146 273

0.150 0.075 0.023 0.001 0.009

95

MOON, 2020 EPHEMERIS FOR PHYSICAL OBSERVATIONS FOR 0h TERRESTRIAL TIME Date 0h TT

The Earth's Selenographic Long. Lat. ° °

The Sun's Selenographic Colong. Lat. ° °

Position Angle of Fraction Axis Bright Illuminated Limb ° °

Nov. 16 17 18 19 20 21

+3.438 5 049 5.049 6.287 7.096 7.465 7.416

-1.731 +0.008 +0 008 1.708 3.258 4.577 5.612

277.68 289 88 289.88 302.08 314.27 326.46 338.64

+0.65 0 63 0.63 0.61 0.59 0.57 0.55

9 3 357 351 346 342

273 274 270 264 258 254

0.009 0 047 0.047 0.108 0.189 0.281 0.381

22 23 24 25 26 27

+6.997 6.268 5.295 4.145 2.879 1 553 1.553

+6.339 6.750 6.848 6.646 6.161 5 416 5.416

350.81 2.98 15.14 27.29 39.44 51 59 51.59

+0.54 0.53 0.51 0.49 0.48 0 46 0.46

339 337 337 337 338 340

250 247 245 244 243 244

0.482 0.580 0.674 0.760 0.835 0 899 0.899

28 29 30 Dec. 1 2 3

+0.218 -1.084 2.315 3.440 4.427 5.243

+4.441 3.271 1.951 +0.532 -0.925 2.358

63.73 75.87 88.00 100.14 112.27 124.41

+0.43 0.41 0.38 0.35 0.32 0.28

343 347 351 356 1 6

245 246 241 87 87 91

0.948 0.982 0.998 0.997 0.976 0.936

4 5 6 7 8 9

-5.856 6.231 6.336 6.144 5.634 4.806

-3.697 4.873 5.820 6.473 6.776 6.689

136.55 148.69 160.84 172.99 185.15 197.32

+0.24 0.21 0.17 0.13 0.09 0.06

11 16 19 22 23 23

97 102 106 110 113 115

0.878 0.803 0.714 0.613 0.504 0.392

10 11 12 13 14 15

-3.679 2.299 -0.743 +0.891 2.490 3 936 3.936

-6.188 5.283 4.017 2.471 -0.758 +0 992 +0.992

209.49 221.67 233.85 246.04 258.23 270 42 270.42

+0.02 -0.02 0.05 0.08 0.12 0 15 0.15

22 20 16 11 6 359

115 114 111 107 101 280

0.284 0.184 0.101 0.040 0.007 0 002 0.002

16 17 18 19 20 21

+5.129 5.987 6.463 6.541 6.237 5.591

+2.650 4.109 5.292 6.154 6.681 6.874

282.61 294.80 306.99 319.17 331.35 343.52

-0.17 0.20 0.22 0.25 0.27 0.28

353 348 343 340 338 337

271 264 258 254 250 248

0.024 0.071 0.138 0.220 0.310 0.406

22 23 24 25 26 27

+4.659 3.514 2 229 2.229 +0.881 -0.458 1.719

+6.751 6.335 5 652 5.652 4.733 3.612 2.329

355.68 7.84 19 99 19.99 32.13 44.27 56.41

-0.30 0.32 0 34 0.34 0.36 0.38 0.40

337 338 340 342 345 349

246 246 247 249 251 255

0.503 0.597 0 688 0.688 0.771 0.845 0.908

28 29 30 31 32

-2.845 3.788 4.513 4.998 -5.232

+0.929 -0.531 1.987 3.369 -4.600

68.54 80.67 92.80 104.93 117.06

-0.43 0.46 0.48 0.51 -0.55

354 359 5 10 15

261 269 316 84 95

0.956 0.987 1.000 0.992 0.963

96

MERCURY, 2020 HELIOCENTRIC POSITIONS FOR 0h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

0 1 2 3 4 5

º 259 262 265 267 270 273

' 42 27 12 58 45 33

" º ' " 17.2 -3 38 07.9 14.9 3 55 09.0 40.2 4 11 39.7 45.5 4 27 38.8 43.1 4 43 04.5 45.6 4 57 55.3

º ' " º ' " 0.466 6212 Feb. 15 95 09 08.5 +5 06 01.5 0.309 9640 0.466 2660 16 101 22 01.5 5 35 23.6 0.312 0174 0.465 6319 17 107 29 55.5 6 00 29.6 0.314 6420 0.464 7197 18 113 31 37.7 6 21 08.8 0.317 7990 0.463 5304 19 119 26 05.3 6 37 18.5 0.321 4436 0.462 0654 20 125 12 27.0 6 49 03.0 0.325 5271

6 7 8 9 10 11

276 279 282 285 287 290

23 13 06 01 57 56

05.7 -5 12 09.3 56.5 5 25 44.6 31.3 5 38 38.8 03.9 5 50 49.5 48.3 6 02 14.1 59.3 6 12 49.4

0.460 3265 0.458 3157 0.456 0358 0.453 4898 0.450 6812 0.447 6142

12 13 14 15 16 17

293 297 300 303 306 309

58 03 11 23 38 58

51.8 -6 22 32.2 41.6 6 31 18.9 44.9 6 39 05.5 18.7 6 45 47.5 40.5 6 51 20.3 08.6 6 55 38.5

0.444 2935 27 161 16 28.4 +6 28 02.3 0.362 1041 0.440 7247 28 165 48 04.5 6 14 07.6 0.367 8958 0.436 9140 29 170 10 59.7 5 58 26.4 0.373 7045 0.432 8686 Mar. 1 174 25 37.1 5 41 14.9 0.379 4967 0.428 5966 2 178 32 21.6 5 22 47.7 0.385 2415 0.424 1071 3 182 31 38.6 5 03 18.1 0.390 9115

18 19 20 21 22 23

313 316 320 324 327 331

22 50 24 03 48 39

02.0 -6 58 36.4 40.4 7 00 08.0 24.2 7 00 06.4 34.5 6 58 24.7 33.0 6 54 55.2 41.6 6 49 30.0

0.419 4107 0.414 5191 0.409 4458 0.404 2057 0.398 8157 0.393 2949

4 5 6 7 8 9

186 190 193 197 200 204

23 09 49 22 51 14

54.2 +4 42 57.7 0.396 4817 34.3 4 21 56.9 0.401 9298 04.2 4 00 24.5 0.407 2359 48.9 3 38 28.5 0.412 3821 12.4 3 16 15.8 0.417 3528 38.0 2 53 52.1 0.422 1338

24 25 26 27 28 29

335 339 343 348 352 357

37 41 53 13 41 16

23.0 -6 42 00.7 59.5 6 32 18.8 53.6 6 20 15.7 27.2 6 05 42.8 01.1 5 48 32.3 54.7 5 28 36.9

0.387 6645 0.381 9483 0.376 1727 0.370 3672 0.364 5639 0.358 7986

10 11 12 13 14 15

207 210 213 217 220 223

33 48 58 05 09 10

27.8 +2 31 22.7 0.426 7126 03.4 2 08 51.8 0.431 0784 45.1 1 46 23.4 0.435 2213 52.4 1 24 00.5 0.439 1328 43.8 1 01 46.1 0.442 8053 37.2 0 39 42.5 0.446 2322

30 31 Feb. 1 2 3 4

2 6 11 17 22 27

01 54 57 08 29 58

25.4 -5 05 50.5 47.4 4 40 09.1 11.1 4 11 30.7 42.2 3 39 56.7 20.4 3 05 32.1 58.5 2 28 26.7

0.353 1099 0.347 5399 0.342 1336 0.336 9387 0.332 0054 0.327 3851

16 17 18 19 20 21

226 229 231 234 237 240

08 04 58 49 40 28

49.6 +0 17 52.0 0.449 4077 37.2 -0 03 43.7 0.452 3267 15.6 0 25 03.0 0.454 9849 59.9 0 46 04.4 0.457 3784 04.5 1 06 46.6 0.459 5040 43.4 1 27 08.5 0.461 3588

5 6 7 8 9 10

33 39 45 51 57 63

37 24 18 19 27 39

20.8 -1 48 55.3 02.8 1 07 18.3 29.9 -0 24 02.1 56.6 +0 20 21.5 27.1 1 05 15.3 55.3 1 49 58.4

0.323 1304 0.319 2929 0.315 9227 0.313 0664 0.310 7656 0.309 0554

22 23 24 25 26 27

243 246 248 251 254 257

16 02 48 33 18 02

10.1 -1 47 08.8 0.462 9406 38.0 2 06 46.5 0.464 2473 19.8 2 26 00.7 0.465 2775 28.2 2 44 50.2 0.466 0300 15.7 3 03 14.1 0.466 5038 54.7 3 21 11.2 0.466 6985

11 12 13 14 15

69 76 82 88 95

56 14 33 52 09

05.8 +2 33 47.4 35.7 3 15 58.4 56.6 3 55 49.3 37.8 4 32 41.3 08.5 +5 06 01.5

0.307 9626 0.307 5048 0.307 6895 0.308 5137 0.309 9640 Apr.

28 29 30 31 1

259 262 265 268 270

47 32 18 04 51

37.2 -3 38 40.4 0.466 6139 35.6 3 55 40.5 0.466 2500 02.1 4 12 10.3 0.465 6072 08.8 4 28 08.3 0.464 6863 08.3 -4 43 32.9 0.463 4884

Jan.

21 22 23 24 25 26

130 136 141 146 151 156

50 18 37 46 45 35

02.8 +6 56 32.0 0.329 9982 24.4 6 59 59.8 0.334 8047 13.9 6 59 43.9 0.339 8946 23.4 6 56 03.8 0.345 2169 53.1 6 49 19.9 0.350 7230 50.4 6 39 52.7 0.356 3665

97

MERCURY, 2020 HELIOCENTRIC POSITIONS FOR 0h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Apr.

May

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 2 3 4 5 6

º 270 273 276 279 282 285

' 51 39 28 19 12 06

" º ' " 08.3 -4 43 32.9 13.0 4 58 22.6 35.8 5 12 35.5 29.7 5 26 09.5 08.0 5 39 02.3 44.5 5 51 11.7

º ' " º ' " 0.463 4884 May 17 119 37 10.5 +6 37 44.4 0.321 5657 0.462 0148 18 125 23 16.2 6 49 20.8 0.325 6620 0.460 2673 19 131 00 35.0 6 56 42.0 0.330 1442 0.458 2481 20 136 28 38.8 7 00 02.6 0.334 9602 0.455 9599 21 141 47 10.3 6 59 40.0 0.340 0579 0.453 4056 22 146 56 01.7 6 55 53.9 0.345 3866

7 8 9 10 11 12

288 291 294 297 300 303

03 02 04 09 17 29

33.3 -6 02 34.7 49.1 6 13 08.5 46.9 6 22 49.6 42.5 6 31 34.5 52.2 6 39 19.1 32.8 6 45 59.0

0.450 5888 0.447 5139 0.444 1854 0.440 6090 0.436 7909 0.432 7383

13 14 15 16 17 18

306 310 313 316 320 324

45 04 28 57 31 10

02.0 -6 51 29.5 38.2 6 55 45.3 40.2 6 58 40.6 27.9 7 00 09.3 21.6 7 00 04.8 42.6 6 58 19.8

0.428 4593 29 178 40 05.1 +5 22 12.2 0.385 4191 0.423 9632 30 182 39 08.7 5 02 40.9 0.391 0863 0.419 2606 31 186 31 11.7 4 42 19.1 0.396 6529 0.414 3632 June 1 190 16 39.9 4 21 17.1 0.402 0967 0.409 2844 2 193 55 58.7 3 59 43.9 0.407 3980 0.404 0394 3 197 29 33.1 3 37 47.3 0.412 5389

19 20 21 22 23 24

327 331 335 339 344 348

55 47 45 49 02 21

52.2 -6 54 46.8 12.8 6 49 17.9 06.8 6 41 44.5 56.6 6 31 58.3 04.8 6 19 50.6 53.0 6 05 13.0

0.398 6451 0.393 1206 0.387 4873 0.381 7689 0.375 9920 0.370 1861

4 5 6 7 8 9

200 204 207 210 214 217

57 21 39 54 04 11

47.1 +3 15 34.1 0.417 5037 03.8 2 53 10.2 0.422 2785 45.5 2 30 40.7 0.426 8508 13.6 2 08 09.8 0.431 2097 48.4 1 45 41.4 0.435 3454 49.4 1 23 18.8 0.439 2495

25 352 49 42.2 -5 47 57.4 26 357 25 51.8 5 27 56.7 27 2 10 38.8 5 05 04.9 28 7 04 17.5 4 39 17.9 29 12 06 58.2 4 10 34.0 30 17 18 46.3 3 38 54.6

0.364 3836 0.358 6202 0.352 9347 0.347 3692 0.341 9688 0.336 7815

10 11 12 13 14 15

220 223 226 229 232 234

15 16 14 10 03 55

35.1 +1 01 04.7 0.442 9144 23.3 0 39 01.5 0.446 3335 31.0 +0 17 11.4 0.449 5010 14.4 -0 04 23.9 0.452 4120 49.2 0 25 42.6 0.455 0620 30.2 0 46 43.5 0.457 4472

23 24 25 26 27 28

151 156 161 165 170 174

55 44 25 56 19 33

13.3 +6 49 04.6 0.350 8975 53.0 6 39 32.7 0.356 5444 13.8 6 27 38.1 0.362 2842 33.4 6 13 39.9 0.368 0768 12.7 5 57 55.6 0.373 8854 35.0 5 40 41.5 0.379 6763

1 2 3 4 5 6

22 28 33 39 45 51

39 09 48 35 29 31

41.5 -3 04 24.9 36.0 2 27 14.7 14.3 1 47 39.0 11.2 1 05 58.5 51.9 -0 22 39.6 30.7 +0 21 45.4

0.331 8572 0.327 2477 0.323 0053 0.319 1818 0.315 8270 0.312 9876

16 17 18 19 20 21

237 240 243 246 248 251

45 34 21 07 53 38

32.0 -1 07 25.1 0.459 5643 08.6 1 27 46.3 0.461 4107 33.4 1 47 45.9 0.462 9839 59.7 2 07 22.9 0.464 2821 40.4 2 26 36.3 0.465 3036 48.1 2 45 25.1 0.466 0475

7 8 9 10 11 12

57 63 70 76 82 89

39 51 08 26 45 04

11.4 +1 06 39.5 47.5 1 51 21.5 03.4 2 35 08.1 36.0 3 17 15.4 56.9 3 57 01.2 35.1 4 33 47.0

0.310 7048 0.309 0135 0.307 9403 0.307 5024 0.307 7072 0.308 5511

22 23 24 25 26 27

254 257 259 262 265 268

23 08 52 37 23 09

35.3 -3 03 48.1 0.466 5127 14.2 3 21 44.4 0.466 6987 57.2 3 39 12.7 0.466 6055 56.4 3 56 11.9 0.466 2330 24.0 4 12 40.7 0.465 5816 32.3 4 28 37.7 0.464 6522

13 14 15 16 17

95 101 107 113 119

21 33 41 42 37

00.2 +5 07 00.1 44.8 5 36 14.5 28.1 6 01 12.2 57.4 6 21 43.0 10.5 +6 37 44.4

0.310 0206 28 270 56 33.7 -4 0.312 0922 29 273 44 40.7 4 0.314 7340 30 276 34 06.2 5 0.317 9068 July 1 279 25 03.2 5 0.321 5657 2 282 17 45.0 -5

44 58 13 26 39

01.3 49.9 01.5 34.2 25.8

0.463 4458 0.461 9638 0.460 2080 0.458 1806 0.455 8842

98

MERCURY, 2020 HELIOCENTRIC POSITIONS FOR 0h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

July

Aug.

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 2 3 4 5 6

º 279 282 285 288 291 294

' 25 17 12 09 08 10

" º ' " 03.2 -5 26 34.2 45.0 5 39 25.8 25.5 5 51 33.7 18.8 6 02 55.3 39.4 6 13 27.4 42.6 6 23 06.8

0.458 1806 Aug. 0.455 8842 0.453 3219 0.450 4973 0.447 4146 0.444 0786

16 17 18 19 20 21

º 136 141 147 152 156 161

' 38 56 05 04 53 33

" º ' " 35.1 +7 00 04.9 0.335 1129 49.0 6 59 35.9 0.340 2178 22.6 6 55 43.9 0.345 5522 16.9 6 48 49.4 0.351 0673 39.4 6 39 12.9 0.356 7172 43.6 6 27 14.3 0.362 4587

7 8 9 10 11 12

297 300 303 306 310 313

15 23 35 51 11 35

44.0 -6 31 49.9 60.0 6 39 32.5 47.4 6 46 10.3 24.0 6 51 38.6 08.1 6 55 51.9 18.7 6 58 44.6

0.440 4948 0.436 6696 0.432 6102 0.428 3247 0.423 8224 0.419 1139

22 23 24 25 26 27

166 170 174 178 182 186

04 27 41 47 46 38

47.2 +6 13 12.6 0.368 2519 11.3 5 57 25.3 0.374 0600 19.2 5 40 08.8 0.379 8496 35.6 5 21 37.4 0.385 5902 26.3 5 02 04.3 0.391 2543 17.1 4 41 41.1 0.396 8172

13 14 15 16 17 18

317 320 324 328 331 335

04 38 17 03 54 52

15.4 -7 00 10.5 18.9 7 00 02.9 50.1 6 58 14.6 10.8 6 54 38.1 43.0 6 49 05.4 49.3 6 41 28.0

0.414 2111 0.409 1274 0.403 8779 0.398 4797 0.392 9520 Sept. 0.387 3160

28 29 30 31 1 2

190 194 197 201 204 207

23 02 36 04 27 45

34.0 +4 20 38.0 0.402 2567 42.3 3 59 04.0 0.407 5532 06.9 3 37 06.8 0.412 6888 11.8 3 14 53.2 0.417 6479 20.1 2 52 29.0 0.422 4166 54.1 2 29 59.3 0.426 9824

19 20 21 22 23 24

339 344 348 352 357 2

57 10 30 58 34 19

52.1 -6 31 37.6 13.8 6 19 25.3 16.2 6 04 42.9 20.2 5 47 22.3 44.9 5 27 16.4 47.6 5 04 19.3

0.381 5959 0.375 8181 0.370 0123 0.364 2109 0.358 4496 0.352 7676

3 4 5 6 7 8

211 214 217 220 223 226

00 10 17 21 22 20

15.1 +2 07 28.4 0.431 3346 43.4 1 45 00.2 0.435 4633 38.4 1 22 37.7 0.439 3602 18.7 1 00 23.9 0.443 0177 02.1 0 38 21.1 0.446 4293 05.4 +0 16 31.3 0.449 5891

25 26 27 28 29 30

7 12 17 22 28 33

13 16 28 49 20 58

42.3 -4 38 26.9 39.1 4 09 37.6 43.4 3 37 52.9 54.5 3 03 18.1 04.7 2 26 03.3 57.8 1 46 23.5

0.347 2069 0.341 8128 0.336 6330 0.331 7180 0.327 1192 0.322 8890

9 10 11 12 13 14

229 232 235 237 240 243

15 09 00 50 39 26

44.9 -0 05 03.5 0.452 4923 16.2 0 26 21.7 0.455 1343 54.2 0 47 22.0 0.457 5115 53.5 1 08 03.0 0.459 6205 27.8 1 28 23.6 0.461 4587 50.9 1 48 22.5 0.463 0237

31 1 2 3 4 5

39 45 51 57 64 70

46 41 42 50 03 19

08.7 -1 04 39.7 02.0 -0 21 18.4 51.8 +0 23 08.0 41.6 1 08 02.2 24.6 1 52 43.0 45.1 2 36 27.1

0.319 0793 0.315 7397 0.312 9167 0.310 6514 0.308 9785 0.307 9243

15 16 17 18 19 20

246 248 251 254 257 259

13 58 44 28 13 58

15.8 -2 07 58.9 0.464 3136 55.5 2 27 11.6 0.465 3269 02.5 2 45 59.6 0.466 0624 49.4 3 04 21.8 0.466 5192 28.5 3 22 17.3 0.466 6969 11.9 3 39 44.7 0.466 5953

6 76 38 7 82 57 8 89 16 9 95 32 10 101 45 11 107 52

19.6 +3 18 30.5 39.7 3 58 11.3 14.4 4 34 51.0 33.2 5 07 57.1 09.2 5 37 03.9 41.6 6 01 53.5

0.307 5057 0.307 7297 0.308 5926 0.310 0803 0.312 1693 0.314 8274

21 22 23 24 25 26

262 265 268 271 273 276

43 28 14 01 50 39

11.9 -3 56 43.0 0.466 2145 40.7 4 13 10.8 0.465 5548 50.5 4 29 06.8 0.464 6171 53.9 4 44 29.3 0.463 4025 03.2 4 59 16.8 0.461 9123 31.4 5 13 27.3 0.460 1483

12 13 14 15 16

58.1 +6 22 16.1 56.6 6 38 09.3 46.5 6 49 37.7 48.6 6 56 51.4 35.1 +7 00 04.9

0.318 0151 0.321 6875 0.325 7956 0.330 2882 0.335 1129 Oct.

27 28 29 30 1

279 282 285 288 291

30 23 18 14 14

31.5 -5 26 58.8 0.458 1128 16.8 5 39 49.0 0.455 8085 01.2 5 51 55.6 0.453 2383 58.7 6 03 15.6 0.450 4059 24.1 -6 13 46.2 0.447 3155

113 119 125 131 136

53 47 33 10 38

99

MERCURY, 2020 HELIOCENTRIC POSITIONS FOR 0h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Oct.

Nov.

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 2 3 4 5 6

º 291 294 297 300 303 306

' 14 16 21 30 41 57

" º ' " 24.1 -6 13 46.2 32.6 6 23 23.9 39.7 6 32 05.1 01.9 6 39 45.8 56.1 6 46 21.6 40.0 6 51 47.6

0.447 3155 Nov. 0.443 9721 0.440 3810 0.436 5487 0.432 4823 0.428 1902

16 17 18 19 20 21

º 157 161 166 170 174 178

' 02 42 13 35 49 55

" º ' " 33.7 +6 38 52.9 0.356 8910 21.2 6 26 50.2 0.362 6347 08.7 6 12 45.0 0.368 4288 17.3 5 56 54.8 0.374 2369 10.4 5 39 35.7 0.380 0254 12.9 5 21 02.2 0.385 7641

7 8 9 10 11 12

310 313 317 320 324 328

17 41 10 45 24 10

31.9 -6 55 58.5 50.9 6 58 48.6 56.7 7 00 11.7 09.9 7 00 01.1 51.4 6 58 09.6 23.0 6 54 29.7

0.423 6816 0.418 9671 0.414 0586 0.408 9696 0.403 7154 0.398 3130

22 23 24 25 26 27

182 186 190 194 197 201

53 45 30 09 42 10

50.4 +5 01 27.4 0.391 4255 28.8 4 41 02.8 0.396 9850 34.1 4 19 58.7 0.402 4205 31.5 3 58 23.8 0.407 7123 46.0 3 36 26.0 0.412 8428 41.4 3 14 11.9 0.417 7963

13 14 15 16 17 18

332 336 340 344 348 353

02 00 05 18 38 06

06.9 -6 48 53.3 25.5 6 41 11.9 41.3 6 31 17.2 16.7 6 19 00.5 33.5 6 04 13.4 52.5 5 46 47.8

0.392 7817 28 204 33 41.1 +2 51 47.5 0.422 5590 0.387 1429 29 207 52 07.0 2 29 17.7 0.427 1186 0.381 4206 30 211 06 20.6 2 06 46.9 0.431 4641 0.375 6415 Dec. 1 214 16 42.0 1 44 18.7 0.435 5859 0.369 8353 2 217 23 30.8 1 21 56.5 0.439 4756 0.364 0346 3 220 27 05.5 0 59 42.9 0.443 1257

19 357 43 32.8 -5 26 36.7 20 2 28 51.4 5 03 34.3 21 7 23 02.5 4 37 36.5 22 12 26 15.9 4 08 41.7 23 17 38 36.9 3 36 51.7 24 23 00 04.6 3 02 11.9

0.358 2752 0.352 5963 0.347 0400 0.341 6516 0.336 4792 0.331 5730

4 5 6 7 8 9

223 226 229 232 235 237

27 25 21 14 06 56

43.7 +0 37 40.5 0.446 5297 42.3 +0 15 51.2 0.449 6818 17.7 -0 05 43.1 0.452 5771 45.3 0 27 00.9 0.455 2111 20.1 0 48 00.6 0.457 5801 16.4 1 08 41.0 0.459 6809

25 26 27 28 29 30

28 34 39 45 51 58

30 09 57 52 54 02

30.9 -2 24 52.3 39.6 1 45 08.5 05.1 1 03 21.2 11.8 -0 19 57.5 13.5 +0 24 30.3 13.2 1 09 24.7

0.326 9847 0.322 7666 0.318 9705 0.315 6460 0.312 8394 0.310 5917

10 11 12 13 14 15

240 243 246 249 251 254

44 32 18 04 49 34

48.4 -1 29 00.9 0.461 5108 09.5 1 48 59.2 0.463 0674 32.8 2 08 34.8 0.464 3489 11.2 2 27 46.8 0.465 3537 17.5 2 46 34.0 0.466 0806 03.9 3 04 55.4 0.466 5290

31 1 2 3 4 5

64 70 76 83 89 95

15 31 50 09 27 44

04.0 +1 54 04.5 29.8 2 37 46.1 07.0 3 19 45.8 27.1 3 59 21.5 59.0 4 35 55.2 12.3 5 08 54.3

0.308 9373 0.307 9022 0.307 5032 0.307 7468 0.308 6289 0.310 1354

16 17 18 19 20 21

257 260 262 265 268 271

18 03 48 33 20 07

42.9 -3 22 50.0 0.466 6981 26.6 3 40 16.6 0.466 5879 27.3 3 57 13.9 0.466 1985 57.2 4 13 40.8 0.465 5303 08.4 4 29 35.8 0.464 5841 13.6 4 44 57.3 0.463 3609

6 7 8 9 10 11

101 108 114 119 125 131

56 04 05 58 44 21

40.2 +5 37 53.4 02.1 6 02 35.0 06.1 6 22 49.3 50.4 6 38 34.3 24.7 6 49 54.7 10.2 6 57 00.8

0.312 2422 0.314 9170 0.318 1201 0.321 8065 0.325 9271 0.330 4305

22 23 24 25 26 27

273 276 279 282 285 288

55 44 35 28 23 20

25.1 -4 59 43.6 0.461 8622 55.9 5 13 52.9 0.460 0899 59.0 5 27 23.2 0.458 0461 47.7 5 40 12.1 0.455 7334 36.0 5 52 17.3 0.453 1551 37.9 6 03 35.8 0.450 3146

12 13 14 15 16

136 142 147 152 157

48 06 14 13 02

39.6 +7 00 07.3 35.8 6 59 31.7 51.7 6 55 33.8 28.4 6 48 34.0 33.7 +6 38 52.9

0.335 2646 0.340 3772 0.345 7178 0.351 2377 0.356 8910

28 29 30 31 32

291 294 297 300 303

20 22 27 36 48

08.0 -6 14 04.8 0.447 2164 21.7 6 23 40.9 0.443 8651 34.6 6 32 20.3 0.440 2665 03.0 6 39 59.0 0.436 4268 04.0 -6 46 32.7 0.432 3533

100

MERCURY, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Jan.

Feb.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

0 1 2 3 4 5

º 272 274 275 277 279 280

' 48 22 57 32 07 43

" 34.9 55.4 34.1 31.6 49.0 27.1

º -1 1 1 1 1 1

' 11 16 21 26 31 35

" 01.4 22.0 29.9 24.7 05.6 32.1

6 7 8 9 10 11

282 283 285 287 288 290

19 55 32 09 47 25

26.9 49.3 35.1 45.3 20.6 21.7

-1 1 1 1 1 1

39 43 47 50 53 56

12 13 14 15 16 17

292 293 295 297 298 300

03 42 22 01 42 22

49.4 44.2 06.4 56.3 14.1 59.4

-1 2 2 2 2 2

18 19 20 21 22 23

302 303 305 307 308 310

04 45 27 10 53 36

11.9 50.6 54.1 20.7 07.8 12.2

24 25 26 27 28 29

312 314 315 317 319 320

19 02 46 29 12 55

30 31 1 2 3 4

322 324 325 327 329 330

5 6 7 8 9 10 11 12 13 14 15

Date

Apparent Geocentric Longitude

Appare Geocent Latitud

15 16 17 18 19 20

º 342 342 342 342 342 342

' 31 47 53 48 33 08

" 47.4 45.1 22.5 33.3 24.4 17.7

º +1 2 2 2 2 3

' 54 10 25 40 54 06

43.7 39.5 19.1 41.6 46.3 32.5

21 22 23 24 25 26

341 340 340 339 338 336

33 50 00 04 03 59

50.0 54.2 37.7 20.8 33.8 53.0

+3 3 3 3 3 3

17 26 34 39 42 43

58 01 02 04 05 05

59.3 05.9 51.5 15.0 15.6 52.0

27 28 29 1 2 3

335 334 333 332 331 331

54 50 47 47 52 02

56.7 20.8 34.8 58.5 39.9 33.9

+3 3 3 3 3 3

41 38 32 25 15 05

-2 2 2 2 2 1

06 05 05 03 02 59

03.4 48.4 05.8 54.5 13.0 59.9

4 5 6 7 8 9

330 329 329 328 328 328

18 40 09 45 27 16

22.3 34.2 27.5 10.3 42.8 58.6

+2 2 2 2 2 1

53 41 27 14 00 45

29.9 55.8 23.8 46.4 54.5 37.3

-1 1 1 1 1 1

57 53 49 45 40 34

13.8 53.2 56.6 22.3 08.9 14.7

10 11 12 13 14 15

328 328 328 328 328 329

12 14 23 36 56 20

46.8 53.1 00.7 51.7 07.4 29.1

+1 1 1 0 0 0

31 17 03 49 36 22

37 18 58 37 13 48

42.1 53.7 54.4 23.8 58.3 11.0

-1 1 1 1 0 0

27 20 12 03 53 43

38.2 18.0 12.9 21.6 43.5 17.9

16 17 18 19 20 21

329 330 331 331 332 333

49 23 01 42 28 17

38.5 17.7 09.9 59.3 31.1 31.3

+0 -0 0 0 0 0

10 02 13 25 36 46

332 333 335 336 337 338

19 47 11 30 44 51

31.8 26.9 19.4 29.4 14.1 49.4

-0 0 -0 +0 0 0

32 20 07 06 20 35

04.9 05.0 19.3 10.1 20.4 07.5

22 23 24 25 26 27

334 335 336 337 338 339

09 05 03 04 07 13

47.5 08.0 22.1 20.2 53.5 54.0

-0 1 1 1 1 1

56 06 15 23 31 38

339 340 341 342 342

52 45 30 05 31

30.0 31.1 09.9 46.6 47.4

+0 1 1 1 +1

50 06 22 38 54

26.3 10.4 11.9 21.5 28.5

28 29 30 31 1

340 341 342 344 345

22 32 45 00 16

14.5 48.6 30.5 15.0 57.5

-1 1 1 2 -2

45 52 58 03 08

Feb.

Mar.

Apr.

101

MERCURY, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Apr.

May

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 345 346 347 349 350 352

' 16 35 56 18 42 07

" 57.5 33.9 00.7 14.7 13.2 54.0

º -2 2 2 2 2 2

' 08 13 17 20 23 26

" 46.8 15.5 14.3 43.3 42.5 11.7

7 8 9 10 11 12

353 355 356 358 359 1

35 04 34 07 40 16

15.2 15.1 52.8 07.0 57.2 22.9

-2 2 2 2 2 2

28 29 30 31 31 30

13 14 15 16 17 18

2 4 6 7 9 11

53 31 12 53 37 22

23.6 59.3 09.9 55.8 17.2 14.6

-2 2 2 2 2 2

19 20 21 22 23 24

13 14 16 18 20 22

08 56 46 38 31 25

48.3 59.0 47.0 12.8 16.5 58.1

25 26 27 28 29 30

24 26 28 30 32 34

22 20 19 20 23 27

1 2 3 4 5 6

36 38 40 42 45 47

7 8 9 10 11 12 13 14 15 16 17

Date

Apparent Geocentric Longitude

Appare Geocent Latitud

17 18 19 20 21 22

º 70 72 74 76 77 79

' 23 18 11 02 49 34

" 01.4 49.2 59.4 24.3 57.9 34.9

º +1 1 1 2 2 2

' 47 53 58 03 07 10

11.0 40.2 39.4 08.4 07.2 35.6

23 24 25 26 27 28

81 82 84 86 87 88

16 54 30 02 31 57

11.2 43.2 08.0 22.7 25.2 12.8

+2 2 2 2 2 2

13 14 15 15 14 13

29 28 25 23 20 16

33.7 01.2 58.2 24.6 20.4 45.6

29 30 31 1 2 3

90 91 92 94 95 96

19 38 54 07 16 21

43.4 54.2 42.8 06.0 00.8 23.5

+2 2 2 1 1 1

10 07 03 57 52 45

-2 2 2 1 1 1

12 08 02 57 51 44

40.2 04.4 58.3 22.2 16.4 41.3

4 5 6 7 8 9

97 98 99 100 100 101

23 21 15 06 52 35

10.3 17.0 39.1 11.6 49.5 27.6

+1 1 1 1 1 0

38 29 20 11 00 49

17.0 12.5 43.0 46.3 19.4 18.0

-1 1 1 1 1 0

37 30 22 13 04 55

37.6 06.0 07.5 43.3 54.7 43.4

10 11 12 13 14 15

102 102 103 103 104 104

14 48 18 44 05 22

00.3 22.5 28.8 14.3 34.6 25.9

+0 0 +0 -0 0 0

37 24 11 02 17 32

32 39 46 55 04 14

37.0 09.7 48.0 22.4 42.5 33.9

-0 0 0 0 -0 +0

46 36 26 15 05 05

11.4 21.1 15.1 56.5 28.8 05.1

16 17 18 19 20 21

104 104 104 104 104 104

34 42 45 44 38 28

45.5 31.7 44.5 25.8 39.4 31.9

-0 1 1 1 1 2

48 03 20 36 53 09

49 51 53 55 58 60

24 34 44 54 03 10

43.9 56.9 56.3 25.0 05.6 40.7

+0 0 0 0 0 1

15 26 36 46 56 06

40.2 12.7 38.1 51.9 49.5 26.7

22 23 24 25 26 27

104 103 103 103 102 102

14 55 33 08 39 08

12.5 53.7 51.2 24.1 55.1 50.3

-2 2 2 3 3 3

26 42 58 13 28 41

62 64 66 68 70

16 21 24 24 23

53.6 28.2 09.8 44.8 01.4

+1 1 1 1 +1

15 24 32 40 47

39.0 22.5 33.6 09.0 05.8

28 29 30 1 2

101 101 100 99 99

35 00 25 48 13

39.0 53.4 08.0 58.7 02.8

-3 4 4 4 -4

54 06 16 25 33

May

June

July

102

MERCURY, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

July

Aug.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 99 99 98 98 97 97

' 48 13 37 04 32 03

" 58.7 02.8 57.6 19.8 44.9 46.2

º -4 4 4 4 4 4

' 25 33 39 44 47 48

" 57.1 36.5 45.2 20.5 20.8 46.1

7 8 9 10 11 12

96 96 95 95 95 95

37 15 57 43 34 29

54.8 38.6 22.4 27.9 13.0 52.7

-4 4 4 4 4 4

48 46 43 39 33 26

13 14 15 16 17 18

95 95 95 96 96 96

30 36 48 04 27 55

39.0 40.9 05.0 55.9 16.1 06.7

-4 4 3 3 3 3

19 20 21 22 23 24

97 98 98 99 100 101

28 07 51 41 36 36

27.3 16.7 32.5 11.7 10.7 25.2

25 26 27 28 29 30

102 103 105 106 107 109

41 52 07 28 53 22

31 1 2 3 4 5

110 112 114 116 117 119

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Appare Geocent Latitud

16 17 18 19 20 21

º 141 143 145 147 149 151

' 51 53 54 53 52 50

" 45.0 19.5 03.7 50.1 32.5 06.1

º +1 1 1 1 1 1

' 44 45 45 45 44 42

37.3 57.0 48.3 15.5 23.3 17.2

22 23 24 25 26 27

153 155 157 159 161 163

46 41 35 27 19 08

27.3 33.3 22.3 52.9 04.5 56.9

+1 1 1 1 1 1

40 37 34 30 26 22

18 08 58 47 35 23

02.6 45.5 31.8 27.2 37.7 08.8

28 29 30 31 1 2

164 166 168 170 171 173

57 44 30 15 58 40

30.1 44.5 40.7 19.5 41.8 48.4

+1 1 1 1 0 0

17 11 06 00 54 48

-3 2 2 2 2 1

10 56 42 28 13 59

06.0 34.7 39.9 26.6 59.6 23.6

3 4 5 6 7 8

175 177 178 180 181 183

21 01 39 16 53 27

40.5 18.8 44.4 58.2 00.8 53.0

+0 0 0 0 0 +0

41 34 27 20 13 05

50.2 20.1 48.5 08.1 10.3 45.2

-1 1 1 1 0 0

44 30 15 01 46 32

43.3 03.1 27.5 00.9 47.9 52.7

9 10 11 12 13 14

185 186 188 189 191 192

01 34 05 35 04 32

35.3 08.1 31.6 45.9 50.9 46.1

-0 0 0 0 0 0

01 09 17 24 32 40

56 34 16 02 51 43

41.6 46.4 45.1 21.2 16.7 11.9

-0 -0 +0 0 0 0

19 06 06 18 29 40

19.7 13.3 22.6 24.0 47.1 28.8

15 16 17 18 19 20

193 195 196 198 199 200

59 25 49 12 34 54

30.9 04.6 25.9 33.3 25.2 59.3

-0 0 1 1 1 1

48 56 04 12 20 28

121 123 125 127 129 131

37 34 33 33 35 37

46.3 38.0 25.1 45.3 17.0 39.5

+0 0 1 1 1 1

50 59 07 15 22 27

25.9 36.1 57.4 28.4 08.2 56.6

21 22 23 24 25 26

202 203 204 206 207 208

14 32 48 03 16 28

13.0 03.4 26.9 19.3 36.1 11.8

-1 1 1 1 2 2

35 43 51 58 06 13

133 135 137 139 141

40 43 46 49 51

33.1 39.9 43.5 29.4 45.0

+1 1 1 1 +1

32 37 40 42 44

53.8 00.3 17.4 46.5 29.1

27 28 29 30 1

209 210 211 212 213

38 45 51 55 56

00.5 55.1 48.0 30.2 52.0

-2 2 2 2 -2

20 27 34 40 46

Aug.

Sept.

Oct.

103

MERCURY, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Oct.

Nov.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 213 214 215 216 217 218

' 56 55 51 44 34 21

" 52.0 42.2 48.2 56.0 50.1 12.9

º -2 2 2 3 3 3

' 46 52 58 03 07 11

" 40.7 30.9 00.4 06.7 47.0 58.3

7 8 9 10 11 12

219 219 220 220 221 221

03 42 15 44 07 25

45.3 05.8 51.3 36.5 54.1 15.5

-3 3 3 3 3 3

15 18 21 22 23 23

13 14 15 16 17 18

221 221 221 221 221 220

36 40 36 25 05 37

10.7 09.5 42.2 21.4 44.1 33.8

-3 3 3 3 3 2

19 20 21 22 23 24

220 219 218 217 216 215

00 15 21 20 13 01

43.9 21.1 48.9 51.0 33.1 24.1

25 26 27 28 29 30

213 212 211 210 208 208

46 30 15 04 59 02

31 1 2 3 4 5

207 206 206 205 205 206

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Appare Geocent Latitud

16 17 18 19 20 21

º 216 217 218 220 221 223

' 09 32 56 23 50 19

" 41.2 09.4 44.4 05.2 53.9 55.3

º +2 2 1 1 1 1

' 06 02 57 52 46 40

37.2 39.7 01.6 38.1 24.0 13.4

22 23 24 25 26 27

224 226 227 229 230 232

49 20 52 24 56 29

56.4 46.1 15.2 15.9 41.9 27.6

+1 1 1 1 1 1

34 28 21 15 08 01

22 19 15 10 04 56

00.0 36.9 57.1 53.3 18.1 05.1

28 29 30 1 2 3

234 235 237 238 240 241

02 35 09 42 16 49

28.8 41.8 03.8 32.5 06.0 43.0

+0 0 0 0 0 0

54 47 40 33 26 19

-2 2 2 2 1 1

46 34 20 05 48 30

08.8 25.7 54.7 38.7 44.7 24.5

4 5 6 7 8 9

243 244 246 248 249 251

23 57 30 04 38 12

22.6 04.1 47.1 31.4 17.3 04.7

+0 +0 -0 0 0 0

12 05 01 08 15 22

13.8 09.3 27.8 28.5 23.6 09.8

-1 0 0 -0 +0 0

10 50 29 09 10 30

55.0 37.3 55.9 17.1 53.3 11.1

10 11 12 13 14 15

252 254 255 257 259 260

45 19 53 27 01 35

54.3 46.4 41.7 40.9 44.6 53.6

-0 0 0 0 0 0

28 35 41 47 53 59

14 37 11 56 54 02

22.1 10.0 16.3 58.4 11.7 33.5

+0 1 1 1 1 1

48 04 19 32 44 53

15.9 51.4 46.4 54.0 11.7 40.5

16 17 18 19 20 21

262 263 265 266 268 270

10 44 19 53 28 03

08.6 30.5 00.1 38.2 25.9 24.0

-1 1 1 1 1 1

05 10 16 21 26 31

206 206 207 208 209 210

21 50 27 13 06 05

27.4 08.0 44.3 23.0 11.1 17.4

+2 2 2 2 2 2

01 07 11 15 16 17

23.8 27.1 56.9 00.7 46.0 20.3

22 23 24 25 26 27

271 273 274 276 278 279

38 13 49 25 01 37

33.3 54.6 28.8 16.7 18.8 35.6

-1 1 1 1 1 1

35 40 44 47 51 54

211 212 213 214 216

09 19 32 49 09

53.9 16.5 45.0 43.8 41.2

+2 2 2 2 +2

16 15 13 10 06

51.0 25.0 08.6 07.7 27.9

28 29 30 31 32

281 282 284 286 287

14 50 27 05 42

07.7 55.2 58.1 16.4 49.5

-1 2 2 2 -2

57 00 02 04 06

Nov.

Dec.

104

MERCURY, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Apparent Right Ascension

Date

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Jan. 0 1 2 3 4 5

h 18 18 18 18 18 18

m 12 19 26 33 40 47

s 21.48 16.96 13.95 12.34 12.03 12.93

º -24 24 24 24 24 24

' 35 38 39 39 38 35

" 23.3 08.5 32.3 33.7 11.4 24.6

1.431 445 1.434 024 1.436 054 1.437 534 1.438 463 1.438 837

" 6.14 6.13 6.12 6.12 6.11 6.11

" 2.35 2.34 2.34 2.34 2.34 2.34

h 11 11 11 11 11 11

m 37 40 43 46 49 52

s 16 16 18 21 25 30

6 7 8 9 10 11

18 19 19 19 19 19

54 01 08 15 22 29

14.92 17.91 21.77 26.40 31.67 37.47

-24 24 24 24 23 23

31 25 18 09 59 48

12.2 33.3 26.9 52.3 48.6 15.0

1.438 653 1.437 905 1.436 586 1.434 689 1.432 204 1.429 121

6.11 6.12 6.12 6.13 6.14 6.15

2.34 2.34 2.34 2.34 2.35 2.35

11 11 12 12 12 12

55 58 01 05 08 11

36 44 52 01 10 20

12 13 14 15 16 17

19 19 19 19 20 20

36 43 50 58 05 12

43.65 50.09 56.64 03.15 09.46 15.41

-23 23 23 22 22 22

35 20 04 46 27 06

10.9 35.6 28.6 49.4 37.5 52.8

1.425 428 1.421 110 1.416 153 1.410 539 1.404 250 1.397 266

6.17 6.19 6.21 6.23 6.26 6.29

2.36 2.36 2.37 2.38 2.39 2.40

12 12 12 12 12 12

14 17 20 24 27 30

30 40 51 01 11 21

18 19 20 21 22 23

20 20 20 20 20 20

19 26 33 40 47 54

20.80 25.42 29.04 31.42 32.25 31.22

-21 21 20 20 19 19

44 20 55 28 59 29

35.0 44.3 20.8 25.0 57.6 59.6

1.389 564 1.381 122 1.371 914 1.361 915 1.351 096 1.339 429

6.33 6.37 6.41 6.46 6.51 6.57

2.42 2.43 2.45 2.47 2.49 2.51

12 12 12 12 12 12

33 36 39 42 45 48

30 38 44 50 54 55

24 25 26 27 28 29

21 21 21 21 21 21

01 08 15 22 28 35

27.95 22.03 12.98 00.25 43.22 21.16

-18 18 17 17 16 16

58 25 51 15 38 00

32.5 38.1 18.7 37.3 37.5 24.0

1.326 884 1.313 433 1.299 045 1.283 693 1.267 350 1.249 991

6.63 6.70 6.77 6.85 6.94 7.04

2.53 2.56 2.59 2.62 2.65 2.69

12 12 12 13 13 13

51 54 57 00 03 05

54 51 43 32 16 55

30 31 Feb. 1 2 3 4

21 21 21 22 22 22

41 48 54 00 06 12

53.26 18.57 36.00 44.32 42.15 27.91

-15 14 13 13 12 11

21 40 59 17 34 51

02.0 38.2 20.5 18.0 41.6 43.9

1.231 599 1.212 159 1.191 664 1.170 120 1.147 540 1.123 957

7.14 7.25 7.38 7.52 7.66 7.82

2.73 2.77 2.82 2.87 2.93 2.99

13 13 13 13 13 13

08 10 13 15 17 18

27 52 08 15 10 51

5 6 7 8 9 10

22 22 22 22 22 22

17 23 28 32 37 40

59.87 16.09 14.50 52.83 08.72 59.73

-11 10 9 9 8 7

08 25 43 01 21 42

39.2 43.9 16.2 36.5 06.6 10.2

1.099 416 1.073 985 1.047 752 1.020 828 0.993 350 0.965 478

8.00 8.19 8.39 8.61 8.85 9.11

3.06 3.13 3.21 3.29 3.38 3.48

13 13 13 13 13 13

20 21 22 22 22 22

18 28 19 49 55 34

11 12 13 14 15

22 22 22 22 22

44 47 49 51 52

23.37 17.25 39.07 26.80 38.75

-7 6 5 5 -5

05 30 58 30 05

12.2 38.3 54.5 26.4 38.5

0.937 393 0.909 299 0.881 417 0.853 981 0.827 231

9.38 9.67 9.98 10.30 10.63

3.58 3.70 3.81 3.93 4.06

13 13 13 13 13

21 20 18 16 12

45 25 32 04 59

105

MERCURY, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Feb. 15 16 17 18 19 20

h 22 22 22 22 22 22

m 52 53 53 52 51 49

s 38.75 13.68 10.96 30.65 13.60 21.54

º -5 4 4 4 4 4

' 05 44 28 16 09 07

" 38.5 53.3 30.6 46.2 50.9 49.9

0.827 231 0.801 410 0.776 756 0.753 496 0.731 843 0.711 984

" 10.63 10.97 11.32 11.67 12.02 12.35

" 4.06 4.19 4.33 4.46 4.59 4.72

h 13 13 13 13 12 12

m 12 09 04 00 54 48

s 59 17 58 02 31 26

21 22 23 24 25 26

22 22 22 22 22 22

46 44 40 37 33 29

57.13 03.92 46.31 09.38 18.77 20.38

-4 4 4 4 5 5

10 18 30 46 06 28

41.7 17.5 21.5 30.2 14.2 58.8

0.694 082 0.678 269 0.664 642 0.653 262 0.644 151 0.637 298

12.67 12.97 13.23 13.46 13.65 13.80

4.84 4.95 5.06 5.14 5.22 5.27

12 12 12 12 12 12

41 34 27 19 11 04

51 50 28 49 60 06

27 28 29 Mar. 1 2 3

22 22 22 22 22 22

25 21 17 14 10 07

20.18 23.90 36.86 03.76 48.58 54.48

-5 6 6 7 7 8

54 20 48 17 45 12

05.6 55.0 47.3 04.7 12.7 40.9

0.632 656 0.630 147 0.629 667 0.631 093 0.634 285 0.639 096

13.90 13.96 13.97 13.93 13.86 13.76

5.31 5.33 5.34 5.32 5.30 5.26

11 11 11 11 11 11

56 48 40 33 26 19

13 26 51 32 32 54

4 5 6 7 8 9

22 22 22 22 21 21

05 03 01 00 59 59

23.85 18.32 38.82 25.74 38.93 17.90

-8 9 9 9 10 10

39 03 27 48 07 24

03.6 59.8 13.0 30.9 44.8 48.8

0.645 373 0.652 965 0.661 725 0.671 512 0.682 194 0.693 651

13.63 13.47 13.29 13.10 12.89 12.68

5.21 5.15 5.08 5.00 4.93 4.84

11 11 11 10 10 10

13 07 02 57 53 48

40 51 29 32 01 56

10 11 12 13 14 15

21 21 22 22 22 22

59 59 00 01 03 05

21.86 49.80 40.57 52.96 25.68 17.47

-10 10 11 11 11 11

39 52 02 10 16 20

39.7 16.0 37.9 46.5 44.0 33.0

0.705 769 0.718 450 0.731 602 0.745 144 0.759 007 0.773 126

12.46 12.24 12.02 11.80 11.59 11.37

4.76 4.68 4.59 4.51 4.43 4.35

10 10 10 10 10 10

45 41 39 36 34 32

15 57 01 27 12 15

16 17 18 19 20 21

22 22 22 22 22 22

07 09 12 15 18 22

27.07 53.26 34.89 30.86 40.14 01.77

-11 11 11 11 11 11

22 21 19 15 09 01

16.3 57.1 38.8 24.6 17.7 21.4

0.787 447 0.801 923 0.816 512 0.831 177 0.845 889 0.860 621

11.17 10.97 10.77 10.58 10.40 10.22

4.27 4.19 4.12 4.04 3.97 3.90

10 10 10 10 10 10

30 29 28 27 26 25

36 12 04 09 27 58

22 23 24 25 26 27

22 22 22 22 22 22

25 29 33 37 41 45

34.89 18.65 12.33 15.24 26.76 46.33

-10 10 10 10 9 9

51 40 27 12 56 38

38.6 12.3 05.4 20.4 00.0 06.6

0.875 349 0.890 055 0.904 723 0.919 337 0.933 886 0.948 360

10.05 9.88 9.72 9.57 9.42 9.27

3.84 3.78 3.71 3.65 3.60 3.54

10 10 10 10 10 10

25 25 25 25 26 26

39 30 32 42 00 27

28 29 30 31 Apr. 1

22 22 22 23 23

50 54 59 04 09

13.44 47.65 28.55 15.78 09.03

-9 8 8 8 -7

18 57 35 11 46

42.4 49.7 30.6 47.1 41.0

0.962 749 0.977 047 0.991 247 1.005 342 1.019 327

9.13 9.00 8.87 8.75 8.63

3.49 3.44 3.39 3.34 3.30

10 10 10 10 10

27 27 28 29 30

00 41 28 22 21

106

MERCURY, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Apr. 1 2 3 4 5 6

h 23 23 23 23 23 23

m 09 14 19 24 29 34

s 09.03 08.02 12.54 22.37 37.35 57.37

º -7 7 6 6 5 5

' 46 20 52 23 53 21

" 41.0 14.3 28.6 25.6 07.1 34.5

1.019 327 1.033 197 1.046 947 1.060 572 1.074 066 1.087 424

" 8.63 8.51 8.40 8.29 8.19 8.09

" 3.30 3.25 3.21 3.17 3.13 3.09

h 10 10 10 10 10 10

m 30 31 32 33 35 36

s 21 26 36 52 13 38

7 8 9 10 11 12

23 23 23 23 0 0

40 45 51 57 02 08

22.32 52.15 26.82 06.32 50.67 39.92

-4 4 3 3 2 1

48 14 39 03 26 47

49.3 53.1 47.4 33.6 13.2 47.7

1.100 639 1.113 703 1.126 608 1.139 345 1.151 903 1.164 268

7.99 7.90 7.81 7.72 7.63 7.55

3.05 3.02 2.98 2.95 2.92 2.89

10 10 10 10 10 10

38 39 41 43 45 46

09 45 25 10 00 55

13 14 15 16 17 18

0 0 0 0 0 0

14 20 26 32 39 45

34.11 33.34 37.72 47.37 02.45 23.12

-1 -0 +0 0 1 2

08 27 13 56 39 23

18.8 48.1 42.8 12.0 37.6 57.5

1.176 426 1.188 361 1.200 053 1.211 483 1.222 626 1.233 454

7.48 7.40 7.33 7.26 7.19 7.13

2.86 2.83 2.80 2.77 2.75 2.72

10 10 10 10 10 11

48 51 53 55 57 00

55 01 11 27 48 15

19 20 21 22 23 24

0 0 1 1 1 1

51 58 05 11 18 25

49.56 21.99 00.62 45.66 37.35 35.92

+3 3 4 5 6 7

09 55 41 29 17 06

09.5 11.1 59.7 32.1 45.1 34.8

1.243 938 1.254 043 1.263 732 1.272 963 1.281 688 1.289 857

7.07 7.01 6.96 6.91 6.86 6.82

2.70 2.68 2.66 2.64 2.62 2.60

11 11 11 11 11 11

02 05 08 11 14 17

48 27 12 04 03 09

25 26 27 28 29 30

1 1 1 1 2 2

32 39 47 54 02 10

41.58 54.55 15.01 43.11 18.97 02.64

+7 8 9 10 11 12

55 45 35 26 17 07

57.1 47.0 59.3 27.9 05.9 45.9

1.297 414 1.304 299 1.310 446 1.315 786 1.320 248 1.323 755

6.78 6.74 6.71 6.68 6.66 6.64

2.59 2.58 2.56 2.55 2.54 2.54

11 11 11 11 11 11

20 23 27 30 34 38

22 42 10 46 29 21

May 1 2 3 4 5 6

2 2 2 2 2 2

17 25 33 42 50 59

54.09 53.23 59.85 13.63 34.19 00.81

+12 13 14 15 16 17

58 48 38 27 16 03

19.4 37.1 29.1 44.5 11.6 39.2

1.326 233 1.327 605 1.327 798 1.326 744 1.324 382 1.320 660

6.63 6.62 6.62 6.63 6.64 6.66

2.53 2.53 2.53 2.53 2.54 2.54

11 11 11 11 11 12

42 46 50 55 59 04

20 27 41 03 31 05

7 8 9 10 11 12

3 3 3 3 3 3

07 16 24 33 42 51

32.91 09.59 49.88 32.69 16.81 01.01

+17 18 19 19 20 21

49 34 17 59 38 16

54.2 44.5 57.9 22.8 48.4 04.8

1.315 541 1.309 002 1.301 037 1.291 659 1.280 900 1.268 810

6.68 6.72 6.76 6.81 6.87 6.93

2.55 2.57 2.58 2.60 2.62 2.65

12 12 12 12 12 12

08 13 18 23 27 32

43 26 13 01 49 37

13 14 15 16 17

3 4 4 4 4

59 08 17 25 33

43.97 24.38 00.97 32.48 57.71

+21 22 22 23 +23

51 23 53 21 46

03.6 37.8 42.1 12.7 07.6

1.255 457 1.240 922 1.225 301 1.208 696 1.191 216

7.00 7.09 7.18 7.28 7.38

2.68 2.71 2.74 2.78 2.82

12 12 12 12 12

37 42 46 51 55

24 07 45 18 43

107

MERCURY, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

May 17 18 19 20 21 22

h 4 4 4 4 5 5

m 33 42 50 58 06 13

s 57.71 15.56 24.98 25.04 14.88 53.73

º +23 24 24 24 24 25

' 46 08 28 45 59 12

" 07.6 26.0 08.9 18.3 57.2 09.6

1.191 216 1.172 973 1.154 076 1.134 636 1.114 754 1.094 530

" 7.38 7.50 7.62 7.75 7.89 8.03

" 2.82 2.86 2.91 2.96 3.01 3.07

h 12 13 13 13 13 13

m 55 00 04 08 11 15

s 43 01 09 08 56 33

23 24 25 26 27 28

5 5 5 5 5 5

21 28 35 42 49 55

20.90 35.76 37.74 26.35 01.11 21.60

+25 25 25 25 25 25

22 29 34 38 39 39

00.2 34.3 57.5 15.8 35.5 02.9

1.074 054 1.053 410 1.032 675 1.011 917 0.991 200 0.970 579

8.19 8.35 8.52 8.69 8.87 9.06

3.13 3.19 3.25 3.32 3.39 3.46

13 13 13 13 13 13

18 22 25 27 30 32

57 09 07 52 22 38

29 30 31 June 1 2 3

6 6 6 6 6 6

01 07 12 18 23 28

27.42 18.20 53.56 13.18 16.70 03.80

+25 25 25 25 25 25

36 32 27 20 11 02

44.3 46.3 15.1 17.1 58.7 26.1

0.950 105 0.929 824 0.909 776 0.889 998 0.870 523 0.851 382

9.26 9.46 9.67 9.88 10.10 10.33

3.54 3.61 3.69 3.78 3.86 3.95

13 13 13 13 13 13

34 36 37 39 40 40

39 25 55 09 06 47

4 5 6 7 8 9

6 6 6 6 6 6

32 36 40 44 47 50

34.14 47.39 43.23 21.32 41.33 42.94

+24 24 24 24 23 23

51 40 27 13 59 44

45.3 02.6 23.8 54.9 41.6 49.8

0.832 604 0.814 216 0.796 242 0.778 708 0.761 637 0.745 054

10.56 10.80 11.04 11.29 11.55 11.80

4.04 4.13 4.22 4.31 4.41 4.51

13 13 13 13 13 13

41 41 41 40 39 38

12 18 08 39 52 46

10 11 12 13 14 15

6 6 6 6 7 7

53 55 57 59 01 02

25.83 49.72 54.33 39.43 04.82 10.38

+23 23 22 22 22 22

29 13 57 40 24 07

25.1 33.2 19.5 49.6 09.0 23.1

0.728 982 0.713 446 0.698 472 0.684 085 0.670 314 0.657 187

12.06 12.33 12.59 12.86 13.12 13.38

4.61 4.71 4.81 4.91 5.01 5.11

13 13 13 13 13 13

37 35 33 31 28 25

22 39 36 13 31 30

16 17 18 19 20 21

7 7 7 7 7 7

02 03 03 03 02 01

56.05 21.89 28.03 14.77 42.55 51.98

+21 21 21 21 20 20

50 33 17 01 45 29

37.4 57.3 28.1 15.3 24.1 59.9

0.644 734 0.632 987 0.621 980 0.611 747 0.602 322 0.593 744

13.64 13.89 14.14 14.38 14.60 14.81

5.21 5.31 5.40 5.49 5.58 5.66

13 13 13 13 13 13

22 18 14 10 05 00

08 27 27 07 29 33

22 23 24 25 26 27

7 6 6 6 6 6

00 59 57 55 53 51

43.86 19.22 39.27 45.48 39.54 23.34

+20 20 19 19 19 19

15 00 47 34 22 11

08.0 53.6 21.8 37.6 45.9 51.5

0.586 048 0.579 271 0.573 451 0.568 624 0.564 823 0.562 082

15.01 15.18 15.34 15.47 15.57 15.65

5.73 5.80 5.86 5.91 5.95 5.98

12 12 12 12 12 12

55 49 44 38 32 25

21 52 10 14 08 52

28 29 30 July 1 2

6 6 6 6 6

48 46 43 41 38

58.99 28.76 55.06 20.40 47.33

+19 18 18 18 +18

01 53 45 39 34

58.6 11.6 34.0 09.3 00.1

0.560 429 0.559 891 0.560 491 0.562 247 0.565 171

15.69 15.71 15.69 15.64 15.56

6.00 6.00 5.99 5.98 5.95

12 12 12 12 11

19 13 06 00 53

29 02 33 04 38

108

MERCURY, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

July 1 2 3 4 5 6

h 6 6 6 6 6 6

m 41 38 36 33 31 29

s 20.40 47.33 18.41 56.14 42.92 41.01

º +18 18 18 18 18 18

' 39 34 30 27 26 26

" 09.3 00.1 08.7 36.4 24.0 31.3

0.562 247 0.565 171 0.569 273 0.574 556 0.581 018 0.588 653

" 15.64 15.56 15.45 15.31 15.14 14.94

" 5.98 5.95 5.90 5.85 5.78 5.71

h 12 11 11 11 11 11

m 00 53 47 41 35 29

s 04 38 17 04 01 10

7 8 9 10 11 12

6 6 6 6 6 6

27 26 25 24 23 23

52.53 19.37 03.22 05.58 27.71 10.66

+18 18 18 18 18 18

27 30 34 39 46 53

57.3 40.3 37.6 45.8 00.5 16.9

0.597 450 0.607 393 0.618 464 0.630 642 0.643 900 0.658 212

14.72 14.48 14.22 13.94 13.66 13.36

5.62 5.53 5.43 5.33 5.22 5.10

11 11 11 11 11 10

23 18 13 08 04 59

33 13 10 25 01 58

13 14 15 16 17 18

6 6 6 6 6 6

23 23 24 25 27 29

15.32 42.36 32.33 45.61 22.47 23.07

+19 19 19 19 19 19

01 10 20 30 41 52

29.2 31.1 15.7 35.5 22.7 28.6

0.673 547 0.689 873 0.707 156 0.725 358 0.744 441 0.764 363

13.06 12.75 12.44 12.12 11.81 11.51

4.99 4.87 4.75 4.63 4.51 4.40

10 10 10 10 10 10

56 52 50 47 45 43

17 58 03 30 21 36

19 20 21 22 23 24

6 6 6 6 6 6

31 34 37 41 45 49

47.49 35.72 47.67 23.19 22.07 44.03

+20 20 20 20 20 20

03 15 26 36 47 56

44.4 00.7 07.8 55.5 13.2 50.2

0.785 079 0.806 539 0.828 691 0.851 476 0.874 830 0.898 683

11.20 10.90 10.61 10.33 10.05 9.79

4.28 4.17 4.05 3.95 3.84 3.74

10 10 10 10 10 10

42 41 40 40 40 41

15 17 43 32 45 21

25 26 27 28 29 30

6 6 7 7 7 7

54 59 05 10 17 23

28.71 35.68 04.41 54.24 04.42 34.03

+21 21 21 21 21 21

05 13 19 24 28 29

35.2 16.8 43.5 43.8 06.2 39.6

0.922 956 0.947 564 0.972 411 0.997 395 1.022 402 1.047 314

9.53 9.28 9.04 8.82 8.60 8.40

3.64 3.55 3.46 3.37 3.29 3.21

10 10 10 10 10 10

42 43 45 47 49 52

19 39 21 23 46 28

31 Aug. 1 2 3 4 5

7 7 7 7 8 8

30 37 44 52 00 08

22.03 27.20 48.15 23.37 11.18 09.81

+21 21 21 21 21 20

29 26 21 14 04 52

13.3 37.4 43.1 22.6 29.9 00.6

1.072 002 1.096 333 1.120 171 1.143 381 1.165 828 1.187 385

8.20 8.02 7.85 7.69 7.54 7.41

3.13 3.06 3.00 2.94 2.88 2.83

10 10 11 11 11 11

55 58 02 06 09 14

28 44 16 01 58 05

6 7 8 9 10 11

8 8 8 8 8 8

16 24 32 41 49 58

17.38 31.99 51.74 14.75 39.24 03.56

+20 20 19 19 19 18

36 19 58 35 10 42

52.2 04.2 38.1 37.1 06.5 12.7

1.207 936 1.227 377 1.245 621 1.262 599 1.278 260 1.292 574

7.28 7.16 7.06 6.97 6.88 6.80

2.78 2.74 2.70 2.66 2.63 2.60

11 11 11 11 11 11

18 22 27 31 36 40

21 42 08 36 05 33

12 13 14 15 16

9 9 9 9 9

06 14 23 31 39

26.19 45.80 01.23 11.50 15.82

+18 17 17 16 +15

12 39 05 29 51

03.7 48.1 35.5 35.5 58.2

1.305 527 1.317 126 1.327 388 1.336 347 1.344 043

6.74 6.68 6.63 6.58 6.54

2.57 2.55 2.53 2.51 2.50

11 11 11 11 12

44 49 53 57 01

59 21 38 49 55

109

MERCURY, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Aug. 16 17 18 19 20 21

h 9 9 9 10 10 10

m 39 47 55 02 10 17

s 15.82 13.55 04.23 47.51 23.19 51.14

º +15 15 14 13 13 12

' 51 12 32 50 08 25

" 58.2 53.3 30.4 58.7 26.9 03.3

1.344 043 1.350 528 1.355 854 1.360 081 1.363 266 1.365 470

" 6.54 6.51 6.49 6.47 6.45 6.44

" 2.50 2.49 2.48 2.47 2.46 2.46

h 12 12 12 12 12 12

m 01 05 09 13 17 20

s 55 53 44 28 03 31

22 23 24 25 26 27

10 10 10 10 10 10

25 32 39 46 53 59

11.35 23.87 28.79 26.28 16.50 59.67

+11 10 10 9 8 7

40 56 10 25 39 53

55.4 10.4 54.8 14.5 15.3 02.0

1.366 751 1.367 164 1.366 764 1.365 599 1.363 719 1.361 166

6.43 6.43 6.43 6.44 6.45 6.46

2.46 2.46 2.46 2.46 2.46 2.47

12 12 12 12 12 12

23 27 30 33 35 38

51 04 09 06 56 40

28 29 30 31 Sept. 1 2

11 11 11 11 11 11

06 13 19 25 31 38

36.01 05.76 29.15 46.43 57.85 03.64

+7 6 5 4 4 3

06 20 33 47 00 14

39.3 11.5 42.3 15.4 54.0 40.9

1.357 981 1.354 200 1.349 857 1.344 982 1.339 602 1.333 742

6.48 6.49 6.51 6.54 6.56 6.59

2.47 2.48 2.49 2.50 2.51 2.52

12 12 12 12 12 12

41 43 46 48 50 52

16 46 10 28 40 46

3 4 5 6 7 8

11 11 11 12 12 12

44 49 55 01 07 12

04.03 59.23 49.48 34.95 15.83 52.31

+2 1 0 +0 -0 1

28 42 57 12 32 17

39.1 51.0 19.1 05.4 47.8 18.6

1.327 424 1.320 666 1.313 485 1.305 896 1.297 913 1.289 546

6.62 6.66 6.70 6.73 6.78 6.82

2.53 2.54 2.56 2.57 2.59 2.61

12 12 12 13 13 13

54 56 58 00 02 03

48 44 35 22 04 41

9 10 11 12 13 14

12 12 12 12 12 12

18 23 29 34 39 45

24.52 52.61 16.70 36.89 53.27 05.90

-2 2 3 4 4 5

01 45 28 11 53 34

25.1 05.5 18.0 00.8 12.4 50.9

1.280 805 1.271 697 1.262 230 1.252 409 1.242 239 1.231 722

6.87 6.92 6.97 7.02 7.08 7.14

2.62 2.64 2.66 2.68 2.70 2.73

13 13 13 13 13 13

05 06 08 09 10 12

15 44 10 31 49 03

15 16 17 18 19 20

12 12 13 13 13 13

50 55 00 05 10 15

14.81 20.03 21.55 19.35 13.35 03.48

-6 6 7 8 8 9

15 56 36 15 53 31

54.6 21.9 10.9 19.9 47.0 30.3

1.220 862 1.209 660 1.198 117 1.186 236 1.174 016 1.161 457

7.20 7.27 7.34 7.41 7.49 7.57

2.75 2.78 2.80 2.83 2.86 2.89

13 13 13 13 13 13

13 14 15 16 17 18

14 20 23 22 18 09

21 22 23 24 25 26

13 13 13 13 13 13

19 24 29 33 38 42

49.62 31.60 09.23 42.27 10.44 33.40

-10 10 11 11 12 13

08 44 19 54 27 00

27.7 37.1 56.1 22.5 53.5 26.3

1.148 560 1.135 326 1.121 756 1.107 851 1.093 611 1.079 041

7.66 7.75 7.84 7.94 8.04 8.15

2.93 2.96 3.00 3.03 3.07 3.11

13 13 13 13 13 13

18 19 20 20 21 21

57 40 18 52 21 44

27 28 29 30 Oct. 1

13 13 13 13 14

46 51 55 59 02

50.77 02.10 06.88 04.51 54.33

-13 14 14 14 -15

31 02 31 59 26

58.0 25.3 44.6 52.1 43.4

1.064 143 1.048 921 1.033 382 1.017 534 1.001 386

8.26 8.38 8.51 8.64 8.78

3.16 3.20 3.25 3.30 3.36

13 13 13 13 13

22 22 22 22 22

02 13 17 14 03

110

MERCURY, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Oct. 1 2 3 4 5 6

h 14 14 14 14 14 14

m 02 06 10 13 16 19

s 54.33 35.58 07.42 28.87 38.89 36.26

º -15 15 16 16 16 17

' 26 52 16 38 59 18

" 43.4 13.8 18.3 50.9 45.4 54.6

1.001 386 0.984 951 0.968 245 0.951 288 0.934 104 0.916 723

" 8.78 8.93 9.08 9.24 9.41 9.59

" 3.36 3.41 3.47 3.53 3.60 3.67

h 13 13 13 13 13 13

m 22 21 21 20 19 18

s 03 42 12 30 37 30

7 8 9 10 11 12

14 14 14 14 14 14

22 24 26 28 30 31

19.69 47.72 58.78 51.17 23.09 32.66

-17 17 18 18 18 18

36 51 04 15 23 28

10.6 24.6 26.8 06.5 11.6 29.1

0.899 180 0.881 520 0.863 794 0.846 066 0.828 407 0.810 907

9.78 9.98 10.18 10.39 10.62 10.84

3.74 3.81 3.89 3.97 4.06 4.14

13 13 13 13 13 13

17 15 13 11 08 05

09 31 36 21 45 45

13 14 15 16 17 18

14 14 14 14 14 14

32 32 32 31 30 28

17.93 36.99 28.02 49.39 39.82 58.53

-18 18 18 18 18 17

30 29 25 16 04 47

44.9 43.8 10.2 48.4 23.4 42.0

0.793 667 0.776 805 0.760 461 0.744 790 0.729 972 0.716 204

11.08 11.32 11.56 11.81 12.05 12.28

4.23 4.33 4.42 4.51 4.60 4.69

13 12 12 12 12 12

02 58 54 49 43 38

20 28 08 17 55 02

19 20 21 22 23 24

14 14 14 14 14 14

26 24 20 17 13 08

45.44 01.36 48.23 09.19 08.78 52.79

-17 17 16 15 15 14

26 00 30 56 18 36

34.3 56.0 49.9 28.8 17.1 52.3

0.703 704 0.692 708 0.683 460 0.676 209 0.671 196 0.668 646

12.50 12.70 12.87 13.01 13.10 13.15

4.77 4.85 4.92 4.97 5.01 5.03

12 12 12 12 12 11

31 24 17 09 01 53

38 44 23 38 35 21

25 26 27 28 29 30

14 14 13 13 13 13

04 00 55 51 48 44

28.21 02.82 44.84 42.41 03.06 53.30

-13 13 12 11 10 10

53 07 22 38 56 18

05.1 57.8 41.5 31.2 40.7 17.5

0.668 747 0.671 645 0.677 425 0.686 106 0.697 638 0.711 899

13.15 13.09 12.98 12.82 12.61 12.35

5.02 5.00 4.96 4.90 4.82 4.72

11 11 11 11 11 11

45 36 28 20 13 06

01 44 39 53 32 43

31 Nov. 1 2 3 4 5

13 13 13 13 13 13

42 40 39 38 38 39

18.30 21.73 05.72 30.99 37.04 22.40

-9 9 8 8 8 8

44 15 52 34 23 17

18.5 27.1 12.0 47.6 15.4 26.3

0.728 705 0.747 817 0.768 957 0.791 821 0.816 093 0.841 456

12.07 11.76 11.44 11.11 10.78 10.45

4.61 4.49 4.37 4.24 4.12 3.99

11 10 10 10 10 10

00 54 50 45 42 39

31 57 04 52 20 26

6 7 8 9 10 11

13 13 13 13 13 13

40 42 45 48 51 55

44.87 41.77 10.18 07.05 29.39 14.34

-8 8 8 8 9 9

17 21 30 44 01 21

02.9 42.0 56.7 18.4 18.1 27.4

0.867 607 0.894 260 0.921 156 0.948 066 0.974 788 1.001 154

10.14 9.83 9.55 9.28 9.02 8.78

3.87 3.76 3.65 3.54 3.45 3.36

10 10 10 10 10 10

37 35 34 33 32 32

07 22 07 19 55 52

12 13 14 15 16

13 14 14 14 14

59 03 08 13 18

19.23 41.63 19.34 10.42 13.16

-9 10 10 11 -11

44 09 36 05 34

19.2 28.4 31.6 08.1 58.9

1.027 024 1.052 283 1.076 843 1.100 634 1.123 608

8.56 8.36 8.17 7.99 7.83

3.27 3.19 3.12 3.05 2.99

10 10 10 10 10

33 33 34 35 36

09 42 29 29 40

111

MERCURY, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Nov. 16 17 18 19 20 21

h 14 14 14 14 14 14

m 18 23 28 34 39 45

s 13.16 26.06 47.84 17.39 53.76 36.16

º -11 12 12 13 13 14

' 34 05 37 09 41 14

" 58.9 47.1 17.9 18.1 36.0 01.5

1.123 608 1.145 730 1.166 978 1.187 342 1.206 817 1.225 409

" 7.83 7.68 7.54 7.41 7.29 7.18

" 2.99 2.93 2.88 2.83 2.78 2.74

h 10 10 10 10 10 10

m 36 38 39 41 42 44

s 40 00 29 05 48 37

22 23 24 25 26 27

14 14 15 15 15 15

51 57 03 09 15 21

23.92 16.46 13.30 14.06 18.40 26.04

-14 15 15 16 16 17

46 18 50 22 53 23

25.6 40.4 38.9 15.2 23.8 59.9

1.243 126 1.259 980 1.275 986 1.291 163 1.305 527 1.319 099

7.07 6.98 6.89 6.81 6.74 6.67

2.70 2.67 2.63 2.60 2.57 2.55

10 10 10 10 10 10

46 48 50 52 54 56

30 28 31 37 46 59

28 29 30 Dec. 1 2 3

15 15 15 15 15 15

27 33 40 46 52 59

36.75 50.36 06.71 25.66 47.11 10.98

-17 18 18 19 19 20

53 23 51 19 46 12

59.2 18.1 53.0 41.0 39.1 44.8

1.331 897 1.343 940 1.355 247 1.365 836 1.375 725 1.384 929

6.60 6.54 6.49 6.44 6.39 6.35

2.52 2.50 2.48 2.46 2.44 2.43

10 11 11 11 11 11

59 01 03 06 08 11

15 33 54 18 44 13

4 5 6 7 8 9

16 16 16 16 16 16

05 12 18 25 31 38

37.19 05.68 36.40 09.30 44.34 21.48

-20 21 21 21 22 22

37 02 25 47 08 28

55.8 09.9 25.1 39.3 50.8 57.9

1.393 464 1.401 344 1.408 583 1.415 193 1.421 185 1.426 569

6.31 6.28 6.24 6.21 6.19 6.16

2.41 2.40 2.39 2.37 2.36 2.36

11 11 11 11 11 11

13 16 18 21 24 26

44 17 53 30 10 52

10 11 12 13 14 15

16 16 16 17 17 17

45 51 58 05 11 18

00.69 41.94 25.17 10.35 57.43 46.35

-22 23 23 23 23 24

47 05 22 38 52 05

58.8 52.1 36.1 09.4 30.6 38.2

1.431 354 1.435 547 1.439 155 1.442 184 1.444 639 1.446 523

6.14 6.13 6.11 6.10 6.09 6.08

2.35 2.34 2.33 2.33 2.33 2.32

11 11 11 11 11 11

29 32 35 37 40 43

36 22 10 60 52 45

16 17 18 19 20 21

17 17 17 17 17 18

25 32 39 46 53 00

37.06 29.49 23.58 19.25 16.41 15.00

-24 24 24 24 24 24

17 28 37 45 52 57

31.0 07.4 26.3 26.3 06.1 24.5

1.447 838 1.448 587 1.448 770 1.448 387 1.447 435 1.445 913

6.07 6.07 6.07 6.07 6.08 6.08

2.32 2.32 2.32 2.32 2.32 2.32

11 11 11 11 11 12

46 49 52 55 58 01

41 38 36 37 38 41

22 23 24 25 26 27

18 18 18 18 18 18

07 14 21 28 35 42

14.89 16.01 18.24 21.45 25.53 30.31

-25 25 25 25 25 24

01 03 04 04 02 59

20.3 52.3 59.5 40.6 54.7 40.7

1.443 817 1.441 141 1.437 879 1.434 024 1.429 568 1.424 500

6.09 6.10 6.12 6.13 6.15 6.17

2.33 2.33 2.34 2.34 2.35 2.36

12 12 12 12 12 12

04 07 10 14 17 20

46 51 58 05 14 23

28 29 30 31 32

18 18 19 19 19

49 56 03 10 17

35.66 41.41 47.36 53.33 59.09

-24 24 24 24 -24

54 48 41 31 20

57.7 44.7 01.1 45.9 58.7

1.418 809 1.412 483 1.405 508 1.397 870 1.389 550

6.20 6.23 6.26 6.29 6.33

2.37 2.38 2.39 2.40 2.42

12 12 12 12 12

23 26 29 33 36

32 42 52 01 11

112

VENUS, 2020 h HELIOCENTRIC POSITIONS FOR 0 TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 4 7 10 13 17 20

' 26 37 48 59 10 22

" º ' " 07.4 -3 14 12.6 08.9 3 10 30.1 16.1 3 06 12.2 29.0 3 01 19.7 47.7 2 55 53.4 12.3 2 49 54.1

º 0.726 2658 Apr. 2 152 0.726 0446 4 155 0.725 8149 6 159 0.725 5773 8 162 0.725 3326 10 165 0.725 0816 12 168

' 40 55 10 25 40 54

" º ' " 29.1 +3 17 29.8 28.3 3 20 00.2 24.7 3 21 52.2 17.7 3 23 05.2 06.5 3 23 39.1 50.5 3 23 34.0

0.718 7671 0.718 8719 0.718 9908 0.719 1233 0.719 2691 0.719 4278

13 15 17 19 21 23

23 26 29 33 36 39

33 45 57 08 20 32

42.9 -2 43 23.1 19.5 2 36 21.4 02.3 2 28 50.3 51.4 2 20 51.1 46.7 2 12 25.2 48.5 2 03 34.2

0.724 8251 0.724 5637 0.724 2984 0.724 0300 0.723 7592 0.723 4870

09 24 38 52 06 20

28.9 +3 22 49.8 01.2 3 21 26.7 26.7 3 19 25.1 44.8 3 16 45.4 55.0 3 13 28.3 56.7 3 09 34.3

0.719 5987 0.719 7813 0.719 9751 0.720 1794 0.720 3936 0.720 6169

25 27 29 31 Feb. 2 4

42 45 49 52 55 58

44 57 09 22 34 47

56.8 -1 54 19.7 11.6 1 44 43.3 33.2 1 34 46.8 01.6 1 24 32.1 36.8 1 14 01.0 18.9 1 03 15.5

0.723 2142 26 191 34 49.6 +3 05 04.4 0.722 9416 28 194 48 33.0 2 59 59.4 0.722 6701 30 198 02 06.8 2 54 20.5 0.722 4006 May 2 201 15 30.5 2 48 08.8 0.722 1339 4 204 28 43.8 2 41 25.5 0.721 8708 6 207 41 46.6 2 34 12.0

0.720 8487 0.721 0883 0.721 3348 0.721 5875 0.721 8456 0.722 1082

6 8 10 12 14 16

62 65 68 71 74 78

00 13 26 39 52 06

08.1 -0 52 17.7 04.3 0 41 09.5 07.7 0 29 53.0 18.3 0 18 30.4 36.0 -0 07 03.9 01.0 +0 04 24.4

0.721 6122 0.721 3589 0.721 1116 0.720 8713 0.720 6386 0.720 4144

8 10 12 14 16 18

210 214 217 220 223 226

54 07 19 32 44 56

38.6 +2 26 29.7 19.9 2 18 20.2 50.2 2 09 45.0 09.6 2 00 45.8 18.1 1 51 24.5 15.8 1 41 42.7

0.722 3747 0.722 6440 0.722 9153 0.723 1879 0.723 4609 0.723 7334

18 20 22 24 26 28

81 84 87 91 94 97

19 33 46 00 14 28

33.1 +0 15 52.4 12.4 0 27 17.6 58.8 0 38 38.1 52.1 0 49 51.5 52.3 1 00 55.8 59.2 1 11 48.7

0.720 1992 0.719 9939 0.719 7990 0.719 6152 0.719 4431 0.719 2833

20 22 24 26 28 30

230 233 236 239 242 246

08 19 31 42 53 04

03.1 +1 31 42.4 39.8 1 21 25.4 06.5 1 10 53.7 23.4 1 00 09.4 30.7 0 49 14.3 29.0 0 38 10.6

0.724 0045 0.724 2735 0.724 5396 0.724 8018 0.725 0594 0.725 3116

1 3 5 7 9 11

100 103 107 110 113 116

43 57 11 26 41 55

12.5 +1 22 28.2 32.2 1 32 52.1 57.8 1 42 58.4 29.2 1 52 45.2 05.9 2 02 10.5 47.5 2 11 12.4

0.719 1362 June 1 0.719 0024 3 0.718 8822 5 0.718 7761 7 0.718 6844 9 0.718 6074 11

249 252 255 258 261 265

15 25 36 46 57 07

18.5 +0 27 00.3 59.8 0 15 45.4 33.4 +0 04 28.1 59.7 -0 06 49.6 19.3 0 18 05.7 32.8 0 29 18.1

0.725 5576 0.725 7967 0.726 0282 0.726 2513 0.726 4653 0.726 6697

13 15 17 19 21 23

120 123 126 129 133 136

10 25 40 55 10 25

33.7 +2 19 49.2 24.0 2 27 59.2 17.9 2 35 40.8 14.9 2 42 52.4 14.4 2 49 32.6 15.7 2 55 40.1

0.718 5454 0.718 4985 0.718 4669 0.718 4508 0.718 4501 0.718 4648

268 271 274 277 280 284

17 27 37 47 57 07

40.5 -0 40 24.7 43.2 0 51 23.6 41.5 1 02 12.7 35.8 1 12 50.1 26.8 1 23 14.0 15.0 1 33 22.3

0.726 8637 0.727 0469 0.727 2186 0.727 3783 0.727 5255 0.727 6598

25 27 29 31 Apr. 2

139 142 146 149 152

40 55 10 25 40

18.4 +3 01 13.8 21.8 3 06 12.5 25.1 3 10 35.3 27.8 3 14 21.3 29.1 +3 17 29.8

0.718 4950 25 287 17 01.0 -1 0.718 5405 27 290 26 45.4 1 0.718 6012 29 293 36 28.6 2 0.718 6768 July 1 296 46 11.3 2 0.718 7671 3 299 55 53.9 -2

Jan.

Mar.

14 16 18 20 22 24

13 15 17 19 21 23

172 175 178 181 185 188

43 52 01 10 19

13.5 45.5 56.9 45.8 10.8

0.727 7808 0.727 8880 0.727 9813 0.728 0602 0.728 1246

113

VENUS, 2020 h HELIOCENTRIC POSITIONS FOR 0 TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

1 3 5 7 9 11

º 296 299 303 306 309 312

' 46 55 05 15 25 34

" º ' " 11.3 -2 10 45.8 53.9 2 19 10.8 36.9 2 27 10.3 20.8 2 34 42.9 06.0 2 41 47.3 53.0 2 48 22.1

0.728 0602 Oct. 1 0.728 1246 3 0.728 1742 5 0.728 2090 7 0.728 2287 9 0.728 2333 11

13 15 17 19 21 23

315 318 322 325 328 331

44 54 04 14 24 34

42.0 -2 54 26.1 33.7 2 59 58.4 28.1 3 04 57.8 25.7 3 09 23.4 26.8 3 13 14.4 31.7 3 16 30.1

0.728 2229 0.728 1973 0.728 1568 0.728 1014 0.728 0313 0.727 9467

25 27 29 31 Aug. 2 4

334 337 341 344 347 350

44 54 05 15 26 36

40.5 -3 19 09.9 53.5 3 21 13.3 11.0 3 22 39.8 33.1 3 23 29.2 00.0 3 23 41.2 31.9 3 23 15.8

July

Sept.

Oct.

Heliocentric Heliocentric Longitude Latitude

Radius Vector

º 83 86 89 93 96 99

' 25 39 52 06 21 35

" º ' " 22.4 +0 23 16.9 06.5 0 34 39.3 57.6 0 45 55.5 55.7 0 57 03.2 00.7 1 08 00.4 12.2 1 18 44.9

0.720 0601 0.719 8592 0.719 6692 0.719 4907 0.719 3243 0.719 1705

13 15 17 19 21 23

102 106 109 112 115 119

49 03 18 33 47 02

30.2 +1 29 14.5 54.4 1 39 27.3 24.5 1 49 21.2 00.1 1 58 54.3 40.8 2 08 04.7 26.3 2 16 50.5

0.719 0298 0.718 9027 0.718 7896 0.718 6909 0.718 6069 0.718 5378

0.727 8478 0.727 7350 0.727 6085 0.727 4687 0.727 3162 Nov. 0.727 1512

25 27 29 31 2 4

122 125 128 132 135 138

17 32 47 02 17 32

16.2 +2 25 10.1 09.9 2 33 01.9 06.9 2 40 24.2 06.6 2 47 15.7 08.5 2 53 34.9 12.0 2 59 20.6

0.718 4839 0.718 4454 0.718 4223 0.718 4148 0.718 4229 0.718 4465

6 353 47 08.8 -3 22 13.0 8 356 57 50.9 3 20 32.9 10 360 08 38.3 3 18 15.8 12 3 19 31.2 3 15 22.1 14 6 30 29.7 3 11 52.1 16 9 41 33.7 3 07 46.6

0.726 9744 0.726 7863 0.726 5873 0.726 3782 0.726 1596 0.725 9321

6 8 10 12 14 16

141 145 148 151 154 158

47 02 17 32 47 02

16.4 +3 04 31.7 21.1 3 09 07.2 25.3 3 13 06.2 28.4 3 16 28.0 29.7 3 19 11.8 28.5 3 21 17.3

0.718 4857 0.718 5401 0.718 6098 0.718 6944 0.718 7937 0.718 9073

18 20 22 24 26 28

12 16 19 22 25 28

52 03 15 26 38 50

43.4 -3 03 06.2 59.0 2 57 51.6 20.5 2 52 03.9 47.9 2 45 43.9 21.4 2 38 52.9 01.1 2 31 32.0

0.725 6964 0.725 4532 0.725 2033 0.724 9475 0.724 6865 0.724 4212

18 20 22 24 26 28

161 164 167 171 174 177

17 32 47 01 16 30

24.1 +3 22 44.0 15.8 3 23 31.7 02.9 3 23 40.2 44.6 3 23 09.6 20.4 3 22 00.1 49.6 3 20 11.9

0.719 0349 0.719 1760 0.719 3303 0.719 4971 0.719 6760 0.719 8664

30 1 3 5 7 9

32 35 38 41 44 48

01 13 25 37 49 02

47.0 -2 23 42.5 39.2 2 15 25.9 37.9 2 06 43.6 43.1 1 57 37.2 54.9 1 48 08.3 13.5 1 38 18.8

0.724 1523 30 0.723 8808 Dec. 2 0.723 6074 4 0.723 3329 6 0.723 0584 8 0.722 7845 10

180 183 187 190 193 196

45 59 13 27 41 54

11.7 +3 17 45.5 25.9 3 14 41.3 31.9 3 11 00.1 29.1 3 06 42.7 17.0 3 01 49.8 55.3 2 56 22.6

0.720 0677 0.720 2792 0.720 5002 0.720 7301 0.720 9681 0.721 2134

11 13 15 17 19 21

51 54 57 60 64 67

14 27 39 52 05 18

38.8 -1 28 10.3 11.1 1 17 44.8 50.3 1 07 04.2 36.6 0 56 10.4 29.9 0 45 05.6 30.5 0 33 51.9

0.722 5123 0.722 2425 0.721 9759 0.721 7135 0.721 4561 0.721 2044

12 14 16 18 20 22

200 203 206 209 213 216

08 21 34 47 00 13

23.6 +2 50 22.1 41.6 2 43 49.6 49.1 2 36 46.5 45.8 2 29 14.0 31.7 2 21 13.7 06.6 2 12 47.3

0.721 4652 0.721 7228 0.721 9854 0.722 2520 0.722 5219 0.722 7942

23 25 27 29 1

70 73 76 80 83

31 44 58 11 25

38.4 53.5 15.9 45.5 22.4

0.720 9593 0.720 7216 0.720 4920 0.720 2713 0.720 0601

24 26 28 30 32

219 222 225 229 232

25 37 49 01 13

30.5 +2 03 56.3 43.5 1 54 42.4 45.6 1 45 07.6 37.1 1 35 13.4 18.0 +1 25 02.1

0.723 0681 0.723 3427 0.723 6171 0.723 8905 0.724 1620

-0 -0 +0 0 +0

22 11 00 11 23

31.2 05.8 22.1 50.4 16.9

114

VENUS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Jan.

Feb.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

0 1 2 3 4 5

º 313 314 315 316 318 319

' 10 24 38 51 04 18

" 56.8 30.7 01.9 30.4 55.9 18.5

º -1 1 1 1 1 1

' 50 50 49 49 48 47

" 47.8 20.6 48.2 10.5 27.5 39.1

6 7 8 9 10 11

320 321 322 324 325 326

31 44 58 11 24 37

38.0 54.3 07.3 16.9 23.0 25.5

-1 1 1 1 1 1

46 45 44 43 42 40

12 13 14 15 16 17

327 329 330 331 332 333

50 03 16 28 41 54

24.4 19.4 10.6 57.8 41.2 20.6

-1 1 1 1 1 1

18 19 20 21 22 23

335 336 337 338 339 341

06 19 31 44 56 08

56.0 27.3 54.5 17.3 35.7 49.5

24 25 26 27 28 29

342 343 344 345 347 348

20 33 45 56 08 20

30 31 1 2 3 4

349 350 351 353 354 355

5 6 7 8 9 10 11 12 13 14 15

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

15 16 17 18 19 20

º 8 9 10 11 12 14

' 21 31 40 49 58 07

" 49.8 17.6 36.5 46.0 46.1 36.5

º -0 +0 0 0 0 0

' 00 03 07 11 16 20

" 58.5 11.9 25.7 42.8 03.0 26.3

45.5 46.5 42.1 32.4 17.2 56.8

21 22 23 24 25 26

15 16 17 18 19 20

16 24 33 41 49 56

16.8 46.8 06.2 14.6 11.9 57.5

+0 0 0 0 0 0

24 29 33 38 43 47

52.5 21.6 53.4 27.8 04.7 43.9

39 37 36 34 32 31

30.9 59.7 23.2 41.3 54.1 01.6

27 28 29 1 2 3

22 23 24 25 26 27

04 11 19 25 32 39

31.3 52.8 01.7 57.6 40.2 08.9

+0 0 1 1 1 1

52 57 01 06 11 16

25.4 09.0 54.6 42.0 31.0 21.7

-1 1 1 1 1 1

29 27 24 22 20 17

03.9 00.8 52.6 39.1 20.4 56.6

4 5 6 7 8 9

28 29 30 32 33 34

45 51 57 02 07 12

23.4 23.1 07.8 36.8 49.7 46.0

+1 1 1 1 1 1

21 26 31 35 40 45

13.7 06.9 01.2 56.5 52.5 49.0

58.6 02.6 01.6 55.2 43.2 25.6

-1 1 1 1 1 1

15 12 10 07 04 01

27.6 53.6 14.5 30.3 41.2 47.1

10 11 12 13 14 15

35 36 37 38 39 40

17 21 25 29 33 36

25.4 47.4 51.7 37.8 05.5 14.1

+1 1 2 2 2 2

50 55 00 05 10 15

46.0 43.2 40.4 37.6 34.5 30.9

32 43 54 06 17 28

02.1 32.6 56.8 14.5 25.7 30.0

-0 0 0 0 0 0

58 55 52 49 46 42

48.2 44.5 35.9 22.7 04.9 42.4

16 17 18 19 20 21

41 42 43 44 45 46

39 41 43 45 46 47

03.2 32.3 40.8 28.1 53.5 56.4

+2 2 2 2 2 2

20 25 30 35 40 44

26.7 21.7 15.8 08.7 00.3 50.4

356 357 359 0 1 2

39 50 00 11 22 32

27.3 17.3 59.9 34.8 01.7 20.7

-0 0 0 0 0 0

39 35 32 28 24 20

15.5 44.2 08.6 28.7 44.6 56.5

22 23 24 25 26 27

47 48 49 50 51 52

48 48 48 48 47 45

36.0 51.6 42.4 07.7 06.5 37.9

+2 2 2 3 3 3

49 54 59 03 08 13

38.8 25.4 09.8 52.0 31.7 08.7

3 4 6 7 8

42 52 02 12 21

31.4 33.8 27.7 13.1 49.8

-0 0 0 0 -0

17 13 09 05 00

04.4 08.5 08.8 05.4 58.5

28 29 30 31 1

53 54 55 56 57

43 41 38 34 30

41.0 14.8 18.3 50.2 49.4

+3 3 3 3 +3

17 22 26 31 35

42.7 13.7 41.2 05.1 25.1

Feb.

Mar.

Apr.

115

VENUS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Apr.

May

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 57 58 59 60 61 62

' 30 26 21 15 08 01

" 49.4 14.8 05.0 18.7 54.6 51.2

º +3 3 3 3 3 3

' 35 39 43 47 52 55

" 25.1 41.0 52.5 59.2 01.0 57.6

7 8 9 10 11 12

62 63 64 65 66 67

54 45 36 26 15 04

07.2 41.2 31.7 37.4 56.7 28.0

+3 4 4 4 4 4

59 03 07 10 14 17

13 14 15 16 17 18

67 68 69 70 70 71

52 38 24 09 54 37

09.7 59.9 56.7 58.3 02.5 07.2

+4 4 4 4 4 4

19 20 21 22 23 24

72 73 73 74 74 75

19 00 40 18 56 32

10.1 08.8 01.0 43.9 14.9 31.1

25 26 27 28 29 30

76 76 77 77 78 78

07 41 13 44 13 41

1 2 3 4 5 6

79 79 79 80 80 80

7 8 9 10 11 12 13 14 15 16 17

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

17 18 19 20 21 22

º 81 81 81 80 80 80

' 33 23 11 56 39 19

" 55.4 48.4 16.5 21.1 03.9 27.7

º +3 3 3 3 3 3

' 51 43 35 27 18 08

" 08.2 40.9 42.1 11.7 09.6 36.0

48.5 33.6 12.4 44.7 10.1 28.4

23 24 25 26 27 28

79 79 79 78 78 77

57 33 07 39 09 37

36.2 34.2 27.4 22.7 27.9 52.2

+2 2 2 2 2 2

58 47 36 25 13 00

31.2 56.0 51.1 17.7 17.4 51.8

20 23 26 29 31 34

39.0 41.8 36.3 22.2 59.0 26.4

29 30 31 1 2 3

77 76 75 75 74 74

04 30 54 18 41 03

45.7 19.6 46.1 18.2 09.8 35.2

+1 1 1 1 0 0

48 34 21 07 53 39

02.9 53.2 25.2 41.7 45.8 40.7

+4 4 4 4 4 4

36 38 40 42 44 45

43.8 51.0 47.2 32.2 05.2 25.9

4 5 6 7 8 9

73 72 72 71 70 70

25 48 10 33 57 22

49.4 07.2 43.7 53.6 51.0 49.5

+0 +0 -0 0 0 0

25 11 02 17 31 44

29.8 16.6 55.6 03.2 03.0 51.7

29.6 07.3 20.9 07.2 22.6 03.7

+4 4 4 4 4 4

46 47 48 48 48 48

33.6 27.7 07.6 32.5 41.9 34.9

10 11 12 13 14 15

69 69 68 68 67 67

49 16 45 16 49 24

01.9 40.0 54.5 55.2 50.4 47.6

-0 1 1 1 1 2

58 11 24 37 49 01

26.3 44.2 42.7 19.6 33.0 21.2

07 31 54 14 33 50

06.8 28.2 04.1 50.9 44.7 42.1

+4 4 4 4 4 4

48 47 46 45 43 41

10.8 28.7 28.0 07.6 26.7 24.4

16 17 18 19 20 21

67 66 66 66 65 65

01 41 22 06 53 41

53.0 11.6 47.4 43.4 01.6 42.9

-2 2 2 2 2 3

12 23 34 43 53 02

42.9 36.9 02.4 58.8 25.8 23.1

81 81 81 81 81 81

05 18 29 37 44 48

39.4 33.2 20.2 57.1 21.1 29.2

+4 4 4 4 4 4

38 36 32 29 25 20

59.8 11.9 59.9 22.8 19.6 49.6

22 23 24 25 26 27

65 65 65 65 65 65

32 26 22 20 20 23

47.9 16.0 06.3 17.2 46.8 33.0

-3 3 3 3 3 3

10 18 26 33 39 45

51.0 49.4 18.7 19.5 52.1 57.2

81 81 81 81 81

50 49 46 41 33

18.9 48.0 54.7 37.4 55.4

+4 4 4 3 +3

15 10 04 58 51

51.9 25.6 30.0 04.4 08.2

28 29 30 1 2

65 65 65 65 66

28 35 45 56 09

33.0 44.2 03.6 28.1 54.6

-3 3 4 4 -4

51 56 01 05 09

35.5 47.6 34.4 56.4 54.7

May

June

July

116

VENUS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

July

Aug.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 65 66 66 66 67 67

' 56 09 25 42 01 22

" 28.1 54.6 19.6 39.7 51.6 51.7

º -4 4 4 4 4 4

' 05 09 13 16 19 22

" 56.4 54.7 29.8 42.6 33.9 04.5

7 8 9 10 11 12

67 68 68 69 69 70

45 10 36 03 32 03

36.4 02.2 05.6 43.1 51.4 27.1

-4 4 4 4 4 4

24 26 27 28 29 30

13 14 15 16 17 18

70 71 71 72 72 73

35 08 43 19 56 34

26.9 47.7 26.4 19.9 25.4 40.1

-4 4 4 4 4 4

19 20 21 22 23 24

74 74 75 76 77 77

14 54 35 18 01 45

01.1 26.0 52.2 17.2 38.7 54.7

25 26 27 28 29 30

78 79 80 80 81 82

31 17 03 51 39 28

31 1 2 3 4 5

83 84 85 85 86 87

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 97 98 99 100 101 102

' 54 53 52 52 52 52

" 46.7 38.0 52.7 30.2 29.5 50.1

º -3 3 2 2 2 2

' 06 02 57 53 49 44

" 29.8 16.0 59.2 39.8 17.9 53.7

15.1 06.6 39.5 54.8 53.0 34.9

22 23 24 25 26 27

103 104 105 106 107 109

53 54 55 57 59 01

31.4 32.7 53.6 33.7 32.4 49.4

-2 2 2 2 2 2

40 35 31 26 22 17

27.4 59.1 29.1 57.4 24.4 50.0

31 31 31 30 30 29

01.2 12.4 09.1 52.1 21.7 Sept. 38.7

28 29 30 31 1 2

110 111 112 113 114 115

04 07 10 13 17 21

24.1 16.3 25.6 51.5 33.7 31.9

-2 2 2 1 1 1

13 08 04 59 54 50

14.6 38.2 01.1 23.3 45.1 06.6

-4 4 4 4 4 4

28 27 26 24 23 21

43.4 36.4 18.3 49.3 10.1 20.9

3 4 5 6 7 8

116 117 118 119 120 121

25 30 34 39 45 50

45.8 15.0 59.3 58.2 11.6 39.1

-1 1 1 1 1 1

45 40 36 31 26 22

28.0 49.4 10.9 32.8 55.2 18.3

03.1 01.9 49.6 24.3 44.4 48.6

-4 4 4 4 4 4

19 17 14 12 09 07

22.2 14.4 57.8 32.8 59.7 18.8

9 10 11 12 13 14

122 124 125 126 127 128

56 02 08 14 21 28

20.4 15.1 23.0 43.7 17.0 02.3

-1 1 1 1 0 0

17 13 08 03 59 54

42.1 06.9 32.8 59.9 28.4 58.5

18 09 00 51 44 37

35.4 03.2 10.9 57.0 20.4 19.9

-4 4 3 3 3 3

04 01 58 55 52 48

30.4 34.9 32.5 23.6 08.3 47.0

15 16 17 18 19 20

129 130 131 132 134 135

34 42 49 56 04 12

59.5 08.2 28.1 58.9 40.3 32.2

-0 0 0 0 0 0

50 46 41 37 32 28

30.2 03.8 39.2 16.8 56.5 38.5

88 89 90 91 92 93

30 25 19 14 10 06

54.2 02.3 43.1 55.5 38.5 51.2

-3 3 3 3 3 3

45 41 38 34 30 26

20.0 47.5 09.8 27.2 39.8 47.9

21 22 23 24 25 26

136 137 138 139 140 142

20 28 37 45 54 03

34.3 46.4 08.4 40.1 21.3 11.8

-0 0 0 0 0 -0

24 20 15 11 07 03

23.0 10.0 59.7 52.1 47.3 45.5

94 95 95 96 97

03 00 58 56 54

32.6 41.7 17.7 19.6 46.7

-3 3 3 3 -3

22 18 14 10 06

51.8 51.8 47.9 40.5 29.8

27 28 29 30 1

143 144 145 146 147

12 21 30 40 49

11.6 20.4 38.1 04.7 40.1

+0 0 0 0 +0

00 04 08 11 15

13.2 08.7 01.0 49.9 35.3

Aug.

Oct.

117

VENUS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Oct.

Nov.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 147 148 150 151 152 153

' 49 59 09 19 29 39

" 40.1 24.0 16.5 17.4 26.5 43.8

º +0 0 0 0 0 0

' 15 19 22 26 30 33

" 35.3 17.2 55.4 29.9 00.5 27.2

7 8 9 10 11 12

154 156 157 158 159 160

50 00 11 22 33 44

09.0 42.1 22.9 11.2 06.9 09.6

+0 0 0 0 0 0

36 40 43 46 49 52

13 14 15 16 17 18

161 163 164 165 166 167

55 06 17 29 41 52

19.4 35.9 59.0 28.5 04.2 46.1

+0 0 1 1 1 1

19 20 21 22 23 24

169 170 171 172 173 175

04 16 28 40 52 04

33.9 27.5 26.8 31.6 41.8 57.3

25 26 27 28 29 30

176 177 178 179 181 182

17 29 42 54 07 20

31 1 2 3 4 5

183 184 185 187 188 189

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 203 204 205 206 208 209

' 08 22 36 50 04 18

" 21.3 19.3 20.1 23.6 29.8 38.5

º +1 1 1 1 1 1

' 46 46 46 46 46 45

" 43.3 44.3 40.4 31.6 17.9 59.6

49.8 08.4 22.7 32.8 38.6 39.9

22 23 24 25 26 27

210 211 213 214 215 216

32 47 01 15 29 44

49.6 03.2 19.1 37.3 57.9 20.8

+1 1 1 1 1 1

45 45 44 43 43 42

36.5 08.7 36.3 59.4 18.0 32.2

55 58 01 03 06 09

36.7 29.0 16.7 59.7 37.9 11.4

28 29 30 1 2 3

217 219 220 221 222 224

58 13 27 42 56 11

45.9 13.3 42.8 14.5 48.3 24.2

+1 1 1 1 1 1

41 40 39 38 37 36

42.0 47.4 48.7 45.7 38.7 27.6

+1 1 1 1 1 1

11 14 16 18 20 22

40.0 03.8 22.7 36.6 45.6 49.6

4 5 6 7 8 9

225 226 227 229 230 231

26 40 55 10 24 39

02.0 41.8 23.5 06.9 52.1 39.0

+1 1 1 1 1 1

35 33 32 31 29 28

12.5 53.6 30.9 04.4 34.3 00.6

18.0 43.8 14.6 50.5 31.3 17.1

+1 1 1 1 1 1

24 26 28 30 31 33

48.5 42.4 31.2 14.9 53.4 26.8

10 11 12 13 14 15

232 234 235 236 237 239

54 09 24 39 53 08

27.5 17.6 09.2 02.2 56.6 52.1

+1 1 1 1 1 1

26 24 22 21 19 17

23.5 43.0 59.2 12.2 22.1 29.1

33 46 59 12 25 38

07.6 02.9 03.0 07.6 16.8 30.4

+1 1 1 1 1 1

34 36 37 38 39 40

55.1 18.2 36.1 48.8 56.3 58.6

16 17 18 19 20 21

240 241 242 244 245 246

23 38 53 08 23 38

48.7 46.3 44.8 44.0 44.0 44.7

+1 1 1 1 1 1

15 13 11 09 07 05

33.2 34.4 33.0 29.1 22.6 13.8

190 192 193 194 195 196

51 05 18 32 45 59

48.4 10.6 37.0 07.3 41.5 19.4

+1 1 1 1 1 1

41 42 43 44 44 45

55.7 47.6 34.3 15.8 52.2 23.4

22 23 24 25 26 27

247 249 250 251 252 254

53 08 23 38 53 09

46.0 48.1 50.9 54.4 58.5 03.3

+1 1 0 0 0 0

03 00 58 56 53 51

02.7 49.5 34.2 16.9 57.8 36.9

198 199 200 201 203

13 26 40 54 08

01.0 46.1 34.6 26.4 21.3

+1 1 1 1 +1

45 46 46 46 46

49.6 10.6 26.5 37.4 43.3

28 29 30 31 32

255 256 257 259 260

24 39 54 09 24

08.7 14.8 21.6 28.9 36.8

+0 0 0 0 +0

49 46 44 41 39

14.4 50.3 24.8 58.0 29.9

Nov.

Dec.

118

VENUS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Jan. 0 1 2 3 4 5

h 21 21 21 21 21 21

m 04 09 14 19 24 29

s 48.44 44.59 39.26 32.47 24.20 14.46

º -18 18 17 17 17 16

' 37 15 53 30 07 44

" 42.3 56.2 40.4 55.7 42.9 02.7

1.283 533 1.277 918 1.272 273 1.266 598 1.260 892 1.255 157

" 6.85 6.88 6.91 6.94 6.97 7.01

" 6.50 6.53 6.56 6.58 6.61 6.64

h 14 14 14 14 14 14

m 28 29 30 31 32 33

s 53 52 49 45 39 32

6 7 8 9 10 11

21 21 21 21 21 21

34 38 43 48 53 57

03.26 50.61 36.52 20.99 04.04 45.70

-16 15 15 15 14 14

19 55 30 05 39 13

56.0 23.5 26.1 04.6 19.7 12.3

1.249 393 1.243 599 1.237 776 1.231 924 1.226 044 1.220 136

7.04 7.07 7.10 7.14 7.17 7.21

6.68 6.71 6.74 6.77 6.80 6.84

14 14 14 14 14 14

34 35 36 36 37 38

23 13 02 49 34 19

12 13 14 15 16 17

22 22 22 22 22 22

02 07 11 16 20 25

25.97 04.88 42.44 18.70 53.66 27.37

-13 13 12 12 11 11

46 19 52 25 57 29

43.2 53.1 42.8 13.1 24.8 18.6

1.214 200 1.208 236 1.202 245 1.196 226 1.190 179 1.184 105

7.24 7.28 7.31 7.35 7.39 7.43

6.87 6.90 6.94 6.97 7.01 7.04

14 14 14 14 14 14

39 39 40 41 41 42

02 43 23 02 40 16

18 19 20 21 22 23

22 22 22 22 22 22

29 34 39 43 47 52

59.85 31.13 01.24 30.20 58.05 24.81

-11 10 10 9 9 8

00 32 03 34 04 35

55.3 15.6 20.3 10.2 46.1 08.7

1.178 002 1.171 871 1.165 712 1.159 524 1.153 307 1.147 061

7.47 7.50 7.54 7.58 7.63 7.67

7.08 7.12 7.15 7.19 7.23 7.27

14 14 14 14 14 14

42 43 43 44 45 45

52 26 58 30 01 30

24 25 26 27 28 29

22 23 23 23 23 23

56 01 05 10 14 18

50.51 15.17 38.82 01.50 23.21 44.01

-8 7 7 6 6 5

05 35 05 34 04 33

18.9 17.3 04.8 42.1 10.1 29.3

1.140 785 1.134 479 1.128 144 1.121 778 1.115 383 1.108 958

7.71 7.75 7.80 7.84 7.88 7.93

7.31 7.35 7.39 7.43 7.48 7.52

14 14 14 14 14 14

45 46 46 47 47 48

59 26 53 18 43 07

30 31 Feb. 1 2 3 4

23 23 23 23 23 23

23 27 31 35 40 44

03.92 22.96 41.16 58.57 15.20 31.09

-5 4 4 3 2 2

02 31 00 29 58 27

40.7 44.9 42.8 35.0 22.3 05.5

1.102 503 1.096 018 1.089 504 1.082 960 1.076 387 1.069 784

7.98 8.02 8.07 8.12 8.17 8.22

7.56 7.61 7.65 7.70 7.75 7.80

14 14 14 14 14 14

48 48 49 49 49 50

30 51 13 33 53 12

5 6 7 8 9 10

23 23 23 0 0 0

48 53 57 01 05 09

46.27 00.76 14.59 27.80 40.41 52.46

-1 1 0 -0 +0 0

55 24 52 21 09 41

45.2 22.3 57.5 31.4 55.2 21.5

1.063 154 1.056 495 1.049 807 1.043 093 1.036 351 1.029 582

8.27 8.32 8.38 8.43 8.49 8.54

7.84 7.89 7.94 8.00 8.05 8.10

14 14 14 14 14 14

50 50 51 51 51 51

30 47 04 20 36 51

11 12 13 14 15

0 0 0 0 0

14 18 22 26 30

03.96 14.97 25.51 35.62 45.32

+1 1 2 2 +3

12 44 15 46 18

46.9 10.7 32.3 51.0 06.1

1.022 788 1.015 967 1.009 120 1.002 248 0.995 350

8.60 8.66 8.71 8.77 8.84

8.15 8.21 8.26 8.32 8.38

14 14 14 14 14

52 52 52 52 53

06 20 34 47 00

119

VENUS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Feb. 15 16 17 18 19 20

h 0 0 0 0 0 0

m 30 34 39 43 47 51

s 45.32 54.66 03.64 12.31 20.69 28.78

º +3 3 4 4 5 5

' 18 49 20 51 22 53

" 06.1 16.9 22.9 23.4 17.6 04.9

0.995 350 0.988 426 0.981 477 0.974 501 0.967 500 0.960 473

" 8.84 8.90 8.96 9.02 9.09 9.16

" 8.38 8.44 8.50 8.56 8.62 8.68

h 14 14 14 14 14 14

m 53 53 53 53 53 53

s 00 13 25 37 48 60

21 22 23 24 25 26

0 0 1 1 1 1

55 59 03 07 12 16

36.63 44.23 51.61 58.79 05.77 12.58

+6 6 7 7 8 8

23 54 24 54 24 54

44.7 16.2 38.7 51.7 54.4 46.2

0.953 419 0.946 340 0.939 234 0.932 102 0.924 945 0.917 762

9.22 9.29 9.36 9.43 9.51 9.58

8.75 8.81 8.88 8.95 9.02 9.09

14 14 14 14 14 14

54 54 54 54 54 55

11 22 33 43 53 04

27 28 29 Mar. 1 2 3

1 1 1 1 1 1

20 24 28 32 36 40

19.21 25.69 32.02 38.20 44.23 50.12

+9 9 10 10 11 11

24 53 23 52 20 49

26.4 54.3 09.3 10.7 57.9 30.2

0.910 553 0.903 318 0.896 059 0.888 775 0.881 466 0.874 134

9.66 9.74 9.81 9.89 9.98 10.06

9.16 9.23 9.31 9.38 9.46 9.54

14 14 14 14 14 14

55 55 55 55 55 56

14 23 33 43 52 01

4 5 6 7 8 9

1 1 1 1 2 2

44 49 53 57 01 05

55.87 01.46 06.90 12.17 17.26 22.17

+12 12 13 13 14 14

17 45 13 40 08 34

46.9 47.5 31.2 57.5 05.6 55.0

0.866 778 0.859 400 0.851 999 0.844 577 0.837 134 0.829 672

10.15 10.23 10.32 10.41 10.51 10.60

9.62 9.70 9.79 9.87 9.96 10.05

14 14 14 14 14 14

56 56 56 56 56 56

10 19 28 37 45 53

10 11 12 13 14 15

2 2 2 2 2 2

09 13 17 21 25 29

26.88 31.39 35.68 39.75 43.57 47.12

+15 15 15 16 16 17

01 27 53 18 44 08

25.2 35.4 25.2 54.0 01.4 46.8

0.822 190 0.814 690 0.807 173 0.799 639 0.792 089 0.784 523

10.70 10.79 10.89 11.00 11.10 11.21

10.14 10.24 10.33 10.43 10.53 10.63

14 14 14 14 14 14

57 57 57 57 57 57

01 09 17 24 31 38

16 17 18 19 20 21

2 2 2 2 2 2

33 37 41 45 49 54

50.39 53.33 55.92 58.12 59.87 01.15

+17 17 18 18 19 19

33 57 20 43 06 29

09.7 09.6 46.0 58.5 46.4 09.4

0.776 942 0.769 346 0.761 736 0.754 111 0.746 474 0.738 823

11.32 11.43 11.54 11.66 11.78 11.90

10.73 10.84 10.95 11.06 11.17 11.29

14 14 14 14 14 14

57 57 57 58 58 58

45 51 57 02 07 11

22 23 24 25 26 27

2 3 3 3 3 3

58 02 06 10 13 17

01.89 02.04 01.54 00.33 58.33 55.47

+19 20 20 20 21 21

51 12 33 54 14 34

07.0 38.7 44.0 22.6 34.0 17.8

0.731 160 0.723 485 0.715 798 0.708 101 0.700 395 0.692 679

12.03 12.16 12.29 12.42 12.56 12.70

11.41 11.53 11.65 11.78 11.91 12.04

14 14 14 14 14 14

58 58 58 58 58 58

15 18 21 23 23 23

28 29 30 31 Apr. 1

3 3 3 3 3

21 25 29 33 37

51.67 46.85 40.91 33.75 25.27

+21 22 22 22 +23

53 12 30 48 05

33.7 21.2 40.1 29.9 50.4

0.684 955 0.677 224 0.669 487 0.661 745 0.653 999

12.84 12.99 13.14 13.29 13.45

12.18 12.31 12.46 12.60 12.75

14 14 14 14 14

58 58 58 58 58

22 20 17 13 07

120

VENUS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Apr. 1 2 3 4 5 6

h 3 3 3 3 3 3

m 37 41 45 48 52 56

s 25.27 15.36 03.91 50.79 35.88 19.04

º +23 23 23 23 24 24

' 05 22 39 54 10 25

" 50.4 41.2 02.0 52.6 12.7 02.2

0.653 999 0.646 251 0.638 502 0.630 754 0.623 008 0.615 266

" 13.45 13.61 13.77 13.94 14.12 14.29

" 12.75 12.91 13.06 13.22 13.39 13.56

h 14 14 14 14 14 14

m 58 57 57 57 57 57

s 07 59 50 39 27 12

7 8 9 10 11 12

4 4 4 4 4 4

00 03 07 10 14 17

00.16 39.10 15.72 49.87 21.43 50.23

+24 24 25 25 25 25

39 53 06 19 31 43

20.6 08.1 24.3 09.3 22.9 05.2

0.607 530 0.599 802 0.592 084 0.584 378 0.576 686 0.569 010

14.48 14.66 14.85 15.05 15.25 15.46

13.73 13.90 14.09 14.27 14.46 14.66

14 14 14 14 14 14

56 56 56 55 55 54

55 36 15 51 24 55

13 14 15 16 17 18

4 4 4 4 4 4

21 24 27 31 34 37

16.10 38.89 58.42 14.51 26.96 35.57

+25 26 26 26 26 26

54 04 15 24 33 42

16.2 55.7 03.9 40.7 46.2 20.4

0.561 351 0.553 713 0.546 096 0.538 503 0.530 936 0.523 397

15.67 15.88 16.10 16.33 16.56 16.80

14.86 15.06 15.27 15.49 15.71 15.93

14 14 14 14 14 14

54 53 53 52 51 50

22 46 07 25 38 48

19 20 21 22 23 24

4 4 4 4 4 4

40 43 46 49 52 54

40.15 40.47 36.31 27.46 13.65 54.66

+26 26 27 27 27 27

50 57 04 11 17 22

23.3 55.1 55.7 25.2 23.6 51.1

0.515 889 0.508 413 0.500 974 0.493 573 0.486 213 0.478 898

17.05 17.30 17.55 17.82 18.09 18.36

16.17 16.40 16.65 16.90 17.15 17.41

14 14 14 14 14 14

49 48 47 46 45 44

53 54 51 42 29 10

25 26 27 28 29 30

4 5 5 5 5 5

57 00 02 04 06 08

30.22 00.07 23.93 41.53 52.58 56.79

+27 27 27 27 27 27

27 32 36 39 42 44

47.7 13.3 08.1 32.0 24.9 46.8

0.471 630 0.464 414 0.457 254 0.450 152 0.443 114 0.436 144

18.65 18.94 19.23 19.54 19.85 20.16

17.68 17.96 18.24 18.53 18.82 19.12

14 14 14 14 14 14

42 41 39 37 36 34

46 16 39 56 07 10

May 1 2 3 4 5 6

5 5 5 5 5 5

10 12 14 15 17 18

53.85 43.47 25.35 59.19 24.69 41.58

+27 27 27 27 27 27

46 47 48 49 48 47

37.6 57.1 45.1 01.2 45.3 57.0

0.429 247 0.422 428 0.415 693 0.409 047 0.402 496 0.396 048

20.49 20.82 21.16 21.50 21.85 22.20

19.43 19.74 20.06 20.39 20.72 21.06

14 14 14 14 14 14

32 29 27 25 22 19

07 55 36 08 33 48

7 8 9 10 11 12

5 5 5 5 5 5

19 20 21 22 22 23

49.57 48.41 37.85 17.64 47.56 07.43

+27 27 27 27 27 27

46 44 42 39 35 31

35.8 41.3 12.9 10.2 32.4 18.9

0.389 709 0.383 485 0.377 385 0.371 414 0.365 581 0.359 893

22.57 22.93 23.30 23.68 24.06 24.44

21.40 21.75 22.10 22.45 22.81 23.17

14 14 14 14 14 14

16 13 10 07 03 00

54 51 39 17 45 03

13 14 15 16 17

5 5 5 5 5

23 23 23 22 22

17.06 16.31 05.07 43.26 10.85

+27 27 27 27 +27

26 21 14 08 00

28.7 01.1 55.3 10.1 44.9

0.354 358 0.348 985 0.343 781 0.338 755 0.333 915

24.82 25.20 25.58 25.96 26.34

23.54 23.90 24.26 24.62 24.98

13 13 13 13 13

56 52 47 43 38

11 08 55 31 57

121

VENUS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

May 17 18 19 20 21 22

h 5 5 5 5 5 5

m 22 21 20 19 18 16

s 10.85 27.86 34.36 30.48 16.42 52.45

º +27 26 26 26 26 26

' 00 52 43 34 24 13

" 44.9 38.5 50.2 19.2 04.9 06.6

0.333 915 0.329 271 0.324 832 0.320 606 0.316 603 0.312 832

" 26.34 26.71 27.07 27.43 27.78 28.11

" 24.98 25.33 25.67 26.01 26.34 26.66

h 13 13 13 13 13 13

m 38 34 29 24 18 13

s 57 12 17 12 57 33

23 24 25 26 27 28

5 5 5 5 5 5

15 13 11 09 07 05

18.90 36.18 44.79 45.28 38.32 24.62

+26 25 25 25 25 24

01 48 35 21 07 52

24.2 57.7 47.2 53.5 17.5 00.7

0.309 301 0.306 020 0.302 998 0.300 243 0.297 762 0.295 564

28.43 28.74 29.02 29.29 29.53 29.75

26.96 27.25 27.52 27.78 28.01 28.22

13 13 12 12 12 12

07 02 56 50 44 38

59 16 25 27 21 09

29 30 31 June 1 2 3

5 5 4 4 4 4

03 00 58 55 53 50

04.97 40.24 11.35 39.28 05.05 29.69

+24 24 24 23 23 23

36 19 02 44 26 08

05.2 33.2 27.9 52.8 51.8 29.5

0.293 656 0.292 044 0.290 733 0.289 729 0.289 035 0.288 655

29.95 30.11 30.25 30.35 30.43 30.47

28.40 28.56 28.69 28.79 28.85 28.89

12 12 12 12 12 11

31 25 19 12 06 59

52 30 04 36 06 36

4 5 6 7 8 9

4 4 4 4 4 4

47 45 42 40 37 35

54.27 19.83 47.42 18.01 52.58 32.00

+22 22 22 21 21 21

49 31 12 53 34 15

50.8 01.0 05.7 10.6 21.4 43.9

0.288 589 0.288 839 0.289 403 0.290 280 0.291 466 0.292 958

30.47 30.45 30.39 30.30 30.17 30.02

28.90 28.87 28.82 28.73 28.61 28.47

11 11 11 11 11 11

53 46 40 33 27 21

06 38 12 50 31 19

10 11 12 13 14 15

4 4 4 4 4 4

33 31 29 27 25 23

17.10 08.63 07.26 13.57 28.06 51.17

+20 20 20 20 19 19

57 39 21 04 48 32

23.7 26.1 56.2 58.6 37.7 57.2

0.294 749 0.296 835 0.299 208 0.301 861 0.304 785 0.307 971

29.84 29.63 29.39 29.13 28.85 28.56

28.30 28.10 27.87 27.63 27.36 27.08

11 11 11 10 10 10

15 09 03 57 51 46

12 11 18 33 56 28

16 17 18 19 20 21

4 4 4 4 4 4

22 21 19 18 18 17

23.23 04.53 55.25 55.54 05.47 25.07

+19 19 18 18 18 18

18 03 50 37 26 15

00.3 50.1 28.6 57.9 19.1 33.3

0.311 412 0.315 098 0.319 019 0.323 166 0.327 530 0.332 101

28.24 27.91 27.57 27.21 26.85 26.48

26.78 26.47 26.14 25.81 25.46 25.11

10 10 10 10 10 10

41 35 30 26 21 16

09 59 58 07 26 54

22 23 24 25 26 27

4 4 4 4 4 4

16 16 16 16 16 16

54.30 33.10 21.38 19.00 25.82 41.68

+18 17 17 17 17 17

05 56 48 41 35 29

40.8 41.7 35.9 22.7 01.3 30.6

0.336 869 0.341 827 0.346 965 0.352 275 0.357 748 0.363 377

26.11 25.73 25.35 24.96 24.58 24.20

24.76 24.40 24.04 23.67 23.31 22.95

10 10 10 10 9 9

12 08 04 00 56 52

31 18 15 20 35 58

28 29 30 July 1 2

4 4 4 4 4

17 17 18 19 20

06.38 39.74 21.57 11.66 09.81

+17 17 17 17 +17

24 20 17 15 13

49.3 56.1 49.4 27.5 48.7

0.369 153 0.375 070 0.381 121 0.387 298 0.393 594

23.82 23.45 23.07 22.71 22.34

22.59 22.24 21.88 21.53 21.19

9 9 9 9 9

49 46 43 39 37

31 11 00 58 03

122

VENUS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

July 1 2 3 4 5 6

h 4 4 4 4 4 4

m 19 20 21 22 23 25

s 11.66 09.81 15.81 29.43 50.47 18.71

º +17 17 17 17 17 17

' 15 13 12 12 12 13

" 27.5 48.7 51.0 32.6 51.5 45.6

0.387 298 0.393 594 0.400 004 0.406 520 0.413 137 0.419 849

" 22.71 22.34 21.99 21.63 21.29 20.95

" 21.53 21.19 20.85 20.52 20.19 19.86

h 9 9 9 9 9 9

m 39 37 34 31 29 26

s 58 03 16 36 03 38

7 8 9 10 11 12

4 4 4 4 4 4

26 28 30 32 34 36

53.94 35.93 24.48 19.37 20.41 27.40

+17 17 17 17 17 17

15 17 19 22 25 29

12.9 11.2 38.6 32.9 52.1 34.1

0.426 650 0.433 534 0.440 496 0.447 531 0.454 634 0.461 801

20.61 20.28 19.96 19.65 19.34 19.04

19.55 19.24 18.93 18.64 18.34 18.06

9 9 9 9 9 9

24 22 20 18 16 14

20 08 03 04 11 23

13 14 15 16 17 18

4 4 4 4 4 4

38 40 43 45 48 51

40.13 58.43 22.10 50.97 24.86 03.62

+17 17 17 17 17 17

33 37 42 47 52 57

36.9 58.5 37.1 30.7 37.5 55.7

0.469 027 0.476 309 0.483 642 0.491 022 0.498 448 0.505 914

18.75 18.46 18.18 17.91 17.64 17.38

17.78 17.51 17.24 16.98 16.73 16.49

9 9 9 9 9 9

12 11 09 08 06 05

42 06 35 09 49 33

19 20 21 22 23 24

4 4 4 5 5 5

53 56 59 02 05 08

47.06 35.05 27.42 24.02 24.73 29.40

+18 18 18 18 18 18

03 08 14 20 26 32

23.5 59.2 41.2 27.7 17.3 08.5

0.513 418 0.520 958 0.528 531 0.536 134 0.543 765 0.551 422

17.13 16.88 16.64 16.40 16.17 15.95

16.24 16.01 15.78 15.56 15.34 15.12

9 9 9 9 9 8

04 03 02 01 00 59

21 14 12 14 19 29

25 26 27 28 29 30

5 5 5 5 5 5

11 14 18 21 24 28

37.92 50.16 06.03 25.41 48.21 14.32

+18 18 18 18 19 19

37 43 49 55 00 06

59.6 49.4 36.4 19.4 57.0 28.1

0.559 104 0.566 808 0.574 533 0.582 277 0.590 039 0.597 817

15.73 15.52 15.31 15.10 14.90 14.71

14.92 14.71 14.52 14.32 14.13 13.95

8 8 8 8 8 8

58 57 57 56 56 55

42 59 20 44 12 42

31 Aug. 1 2 3 4 5

5 5 5 5 5 5

31 35 38 42 46 49

43.66 16.13 51.64 30.10 11.43 55.53

+19 19 19 19 19 19

11 17 22 27 31 36

51.4 05.7 09.8 02.8 43.3 10.5

0.605 609 0.613 414 0.621 230 0.629 056 0.636 890 0.644 730

14.52 14.34 14.16 13.98 13.81 13.64

13.77 13.60 13.42 13.26 13.09 12.94

8 8 8 8 8 8

55 54 54 54 54 53

16 53 33 16 02 51

6 7 8 9 10 11

5 5 6 6 6 6

53 57 01 05 09 13

42.33 31.73 23.66 18.03 14.76 13.76

+19 19 19 19 19 19

40 44 48 51 54 57

23.2 20.4 01.3 24.7 29.9 15.9

0.652 575 0.660 423 0.668 273 0.676 124 0.683 973 0.691 821

13.48 13.32 13.16 13.01 12.86 12.71

12.78 12.63 12.48 12.34 12.19 12.06

8 8 8 8 8 8

53 53 53 53 53 53

42 36 32 31 32 35

12 13 14 15 16

6 6 6 6 6

17 21 25 29 33

14.97 18.28 23.64 30.94 40.12

+19 20 20 20 +20

59 01 03 04 05

42.0 47.4 31.2 52.8 51.5

0.699 664 0.707 504 0.715 337 0.723 164 0.730 983

12.57 12.43 12.29 12.16 12.03

11.92 11.79 11.66 11.53 11.41

8 8 8 8 8

53 53 53 54 54

41 48 58 09 22

123

VENUS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Aug. 16 17 18 19 20 21

h 6 6 6 6 6 6

m 33 37 42 46 50 54

s 40.12 51.09 03.77 18.08 33.94 51.29

º +20 20 20 20 20 20

' 05 06 06 06 05 04

" 51.5 26.7 37.6 23.7 44.5 39.4

0.730 983 0.738 794 0.746 595 0.754 385 0.762 166 0.769 934

" 12.03 11.90 11.78 11.66 11.54 11.42

" 11.41 11.29 11.17 11.06 10.94 10.83

h 8 8 8 8 8 8

m 54 54 54 55 55 55

s 22 37 54 13 32 54

22 23 24 25 26 27

6 7 7 7 7 7

59 03 07 12 16 21

10.05 30.15 51.53 14.13 37.88 02.73

+20 20 19 19 19 19

03 01 58 55 52 48

07.9 09.6 44.1 50.9 29.8 40.3

0.777 692 0.785 437 0.793 170 0.800 891 0.808 598 0.816 293

11.31 11.20 11.09 10.98 10.88 10.77

10.72 10.62 10.51 10.41 10.31 10.22

8 8 8 8 8 8

56 56 57 57 57 58

16 41 06 32 60 29

28 29 30 31 Sept. 1 2

7 7 7 7 7 7

25 29 34 38 43 47

28.62 55.48 23.27 51.91 21.37 51.57

+19 19 19 19 19 19

44 39 34 28 22 15

22.3 35.4 19.4 34.0 19.1 34.5

0.823 974 0.831 640 0.839 292 0.846 928 0.854 548 0.862 152

10.67 10.57 10.48 10.38 10.29 10.20

10.12 10.03 9.94 9.85 9.76 9.67

8 8 9 9 9 9

58 59 00 00 01 01

58 29 01 33 06 40

3 4 5 6 7 8

7 7 8 8 8 8

52 56 01 05 10 15

22.47 54.02 26.16 58.85 32.02 05.63

+19 19 18 18 18 18

08 00 52 43 34 24

19.9 35.4 20.7 35.9 21.0 35.8

0.869 738 0.877 307 0.884 856 0.892 386 0.899 896 0.907 386

10.11 10.02 9.94 9.85 9.77 9.69

9.59 9.51 9.43 9.35 9.27 9.19

9 9 9 9 9 9

02 02 03 04 04 05

15 50 26 02 39 16

9 10 11 12 13 14

8 8 8 8 8 8

19 24 28 33 37 42

39.64 13.99 48.63 23.52 58.61 33.85

+18 18 17 17 17 17

14 03 52 40 28 15

20.5 35.2 19.8 34.6 19.7 35.2

0.914 853 0.922 299 0.929 722 0.937 121 0.944 497 0.951 848

9.61 9.54 9.46 9.38 9.31 9.24

9.12 9.04 8.97 8.90 8.83 8.76

9 9 9 9 9 9

05 06 07 07 08 09

54 32 10 48 27 06

15 16 17 18 19 20

8 8 8 9 9 9

47 51 56 00 05 10

09.20 44.62 20.06 55.50 30.89 06.22

+17 16 16 16 16 15

02 48 34 19 04 49

21.4 38.5 26.7 46.3 37.5 00.8

0.959 174 0.966 475 0.973 750 0.980 999 0.988 222 0.995 419

9.17 9.10 9.03 8.96 8.90 8.83

8.69 8.63 8.56 8.50 8.44 8.38

9 9 9 9 9 9

09 10 11 11 12 12

45 23 02 41 20 59

21 22 23 24 25 26

9 9 9 9 9 9

14 19 23 28 33 37

41.44 16.54 51.50 26.29 00.89 35.30

+15 15 14 14 14 14

32 16 59 42 24 05

56.4 24.7 26.0 00.8 09.4 52.3

1.002 590 1.009 736 1.016 855 1.023 948 1.031 016 1.038 057

8.77 8.71 8.65 8.59 8.53 8.47

8.32 8.26 8.20 8.14 8.09 8.03

9 9 9 9 9 9

13 14 14 15 16 16

37 16 54 33 11 48

27 28 29 30 Oct. 1

9 9 9 9 10

42 46 51 55 00

09.50 43.48 17.22 50.73 23.99

+13 13 13 12 +12

47 28 08 48 28

09.8 02.3 30.4 34.4 14.9

1.045 072 1.052 060 1.059 021 1.065 955 1.072 861

8.41 8.36 8.30 8.25 8.20

7.98 7.93 7.88 7.82 7.77

9 9 9 9 9

17 18 18 19 19

26 03 40 17 54

124

VENUS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Oct. 1 2 3 4 5 6

h 10 10 10 10 10 10

m 00 04 09 14 18 23

s 23.99 57.00 29.77 02.29 34.56 06.59

º +12 12 11 11 11 10

' 28 07 46 24 03 41

" 14.9 32.2 26.9 59.5 10.5 00.4

1.072 861 1.079 740 1.086 590 1.093 411 1.100 202 1.106 964

" 8.20 8.14 8.09 8.04 7.99 7.94

" 7.77 7.72 7.68 7.63 7.58 7.53

h 9 9 9 9 9 9

m 19 20 21 21 22 22

s 54 30 06 42 18 53

7 8 9 10 11 12

10 10 10 10 10 10

27 32 36 41 45 50

38.37 09.91 41.21 12.28 43.12 13.74

+10 9 9 9 8 8

18 55 32 09 45 21

29.8 39.2 29.3 00.5 13.6 09.0

1.113 696 1.120 397 1.127 066 1.133 704 1.140 309 1.146 882

7.90 7.85 7.80 7.76 7.71 7.67

7.49 7.44 7.40 7.36 7.31 7.27

9 9 9 9 9 9

23 24 24 25 25 26

28 03 38 12 47 21

13 14 15 16 17 18

10 10 11 11 11 11

54 59 03 08 12 17

44.15 14.35 44.36 14.19 43.85 13.36

+7 7 7 6 6 5

56 32 07 42 16 51

47.5 09.6 16.1 07.4 44.4 07.6

1.153 422 1.159 929 1.166 401 1.172 839 1.179 244 1.185 614

7.62 7.58 7.54 7.50 7.46 7.42

7.23 7.19 7.15 7.11 7.07 7.03

9 9 9 9 9 9

26 27 28 28 29 29

54 28 01 35 08 41

19 20 21 22 23 24

11 11 11 11 11 11

21 26 30 35 39 44

42.74 12.00 41.17 10.27 39.31 08.33

+5 4 4 4 3 3

25 59 33 06 40 13

17.7 15.4 01.4 36.3 00.8 15.6

1.191 950 1.198 252 1.204 520 1.210 755 1.216 956 1.223 123

7.38 7.34 7.30 7.26 7.23 7.19

7.00 6.96 6.92 6.89 6.85 6.82

9 9 9 9 9 9

30 30 31 31 32 32

13 46 19 51 24 56

25 26 27 28 29 30

11 11 11 12 12 12

48 53 57 02 06 11

37.35 06.39 35.49 04.68 33.99 03.44

+2 2 1 1 0 0

46 19 52 24 57 29

21.4 18.8 08.5 51.1 27.4 58.0

1.229 258 1.235 358 1.241 426 1.247 459 1.253 459 1.259 424

7.15 7.12 7.08 7.05 7.02 6.98

6.78 6.75 6.72 6.69 6.65 6.62

9 9 9 9 9 9

33 34 34 35 35 36

29 01 34 06 39 12

31 Nov. 1 2 3 4 5

12 12 12 12 12 12

15 20 24 29 33 38

33.08 02.93 33.03 03.41 34.09 05.12

+0 -0 0 1 1 2

02 25 52 20 48 16

23.6 15.1 57.4 42.6 30.0 18.9

1.265 356 1.271 253 1.277 115 1.282 942 1.288 734 1.294 490

6.95 6.92 6.89 6.85 6.82 6.79

6.59 6.56 6.53 6.50 6.47 6.44

9 9 9 9 9 9

36 37 37 38 39 39

45 19 53 26 01 35

6 7 8 9 10 11

12 12 12 12 13 13

42 47 51 56 00 05

36.51 08.31 40.55 13.24 46.43 20.15

-2 3 3 4 4 5

44 11 39 07 35 03

08.6 58.3 47.2 34.7 19.9 02.1

1.300 210 1.305 894 1.311 540 1.317 150 1.322 722 1.328 256

6.76 6.73 6.71 6.68 6.65 6.62

6.41 6.39 6.36 6.33 6.31 6.28

9 9 9 9 9 9

40 40 41 41 42 43

10 46 22 58 35 12

12 13 14 15 16

13 13 13 13 13

09 14 19 23 28

54.42 29.28 04.75 40.87 17.67

-5 5 6 6 -7

30 58 25 53 20

40.6 14.5 43.2 05.7 21.4

1.333 752 1.339 209 1.344 627 1.350 007 1.355 347

6.59 6.57 6.54 6.51 6.49

6.25 6.23 6.20 6.18 6.15

9 9 9 9 9

43 44 45 45 46

50 29 08 48 28

125

VENUS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Nov. 16 17 18 19 20 21

h 13 13 13 13 13 13

m 28 32 37 42 46 51

s 17.67 55.17 33.40 12.38 52.15 32.74

º -7 7 8 8 9 9

' 20 47 14 41 07 34

" 21.4 29.5 29.1 19.4 59.7 29.2

1.355 347 1.360 650 1.365 914 1.371 139 1.376 327 1.381 477

" 6.49 6.46 6.44 6.41 6.39 6.37

" 6.15 6.13 6.11 6.08 6.06 6.04

h 9 9 9 9 9 9

m 46 47 47 48 49 50

s 28 10 52 34 18 02

22 23 24 25 26 27

13 14 14 14 14 14

56 00 05 10 15 19

14.17 56.47 39.68 23.81 08.91 54.99

-10 10 10 11 11 12

00 26 52 18 43 08

47.1 52.6 44.9 23.3 47.0 55.2

1.386 590 1.391 665 1.396 703 1.401 704 1.406 668 1.411 595

6.34 6.32 6.30 6.27 6.25 6.23

6.01 5.99 5.97 5.95 5.93 5.91

9 9 9 9 9 9

50 51 52 53 53 54

48 34 21 09 58 48

28 29 30 Dec. 1 2 3

14 14 14 14 14 14

24 29 34 39 44 48

42.09 30.23 19.43 09.71 01.10 53.60

-12 12 13 13 14 14

33 58 22 46 10 33

47.1 21.9 39.0 37.4 16.3 35.1

1.416 485 1.421 338 1.426 153 1.430 932 1.435 673 1.440 377

6.21 6.19 6.17 6.15 6.13 6.11

5.89 5.87 5.85 5.83 5.81 5.79

9 9 9 9 9 10

55 56 57 58 59 00

39 31 24 18 13 10

4 5 6 7 8 9

14 14 15 15 15 15

53 58 03 08 13 18

47.24 42.04 37.99 35.12 33.43 32.92

-14 15 15 16 16 16

56 19 41 03 24 45

33.0 09.0 22.4 12.5 38.4 39.3

1.445 043 1.449 671 1.454 260 1.458 812 1.463 324 1.467 797

6.09 6.07 6.05 6.03 6.01 5.99

5.77 5.75 5.73 5.72 5.70 5.68

10 10 10 10 10 10

01 02 03 04 05 06

08 06 06 07 10 13

10 11 12 13 14 15

15 15 15 15 15 15

23 28 33 38 43 48

33.61 35.50 38.58 42.86 48.32 54.95

-17 17 17 18 18 18

06 26 46 05 24 42

14.5 23.1 04.4 17.6 02.1 16.9

1.472 231 1.476 625 1.480 980 1.485 294 1.489 569 1.493 803

5.97 5.96 5.94 5.92 5.90 5.89

5.66 5.65 5.63 5.62 5.60 5.58

10 10 10 10 10 10

07 08 09 10 11 12

18 24 31 39 49 59

16 17 18 19 20 21

15 15 16 16 16 16

54 59 04 09 14 19

02.75 11.68 21.75 32.92 45.19 58.53

-19 19 19 19 20 20

00 17 33 50 05 20

01.4 14.8 56.4 05.5 41.4 43.5

1.497 998 1.502 153 1.506 268 1.510 345 1.514 383 1.518 383

5.87 5.85 5.84 5.82 5.81 5.79

5.57 5.55 5.54 5.52 5.51 5.49

10 10 10 10 10 10

14 15 16 17 19 20

11 24 38 53 09 27

22 23 24 25 26 27

16 16 16 16 16 16

25 30 35 41 46 51

12.91 28.33 44.75 02.14 20.47 39.70

-20 20 21 21 21 21

35 49 02 15 27 38

11.0 03.4 20.1 00.4 03.9 29.9

1.522 345 1.526 269 1.530 155 1.534 003 1.537 815 1.541 589

5.78 5.76 5.75 5.73 5.72 5.70

5.48 5.46 5.45 5.44 5.42 5.41

10 10 10 10 10 10

21 23 24 25 27 28

45 04 25 46 08 31

28 29 30 31 32

16 17 17 17 17

56 02 07 13 18

59.82 20.76 42.50 04.99 28.18

-21 21 22 22 -22

49 59 08 17 26

18.0 27.6 58.3 49.7 01.2

1.545 326 1.549 026 1.552 689 1.556 315 1.559 904

5.69 5.68 5.66 5.65 5.64

5.40 5.38 5.37 5.36 5.35

10 10 10 10 10

29 31 32 34 35

55 20 46 12 39

126

MARS, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 214 215 216 217 217 218

' 08 05 03 01 59 57

" º ' " 23.9 +0 29 48.3 58.0 0 28 00.6 41.8 0 26 12.2 35.5 0 24 23.0 39.1 0 22 33.0 52.9 0 20 42.4

º 1.589 7929 Apr. 2 261 1.587 5695 4 262 1.585 3231 6 263 1.583 0545 8 264 1.580 7641 10 266 1.578 4526 12 267

' 35 42 49 57 04 12

" º ' " 24.6 -0 58 36.7 23.3 1 00 26.2 35.8 1 02 14.7 02.1 1 04 02.1 42.2 1 05 48.4 36.1 1 07 33.5

1.474 3177 1.471 7992 1.469 2951 1.466 8063 1.464 3340 1.461 8791

13 15 17 19 21 23

219 220 221 222 223 224

56 54 53 52 51 50

17.0 +0 18 51.0 51.4 0 16 59.1 36.4 0 15 06.5 32.1 0 13 13.2 38.6 0 11 19.4 56.1 0 09 25.0

1.576 1207 1.573 7688 1.571 3977 1.569 0079 1.566 6001 1.564 1751

20 29 37 46 55 04

43.7 -1 09 17.4 05.0 1 10 60.0 40.0 1 12 41.2 28.6 1 14 21.0 30.7 1 15 59.3 46.3 1 17 36.2

1.459 4426 1.457 0256 1.454 6290 1.452 2540 1.449 9015 1.447 5725

25 27 29 31 Feb. 2 4

225 226 227 228 229 230

50 50 49 49 50 50

24.6 +0 07 30.2 04.4 0 05 34.7 55.4 0 03 38.9 58.0 +0 01 42.6 12.1 -0 00 14.1 37.9 0 02 11.2

1.561 7333 26 275 14 15.3 -1 19 11.4 1.559 2756 28 276 23 57.7 1 20 45.0 1.556 8027 30 277 33 53.3 1 22 16.9 1.554 3151 May 2 278 44 02.0 1 23 47.0 1.551 8137 4 279 54 23.9 1 25 15.3 1.549 2992 6 281 04 58.6 1 26 41.7

1.445 2681 1.442 9894 1.440 7372 1.438 5127 1.436 3168 1.434 1506

6 8 10 12 14 16

231 232 233 234 235 236

51 52 53 54 55 57

15.5 -0 04 08.6 05.1 0 06 06.3 06.7 0 08 04.3 20.6 0 10 02.5 46.6 0 12 00.9 25.1 0 13 59.5

1.546 7722 1.544 2337 1.541 6842 1.539 1246 1.536 5557 1.533 9783

8 10 12 14 16 18

282 283 284 285 287 288

15 26 37 49 01 12

46.1 -1 28 06.2 46.3 1 29 28.6 59.1 1 30 49.0 24.3 1 32 07.3 01.7 1 33 23.4 51.2 1 34 37.3

1.432 0150 1.429 9111 1.427 8399 1.425 8023 1.423 7993 1.421 8319

18 20 22 24 26 28

237 239 240 241 242 243

59 01 03 06 08 11

16.0 -0 15 58.3 19.6 0 17 57.1 35.8 0 19 56.0 04.8 0 21 54.8 46.8 0 23 53.7 41.6 0 25 52.5

1.531 3931 1.528 8010 1.526 2029 1.523 5994 1.520 9916 1.518 3801

20 22 24 26 28 30

289 290 291 293 294 295

24 37 49 02 14 27

52.6 -1 35 48.9 05.7 1 36 58.2 30.4 1 38 05.1 06.5 1 39 09.5 53.7 1 40 11.4 51.9 1 41 10.8

1.419 9010 1.418 0077 1.416 1527 1.414 3371 1.412 5618 1.410 8276

1 3 5 7 9 11

244 245 246 247 248 249

14 18 21 25 29 33

49.5 -0 27 51.1 10.6 0 29 49.7 44.8 0 31 47.9 32.4 0 33 46.0 33.3 0 35 43.8 47.6 0 37 41.2

1.515 7660 June 1 1.513 1501 3 1.510 5333 5 1.507 9164 7 1.505 3004 9 1.502 6862 11

296 297 299 300 301 302

41 54 07 21 35 49

00.7 -1 42 07.6 20.1 1 43 01.7 49.7 1 43 53.1 29.3 1 44 41.8 18.6 1 45 27.8 17.5 1 46 10.9

1.409 1354 1.407 4861 1.405 8806 1.404 3197 1.402 8042 1.401 3348

13 15 17 19 21 23

250 251 252 253 254 256

38 42 47 53 58 03

15.4 -0 39 38.3 56.7 0 41 34.9 51.6 0 43 31.0 00.1 0 45 26.6 22.4 0 47 21.7 58.3 0 49 16.1

1.500 0747 1.497 4668 1.494 8636 1.492 2658 1.489 6746 1.487 0907

304 305 306 307 309 310

03 17 32 46 01 16

25.6 -1 46 51.0 42.6 1 47 28.4 08.3 1 48 02.7 42.3 1 48 34.1 24.4 1 49 02.5 14.4 1 49 27.8

1.399 9125 1.398 5378 1.397 2116 1.395 9346 1.394 7075 1.393 5308

25 27 29 31 Apr. 2

257 258 259 260 261

09 15 22 28 35

48.0 -0 51 09.8 51.5 0 53 02.8 08.7 0 54 54.9 39.7 0 56 46.3 24.6 -0 58 36.7

1.484 5154 25 311 31 11.7 -1 1.481 9494 27 312 46 16.2 1 1.479 3938 29 314 01 27.5 1 1.476 8495 July 1 315 16 45.2 1 1.474 3177 3 316 32 09.1 -1

Jan.

Mar.

14 16 18 20 22 24

13 15 17 19 21 23

268 269 270 271 272 274

49 50 50 50 50

50.0 09.2 25.2 38.1 47.8

1.392 4053 1.391 3316 1.390 3103 1.389 3419 1.388 4270

127

MARS, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 315 316 317 319 320 321

' 16 32 47 03 18 34

" º ' " 45.2 -1 50 38.1 09.1 1 50 47.8 38.8 1 50 54.3 14.0 1 50 57.6 54.2 1 50 57.7 39.2 1 50 54.5

1.389 3419 Oct. 1 1.388 4270 3 1.387 5660 5 1.386 7595 7 1.386 0079 9 1.385 3116 11

º 13 14 15 16 18 19

' 11 24 38 51 04 17

" º ' " 19.0 -1 06 03.9 49.9 1 04 08.6 10.6 1 02 11.8 21.0 1 00 13.6 20.7 0 58 14.0 09.5 0 56 13.2

1.405 2671 1.406 8540 1.408 4848 1.410 1588 1.411 8749 1.413 6325

13 15 17 19 21 23

322 324 325 326 327 329

50 06 22 38 54 10

28.6 -1 50 48.1 22.0 1 50 38.5 19.0 1 50 25.6 19.3 1 50 09.5 22.5 1 49 50.1 28.2 1 49 27.6

1.384 6710 1.384 0865 1.383 5584 1.383 0870 1.382 6725 1.382 3153

13 15 17 19 21 23

20 21 22 24 25 26

29 42 54 06 18 30

47.3 -0 54 11.1 13.8 0 52 08.0 28.9 0 50 03.7 32.3 0 47 58.5 23.9 0 45 52.3 03.5 0 43 45.4

1.415 4305 1.417 2681 1.419 1444 1.421 0584 1.423 0092 1.424 9958

25 27 29 31 Aug. 2 4

330 331 332 334 335 336

26 42 58 15 31 47

36.0 -1 49 01.7 45.5 1 48 32.7 56.5 1 48 00.5 08.4 1 47 25.0 20.9 1 46 46.4 33.6 1 46 04.7

1.382 0154 1.381 7732 1.381 5886 1.381 4619 1.381 3930 Nov. 1.381 3821

25 27 29 31 2 4

27 28 30 31 32 33

41 52 03 14 25 35

31.0 -0 41 37.6 46.2 0 39 29.1 48.9 0 37 20.0 39.1 0 35 10.3 16.6 0 33 00.1 41.2 0 30 49.4

1.427 0173 1.429 0727 1.431 1611 1.433 2813 1.435 4326 1.437 6137

6 8 10 12 14 16

338 339 340 341 343 344

03 19 36 52 08 24

46.2 -1 45 19.8 58.1 1 44 31.9 09.1 1 43 40.8 18.8 1 42 46.7 26.7 1 41 49.6 32.6 1 40 49.6

1.381 4290 1.381 5339 1.381 6966 1.381 9171 1.382 1951 1.382 5306

6 8 10 12 14 16

34 35 37 38 39 40

45 55 05 15 24 33

53.0 -0 28 38.4 51.6 0 26 27.1 37.2 0 24 15.5 09.5 0 22 03.8 28.6 0 19 51.9 34.2 0 17 40.0

1.439 8239 1.442 0619 1.444 3269 1.446 6178 1.448 9336 1.451 2732

18 20 22 24 26 28

345 346 348 349 350 352

40 56 12 28 44 00

35.9 -1 39 46.6 36.4 1 38 40.8 33.6 1 37 32.0 27.2 1 36 20.5 16.9 1 35 06.3 02.2 1 33 49.3

1.382 9234 1.383 3732 1.383 8797 1.384 4428 1.385 0619 1.385 7369

18 20 22 24 26 28

41 42 43 45 46 47

42 51 59 07 15 23

26.5 -0 15 28.0 05.2 0 13 16.2 30.4 0 11 04.4 42.0 0 08 52.8 40.0 0 06 41.5 24.3 0 04 30.4

1.453 6357 1.456 0201 1.458 4252 1.460 8502 1.463 2939 1.465 7554

30 1 3 5 7 9

353 354 355 357 358 359

15 31 46 02 17 32

42.8 -1 32 29.7 18.3 1 31 07.5 48.4 1 29 42.8 12.7 1 28 15.5 31.0 1 26 45.9 42.8 1 25 13.8

1.386 4673 30 1.387 2527 Dec. 2 1.388 0927 4 1.388 9867 6 1.389 9344 8 1.390 9351 10

48 49 50 51 52 54

30 38 45 52 58 05

55.0 -0 02 19.7 11.9 -0 00 09.3 15.1 +0 02 00.5 04.7 0 04 10.0 40.5 0 06 18.8 02.6 0 08 27.1

1.468 2337 1.470 7277 1.473 2364 1.475 7588 1.478 2940 1.480 8410

11 13 15 17 19 21

0 2 3 4 5 7

47 02 17 32 46 01

47.9 -1 23 39.5 45.9 1 22 02.9 36.5 1 20 24.2 19.4 1 18 43.4 54.2 1 17 00.5 20.8 1 15 15.6

1.391 9883 1.393 0934 1.394 2498 1.395 4569 1.396 7140 1.398 0204

12 14 16 18 20 22

55 56 57 58 59 60

11 17 22 28 33 38

11.0 +0 10 34.8 05.8 0 12 41.8 46.9 0 14 48.1 14.4 0 16 53.6 28.3 0 18 58.3 28.7 0 21 02.2

1.483 3986 1.485 9661 1.488 5423 1.491 1264 1.493 7173 1.496 3142

23 25 27 29 1

8 9 10 11 13

15 29 43 57 11

38.7 -1 13 28.8 47.8 1 11 40.1 47.7 1 09 49.7 38.2 1 07 57.6 19.0 -1 06 03.9

1.399 3755 1.400 7785 1.402 2286 1.403 7251 1.405 2671

24 26 28 30 32

61 62 63 64 66

43 47 52 56 00

15.6 +0 23 05.2 49.0 0 25 07.3 09.1 0 27 08.4 15.8 0 29 08.5 09.2 +0 31 07.6

1.498 9160 1.501 5218 1.504 1307 1.506 7418 1.509 3541

July

Sept.

Oct.

128

MARS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Jan.

Feb.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

0 1 2 3 4 5

º 237 238 239 239 240 241

' 42 23 03 43 24 04

" 42.6 02.7 23.9 46.3 09.9 34.6

º +0 0 0 0 0 0

' 22 21 21 20 19 19

" 17.3 41.7 05.9 29.8 53.3 16.6

6 7 8 9 10 11

241 242 243 243 244 245

45 25 05 46 26 07

00.5 27.6 56.1 25.8 56.8 29.1

+0 0 0 0 0 0

18 18 17 16 16 15

12 13 14 15 16 17

245 246 247 247 248 249

48 28 09 49 30 11

02.7 37.7 13.9 51.5 30.4 10.6

+0 0 0 0 0 0

18 19 20 21 22 23

249 250 251 251 252 253

51 32 13 54 34 15

52.3 35.2 19.5 05.0 51.8 39.7

24 25 26 27 28 29

253 254 255 255 256 257

56 37 18 59 39 20

30 31 1 2 3 4

258 258 259 260 260 261

5 6 7 8 9 10 11 12 13 14 15

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

15 16 17 18 19 20

º 268 269 270 271 271 272

' 58 40 21 02 43 25

" 52.6 06.9 22.2 38.7 56.2 14.6

º -0 0 0 0 0 0

' 10 11 12 13 14 15

" 51.7 43.9 36.6 29.6 23.1 17.0

39.5 02.2 24.5 46.5 08.2 29.6

21 22 23 24 25 26

273 273 274 275 275 276

06 47 29 10 51 33

33.9 54.1 15.0 36.8 59.3 22.5

-0 0 0 0 0 0

16 17 18 18 19 20

11.3 06.0 01.1 56.7 52.6 49.0

14 14 13 12 12 11

50.6 11.3 31.6 51.6 11.2 30.4

27 28 29 1 2 3

277 277 278 279 280 280

14 56 37 19 00 41

46.5 11.2 36.6 02.8 29.7 57.3

-0 0 0 0 0 0

21 22 23 24 25 26

45.8 43.0 40.6 38.7 37.1 36.0

+0 0 0 0 0 0

10 10 09 08 08 07

49.3 07.8 26.0 43.8 01.2 18.3

4 5 6 7 8 9

281 282 282 283 284 284

23 04 46 27 09 50

25.7 54.9 24.8 55.5 26.9 59.1

-0 0 0 0 0 0

27 28 29 30 31 32

35.3 35.0 35.2 35.8 36.9 38.4

28.7 18.7 09.8 01.9 55.0 49.0

+0 0 0 0 0 0

06 05 05 04 03 02

35.0 51.4 07.3 23.0 38.2 53.1

10 11 12 13 14 15

285 286 286 287 288 289

32 14 55 37 18 00

32.1 06.0 40.7 16.4 52.9 30.2

-0 0 0 0 0 0

33 34 35 36 37 38

40.4 42.8 45.7 49.0 52.8 57.1

01 42 23 04 45 26

44.1 40.1 37.2 35.3 34.5 34.7

+0 0 +0 -0 0 0

02 01 00 00 00 01

07.7 21.9 35.7 10.9 57.8 45.1

16 17 18 19 20 21

289 290 291 291 292 293

42 23 05 47 28 10

08.2 47.0 26.3 06.1 46.4 27.0

-0 0 0 0 0 0

40 41 42 43 44 45

01.8 07.0 12.6 18.6 25.1 32.1

262 262 263 264 264 265

07 48 29 10 51 32

36.1 38.6 42.2 46.9 52.8 59.8

-0 0 0 0 0 0

02 03 04 04 05 06

32.8 20.9 09.3 58.2 47.4 37.1

22 23 24 25 26 27

293 294 295 295 296 297

52 33 15 57 38 20

07.9 49.1 30.5 12.1 53.9 35.8

-0 0 0 0 0 0

46 47 48 50 51 52

39.4 47.2 55.4 04.0 13.1 22.5

266 266 267 268 268

14 55 36 17 58

07.9 17.3 27.8 39.6 52.6

-0 0 0 0 -0

07 08 09 10 10

27.2 17.7 08.6 00.0 51.7

28 29 30 31 1

298 298 299 300 300

02 43 25 07 49

17.8 59.8 42.0 24.2 06.4

-0 0 0 0 -0

53 54 55 57 58

32.4 42.8 53.5 04.7 16.2

Feb.

Mar.

Apr.

129

MARS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Apr.

May

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 300 301 302 302 303 304

' 49 30 12 54 35 17

" 06.4 48.6 30.8 13.0 55.1 37.2

º -0 0 1 1 1 1

' 58 59 00 01 03 04

" 16.2 28.3 40.7 53.6 06.9 20.6

7 8 9 10 11 12

304 305 306 307 307 308

59 41 22 04 46 27

19.3 01.5 43.8 26.1 08.5 50.8

-1 1 1 1 1 1

05 06 08 09 10 11

13 14 15 16 17 18

309 309 310 311 311 312

09 51 32 14 56 37

33.0 14.9 56.5 37.5 18.0 57.8

-1 1 1 1 1 1

19 20 21 22 23 24

313 314 314 315 316 316

19 01 42 24 06 47

36.8 15.0 52.3 28.6 03.8 37.9

25 26 27 28 29 30

317 318 318 319 320 320

29 10 52 33 15 56

1 2 3 4 5 6

321 322 323 323 324 325

7 8 9 10 11 12 13 14 15 16 17

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

17 18 19 20 21 22

º 332 333 333 334 335 335

' 36 17 57 38 19 59

" 22.6 11.3 56.8 39.0 17.6 52.6

º -2 2 2 2 2 2

' 00 01 03 04 06 07

" 11.4 39.6 08.1 36.7 05.6 34.6

34.8 49.5 04.5 20.0 36.0 52.3

23 24 25 26 27 28

336 337 338 338 339 340

40 20 01 41 21 01

23.8 51.0 14.2 33.2 47.8 58.0

-2 2 2 2 2 2

09 10 12 13 15 16

03.8 33.2 02.7 32.4 02.3 32.4

13 14 15 17 18 19

09.1 26.3 43.9 01.8 20.2 38.9

29 30 31 1 2 3

340 341 342 342 343 344

42 22 02 41 21 01

03.5 04.4 00.5 51.7 38.2 19.7

-2 2 2 2 2 2

18 19 21 22 24 25

02.5 32.9 03.3 34.0 04.7 35.5

-1 1 1 1 1 1

20 22 23 24 26 27

58.1 17.6 37.4 57.6 18.2 39.1

4 5 6 7 8 9

344 345 345 346 347 347

40 20 59 39 18 57

56.2 27.6 53.7 14.5 29.5 38.7

-2 2 2 2 2 2

27 28 30 31 33 34

06.5 37.6 08.7 39.9 11.1 42.4

10.7 42.4 12.6 41.5 08.9 34.8

-1 1 1 1 1 1

29 30 31 33 34 35

00.4 22.0 44.0 06.3 28.9 51.9

10 11 12 13 14 15

348 349 349 350 351 351

36 15 54 33 11 50

41.8 38.4 28.4 11.6 47.6 16.3

-2 2 2 2 2 2

36 37 39 40 42 43

13.7 45.1 16.4 47.7 18.9 50.2

37 19 00 42 23 04

59.1 21.7 42.7 02.1 19.9 36.0

-1 1 1 1 1 1

37 38 40 41 42 44

15.2 38.9 02.9 27.3 51.9 17.0

16 17 18 19 20 21

352 353 353 354 355 355

28 06 44 22 00 38

37.4 50.5 55.6 52.2 40.1 19.1

-2 2 2 2 2 2

45 46 48 49 51 52

21.3 52.5 23.5 54.5 25.3 56.1

325 326 327 327 328 329

45 27 08 49 30 11

50.4 03.3 14.3 23.5 30.7 35.7

-1 1 1 1 1 1

45 47 48 50 51 52

42.3 08.0 33.9 00.2 26.7 53.5

22 23 24 25 26 27

356 356 357 358 358 359

15 53 30 07 44 20

48.8 09.0 19.5 19.9 10.0 49.7

-2 2 2 2 3 3

54 55 57 58 00 01

26.8 57.3 27.8 58.1 28.2 58.2

329 330 331 331 332

52 33 14 55 36

38.4 38.6 36.1 30.8 22.6

-1 1 1 1 -2

54 55 57 58 00

20.6 48.0 15.5 43.3 11.4

28 29 30 1 2

359 0 1 1 2

57 33 09 45 21

18.8 37.1 44.4 40.5 25.3

-3 3 3 3 -3

03 04 06 07 09

28.1 57.7 27.2 56.5 25.5

May

June

July

130

MARS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

July

Aug.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 23 24 24 24 25 25

' 58 16 34 52 08 24

" 17.0 54.6 54.4 15.6 57.5 59.2

º -4 4 4 4 4 4

' 06 07 08 08 09 10

" 22.8 13.8 03.0 50.2 35.3 18.3

1 2 3 4 5 6

º 1 2 2 3 4 4

' 45 21 56 32 07 42

" 40.5 25.3 58.5 19.7 28.8 25.2

º -3 3 3 3 3 3

' 07 09 10 12 13 15

" 56.5 25.5 54.3 22.9 51.1 19.1

7 8 9 10 11 12

5 5 6 6 7 8

17 51 25 59 33 07

08.7 38.7 55.0 57.0 44.5 16.8

-3 3 3 3 3 3

16 18 19 21 22 23

46.7 14.0 40.9 07.4 33.6 59.3

22 23 24 25 26 27

25 25 26 26 26 26

40 54 08 22 34 46

20.1 59.7 57.3 12.3 44.1 32.0

-4 4 4 4 4 4

10 11 12 12 13 13

59.1 37.5 13.5 46.9 17.7 45.6

13 14 15 16 17 18

8 9 9 10 10 11

40 13 46 18 50 22

33.6 34.3 18.7 46.0 55.9 47.8

-3 3 3 3 3 3

25 26 28 29 31 32

24.6 49.4 13.7 37.6 01.0 Sept. 23.8

28 29 30 31 1 2

26 27 27 27 27 27

57 07 17 26 34 41

35.3 53.4 25.5 10.9 08.9 18.8

-4 4 4 4 4 4

14 14 14 15 15 15

10.6 32.5 51.2 06.7 18.6 27.0

19 20 21 22 23 24

11 12 12 13 13 14

54 25 56 27 57 27

21.2 35.6 30.4 05.2 19.4 12.7

-3 3 3 3 3 3

33 35 36 37 39 40

46.1 07.9 29.0 49.6 09.5 28.8

3 4 5 6 7 8

27 27 27 28 28 28

47 53 57 01 04 06

40.0 11.6 53.2 44.1 43.7 51.5

-4 4 4 4 4 4

15 15 15 15 15 14

31.7 32.4 29.2 21.8 10.1 53.9

25 26 27 28 29 30

14 15 15 16 16 17

56 25 54 23 51 18

44.5 54.6 42.4 07.6 09.8 48.4

-3 3 3 3 3 3

41 43 44 45 46 48

47.4 05.3 22.4 38.7 54.3 09.0

9 10 11 12 13 14

28 28 28 28 28 28

08 08 07 06 04 01

07.0 29.9 59.8 36.5 19.8 09.7

-4 4 4 4 4 4

14 14 13 13 12 11

33.1 07.6 37.1 01.6 20.8 34.7

31 1 2 3 4 5

17 18 18 19 19 19

46 12 39 05 30 55

03.0 53.0 17.8 16.7 49.1 54.3

-3 3 3 3 3 3

49 50 51 52 54 55

22.7 35.6 47.4 58.2 08.0 16.6

15 16 17 18 19 20

27 27 27 27 27 27

57 52 46 39 32 23

06.2 09.7 20.5 39.4 07.0 44.5

-4 4 4 4 4 4

10 09 08 07 06 04

43.0 45.7 42.5 33.3 18.0 56.5

6 7 8 9 10 11

20 20 21 21 21 22

20 44 08 31 54 16

31.6 40.1 19.3 28.3 06.3 12.5

-3 3 3 3 4 4

56 57 58 59 00 01

24.0 30.2 35.2 38.8 41.1 42.0

21 22 23 24 25 26

27 27 26 26 26 26

14 04 53 42 30 17

32.8 33.3 47.3 16.1 01.2 04.3

-4 4 4 3 3 3

03 01 00 58 56 54

28.5 54.1 13.0 25.3 30.7 29.4

12 13 14 15 16

22 22 23 23 23

37 58 19 39 58

46.0 46.1 11.9 02.5 17.0

-4 4 4 4 -4

02 03 04 05 06

41.3 39.2 35.4 30.0 22.8

27 28 29 30 1

26 25 25 25 25

03 49 34 18 02

26.9 10.8 18.0 50.5 50.3

-3 3 3 3 -3

52 50 47 45 42

21.2 06.1 44.2 15.4 39.9

Aug.

Oct.

131

MARS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Oct.

Nov.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 25 24 24 24 23 23

' 02 46 29 11 54 36

" 50.3 19.7 21.0 56.6 09.0 00.9

º -3 3 3 3 3 3

' 42 39 37 34 31 28

" 39.9 57.6 08.6 13.1 11.3 03.2

7 8 9 10 11 12

23 22 22 22 22 21

17 58 40 20 01 42

34.9 53.9 00.6 57.9 48.9 36.6

-3 3 3 3 3 3

24 21 18 14 10 07

13 14 15 16 17 18

21 21 20 20 20 19

23 04 45 26 07 49

24.0 14.4 10.7 16.4 34.6 08.4

-3 2 2 2 2 2

19 20 21 22 23 24

19 19 18 18 18 18

31 13 55 38 22 06

01.0 15.2 53.8 59.3 34.1 40.4

25 26 27 28 29 30

17 17 17 17 16 16

51 36 22 08 56 44

31 1 2 3 4 5

16 16 16 16 15 15

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 15 15 15 15 15 15

' 15 17 20 23 28 33

" 34.1 33.1 19.6 53.1 12.8 18.1

º -0 0 0 0 0 0

' 47 43 40 37 34 31

" 20.5 57.1 37.4 21.3 08.9 00.2

49.0 29.0 03.4 32.3 56.2 15.1

22 23 24 25 26 27

15 15 15 16 16 16

39 45 53 01 09 19

08.4 42.8 00.6 01.0 43.2 06.3

-0 0 0 0 0 0

27 24 21 19 16 13

55.2 53.8 56.1 01.9 11.4 24.4

03 59 55 51 47 43

29.5 39.7 45.8 48.4 47.7 44.0

28 29 30 1 2 3

16 16 16 17 17 17

29 39 51 03 15 28

09.5 52.0 12.9 11.5 46.8 58.0

-0 0 0 0 -0 +0

10 08 05 02 00 02

41.0 01.0 24.6 51.6 22.0 04.2

-2 2 2 2 2 2

39 35 31 27 22 18

37.6 29.0 18.5 06.3 52.9 38.6

4 5 6 7 8 9

17 17 18 18 18 18

42 57 11 27 43 59

44.5 05.3 59.7 27.0 26.6 57.7

+0 0 0 0 0 0

04 06 09 11 13 15

27.1 46.7 03.1 16.3 26.3 33.2

20.2 35.5 27.9 59.1 10.4 03.3

-2 2 2 2 1 1

14 10 05 01 57 53

23.6 08.4 53.3 38.5 24.3 11.1

10 11 12 13 14 15

19 19 19 20 20 20

16 34 52 11 30 49

59.9 32.4 34.8 06.4 06.8 35.1

+0 0 0 0 0 0

17 19 21 23 25 27

37.1 38.1 36.1 31.2 23.6 13.2

32 21 12 02 54 46

38.9 58.2 02.1 51.5 26.9 49.0

-1 1 1 1 1 1

48 44 40 36 32 28

59.1 48.6 39.7 32.9 28.2 25.9

16 17 18 19 20 21

21 21 21 22 22 22

09 29 50 11 33 55

30.9 53.3 41.8 55.5 33.9 36.2

+0 0 0 0 0 0

29 30 32 34 35 37

00.2 44.6 26.5 05.9 43.0 17.6

15 15 15 15 15 15

39 33 28 24 20 17

58.2 54.9 39.4 12.0 32.8 41.9

-1 1 1 1 1 1

24 20 16 12 08 05

26.1 29.1 35.0 43.9 56.0 11.4

22 23 24 25 26 27

23 23 24 24 24 25

18 40 04 27 51 15

01.9 50.2 00.6 32.4 25.1 38.0

+0 0 0 0 0 0

38 40 41 43 44 45

50.0 20.1 48.1 13.8 37.5 59.1

15 15 15 15 15

15 14 14 14 15

39.4 25.5 00.0 23.0 34.1

-1 0 0 0 -0

01 57 54 50 47

30.1 52.4 18.1 47.5 20.5

28 29 30 31 32

25 26 26 26 27

40 05 30 55 21

10.5 02.2 12.4 40.7 26.5

+0 0 0 0 +0

47 48 49 51 52

18.6 36.2 51.8 05.5 17.3

Nov.

Dec.

132

MARS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Jan. 0 1 2 3 4 5

h 15 15 15 15 15 15

m 42 44 47 50 53 56

s º 08.06 -19 54.20 19 40.75 19 27.69 19 15.03 19 02.77 20

' 17 26 36 45 54 03

" 07.1 41.7 07.2 23.4 30.4 27.8

2.191 642 2.184 475 2.177 274 2.170 039 2.162 772 2.155 473

" 4.01 4.03 4.04 4.05 4.07 4.08

" 2.14 2.14 2.15 2.16 2.16 2.17

h 9 9 9 9 9 8

m 05 03 02 01 00 59

s 10 59 50 40 31 23

6 7 8 9 10 11

15 16 16 16 16 16

58 01 04 07 10 12

50.91 -20 39.45 20 28.39 20 17.72 20 07.45 20 57.57 20

12 20 29 37 45 53

15.8 54.1 22.8 41.6 50.5 49.5

2.148 143 2.140 783 2.133 393 2.125 973 2.118 525 2.111 049

4.09 4.11 4.12 4.14 4.15 4.17

2.18 2.19 2.19 2.20 2.21 2.22

8 8 8 8 8 8

58 57 55 54 53 52

14 07 59 52 46 39

12 13 14 15 16 17

16 16 16 16 16 16

15 18 21 24 27 30

48.08 -21 38.97 21 30.24 21 21.89 21 13.91 21 06.31 21

01 09 16 24 31 38

38.4 17.0 45.4 03.4 10.9 07.8

2.103 545 2.096 013 2.088 454 2.080 868 2.073 255 2.065 616

4.18 4.20 4.21 4.23 4.24 4.26

2.22 2.23 2.24 2.25 2.26 2.27

8 8 8 8 8 8

51 50 49 48 47 46

33 28 23 18 14 10

18 19 20 21 22 23

16 16 16 16 16 16

32 35 38 41 44 47

59.07 -21 52.20 21 45.67 21 39.49 22 33.65 22 28.14 22

44 51 57 04 10 16

54.0 29.4 54.0 07.6 10.2 01.7

2.057 950 2.050 258 2.042 540 2.034 797 2.027 030 2.019 239

4.27 4.29 4.31 4.32 4.34 4.36

2.27 2.28 2.29 2.30 2.31 2.32

8 8 8 8 8 8

45 44 43 41 40 39

06 03 00 57 55 53

24 25 26 27 28 29

16 16 16 16 17 17

50 53 56 59 02 05

22.94 -22 18.04 22 13.44 22 09.14 22 05.11 22 01.36 22

21 27 32 37 42 47

42.0 10.9 28.5 34.6 29.1 12.0

2.011 425 2.003 589 1.995 731 1.987 853 1.979 955 1.972 038

4.37 4.39 4.41 4.42 4.44 4.46

2.33 2.34 2.35 2.35 2.36 2.37

8 8 8 8 8 8

38 37 36 35 34 33

52 50 49 49 48 48

30 31 Feb. 1 2 3 4

17 17 17 17 17 17

07 10 13 16 19 22

57.88 -22 54.66 22 51.70 23 48.98 23 46.51 23 44.27 23

51 56 00 04 07 11

43.2 02.7 10.3 06.0 49.8 21.6

1.964 103 1.956 151 1.948 182 1.940 198 1.932 200 1.924 187

4.48 4.50 4.51 4.53 4.55 4.57

2.38 2.39 2.40 2.41 2.42 2.43

8 8 8 8 8 8

32 31 30 29 28 27

48 49 49 50 51 52

5 6 7 8 9 10

17 17 17 17 17 17

25 28 31 34 37 40

42.27 -23 40.48 23 38.92 23 37.56 23 36.39 23 35.42 23

14 17 20 23 25 28

41.4 49.1 44.8 28.3 59.6 18.7

1.916 161 1.908 122 1.900 072 1.892 010 1.883 938 1.875 854

4.59 4.61 4.63 4.65 4.67 4.69

2.44 2.45 2.46 2.47 2.48 2.49

8 8 8 8 8 8

26 25 24 23 23 22

54 56 58 60 02 05

11 12 13 14 15

17 17 17 17 17

43 46 49 52 55

34.63 -23 34.02 23 33.58 23 33.30 23 33.17 -23

30 32 34 35 36

25.4 19.9 02.0 31.7 49.0

1.867 761 1.859 657 1.851 543 1.843 419 1.835 286

4.71 4.73 4.75 4.77 4.79

2.51 2.52 2.53 2.54 2.55

8 8 8 8 8

21 20 19 18 17

08 11 14 17 20

133

MARS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Feb. 15 16 17 18 19 20

h 17 17 18 18 18 18

m 55 58 01 04 07 10

s º 33.17 -23 33.18 23 33.32 23 33.57 23 33.92 23 34.36 23

' 36 37 38 39 39 40

" 49.0 53.8 46.2 26.1 53.5 08.4

1.835 286 1.827 143 1.818 991 1.810 831 1.802 663 1.794 487

" 4.79 4.81 4.83 4.86 4.88 4.90

" 2.55 2.56 2.57 2.58 2.60 2.61

h 8 8 8 8 8 8

m 17 16 15 14 13 12

s 20 24 28 31 35 39

21 22 23 24 25 26

18 18 18 18 18 18

13 16 19 22 25 28

34.87 -23 35.44 23 36.06 23 36.71 23 37.39 23 38.08 23

40 40 39 39 38 37

10.8 00.7 38.1 02.8 15.1 14.8

1.786 305 1.778 117 1.769 923 1.761 726 1.753 524 1.745 319

4.92 4.95 4.97 4.99 5.02 5.04

2.62 2.63 2.64 2.66 2.67 2.68

8 8 8 8 8 8

11 10 09 08 07 07

43 47 51 55 60 04

27 28 29 Mar. 1 2 3

18 18 18 18 18 18

31 34 37 40 43 46

38.77 -23 39.46 23 40.13 23 40.78 23 41.39 23 41.97 23

36 34 32 31 29 26

02.0 36.6 58.8 08.5 05.7 50.5

1.737 112 1.728 904 1.720 695 1.712 487 1.704 279 1.696 073

5.06 5.09 5.11 5.14 5.16 5.19

2.69 2.71 2.72 2.73 2.75 2.76

8 8 8 8 8 8

06 05 04 03 02 01

08 12 16 20 25 29

4 5 6 7 8 9

18 18 18 18 19 19

49 52 55 58 01 04

42.50 -23 42.96 23 43.36 23 43.69 23 43.93 23 44.07 23

24 21 18 15 12 09

23.0 43.1 51.0 46.6 29.9 01.1

1.687 870 1.679 670 1.671 473 1.663 280 1.655 092 1.646 909

5.21 5.24 5.26 5.29 5.31 5.34

2.77 2.79 2.80 2.81 2.83 2.84

8 7 7 7 7 7

00 59 58 57 56 55

33 36 40 44 48 51

10 11 12 13 14 15

19 19 19 19 19 19

07 10 13 16 19 22

44.13 -23 44.07 23 43.91 22 43.64 22 43.24 22 42.70 22

05 01 57 53 48 43

20.1 27.0 21.9 04.7 35.5 54.5

1.638 731 1.630 558 1.622 390 1.614 228 1.606 071 1.597 920

5.37 5.39 5.42 5.45 5.48 5.50

2.86 2.87 2.88 2.90 2.91 2.93

7 7 7 7 7 7

54 53 53 52 51 50

55 58 02 05 08 11

16 17 18 19 20 21

19 19 19 19 19 19

25 28 31 34 37 40

42.01 -22 41.17 22 40.14 22 38.93 22 37.53 22 35.91 22

39 33 28 23 17 11

01.6 57.0 40.7 12.9 33.5 42.7

1.589 774 1.581 635 1.573 502 1.565 375 1.557 256 1.549 145

5.53 5.56 5.59 5.62 5.65 5.68

2.94 2.96 2.97 2.99 3.01 3.02

7 7 7 7 7 7

49 48 47 46 45 44

13 16 18 21 23 24

22 23 24 25 26 27

19 19 19 19 19 19

43 46 49 52 55 58

34.07 -22 31.99 21 29.68 21 27.13 21 24.31 21 21.24 21

05 59 53 46 39 32

40.5 27.1 02.5 26.8 40.0 42.4

1.541 043 1.532 949 1.524 865 1.516 791 1.508 728 1.500 676

5.71 5.74 5.77 5.80 5.83 5.86

3.04 3.05 3.07 3.09 3.10 3.12

7 7 7 7 7 7

43 42 41 40 39 38

26 27 28 29 30 30

28 29 30 31 Apr. 1

20 20 20 20 20

01 04 07 10 13

17.90 -21 14.28 21 10.39 21 06.20 21 01.73 -20

25 18 10 03 55

33.9 14.8 45.1 04.9 14.3

1.492 637 1.484 610 1.476 597 1.468 598 1.460 614

5.89 5.92 5.96 5.99 6.02

3.14 3.15 3.17 3.19 3.20

7 7 7 7 7

37 36 35 34 33

30 30 30 29 28

134

MARS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Apr. 1 2 3 4 5 6

h 20 20 20 20 20 20

m 13 15 18 21 24 27

s º 01.73 -20 56.96 20 51.89 20 46.51 20 40.83 20 34.83 20

' 55 47 39 30 22 13

" 14.3 13.5 02.6 41.6 10.7 30.0

1.460 614 1.452 644 1.444 691 1.436 753 1.428 832 1.420 928

" 6.02 6.05 6.09 6.12 6.15 6.19

" 3.20 3.22 3.24 3.26 3.28 3.29

h 7 7 7 7 7 7

m 33 32 31 30 29 28

s 28 26 25 23 20 18

7 8 9 10 11 12

20 20 20 20 20 20

30 33 36 39 42 44

28.53 -20 21.91 19 14.98 19 07.74 19 00.18 19 52.30 19

04 55 46 37 27 18

39.5 39.4 29.8 10.8 42.5 05.1

1.413 040 1.405 169 1.397 315 1.389 477 1.381 656 1.373 851

6.22 6.26 6.29 6.33 6.36 6.40

3.31 3.33 3.35 3.37 3.39 3.41

7 7 7 7 7 7

27 26 25 24 23 21

15 12 08 04 00 56

13 14 15 16 17 18

20 20 20 20 20 21

47 50 53 56 59 01

44.09 -19 35.53 18 26.62 18 17.36 18 07.73 18 57.72 18

08 58 48 38 27 17

18.7 23.5 19.6 07.1 46.2 17.1

1.366 062 1.358 290 1.350 535 1.342 796 1.335 074 1.327 369

6.44 6.47 6.51 6.55 6.59 6.63

3.43 3.45 3.47 3.49 3.51 3.53

7 7 7 7 7 7

20 19 18 17 16 15

51 46 40 34 28 21

19 20 21 22 23 24

21 21 21 21 21 21

04 07 10 13 16 18

47.34 -18 36.58 17 25.43 17 13.89 17 01.95 17 49.62 17

06 55 45 34 22 11

39.8 54.6 01.5 00.8 52.6 37.0

1.319 682 1.312 013 1.304 363 1.296 731 1.289 118 1.281 525

6.66 6.70 6.74 6.78 6.82 6.86

3.55 3.57 3.59 3.61 3.63 3.65

7 7 7 7 7 7

14 13 11 10 09 08

14 07 59 51 43 34

25 26 27 28 29 30

21 21 21 21 21 21

21 24 27 29 32 35

36.88 -17 23.74 16 10.20 16 56.24 16 41.88 16 27.11 16

00 48 37 25 13 01

14.2 44.4 07.7 24.3 34.4 38.0

1.273 952 1.266 400 1.258 869 1.251 359 1.243 872 1.236 406

6.90 6.94 6.99 7.03 7.07 7.11

3.67 3.70 3.72 3.74 3.76 3.79

7 7 7 7 7 7

07 06 05 03 02 01

24 15 04 54 43 31

May 1 2 3 4 5 6

21 21 21 21 21 21

38 40 43 46 49 51

11.92 -15 56.33 15 40.32 15 23.91 15 07.09 15 49.88 14

49 37 25 12 00 47

35.4 26.8 12.2 51.8 25.7 54.0

1.228 963 1.221 544 1.214 147 1.206 774 1.199 424 1.192 097

7.16 7.20 7.24 7.29 7.33 7.38

3.81 3.83 3.85 3.88 3.90 3.93

7 6 6 6 6 6

00 59 57 56 55 54

20 07 55 42 28 15

7 8 9 10 11 12

21 21 21 22 22 22

54 57 59 02 05 07

32.26 -14 14.26 14 55.85 14 37.05 13 17.85 13 58.23 13

35 22 09 56 43 30

17.0 34.7 47.3 55.0 58.0 56.4

1.184 793 1.177 511 1.170 252 1.163 015 1.155 800 1.148 607

7.42 7.47 7.51 7.56 7.61 7.66

3.95 3.97 4.00 4.02 4.05 4.07

6 6 6 6 6 6

53 51 50 49 47 46

00 46 31 15 59 43

13 14 15 16 17

22 22 22 22 22

10 13 15 18 21

38.20 -13 17.74 13 56.85 12 35.54 12 13.78 -12

17 04 51 38 24

50.5 40.4 26.3 08.4 46.9

1.141 435 1.134 284 1.127 155 1.120 048 1.112 962

7.70 7.75 7.80 7.85 7.90

4.10 4.13 4.15 4.18 4.20

6 6 6 6 6

45 44 42 41 40

27 09 52 34 16

135

MARS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

May 17 18 19 20 21 22

h 22 22 22 22 22 22

m 21 23 26 29 31 34

s º 13.78 -12 51.59 12 28.94 11 05.85 11 42.31 11 18.31 11

' 24 11 57 44 30 17

" 46.9 21.9 53.7 22.4 48.3 11.5

1.112 962 1.105 898 1.098 855 1.091 835 1.084 838 1.077 863

" 7.90 7.95 8.00 8.05 8.11 8.16

" 4.20 4.23 4.26 4.29 4.31 4.34

h 6 6 6 6 6 6

m 40 38 37 36 34 33

s 16 57 38 18 58 37

23 24 25 26 27 28

22 22 22 22 22 22

36 39 42 44 47 49

53.86 -11 28.94 10 03.55 10 37.70 10 11.37 10 44.57 9

03 49 36 22 08 54

32.1 50.5 06.8 21.1 33.8 44.8

1.070 911 1.063 982 1.057 077 1.050 196 1.043 338 1.036 506

8.21 8.27 8.32 8.37 8.43 8.48

4.37 4.40 4.43 4.46 4.49 4.52

6 6 6 6 6 6

32 30 29 28 26 25

16 55 33 10 47 24

29 30 31 June 1 2 3

22 22 22 22 23 23

52 54 57 59 02 04

17.30 49.54 21.32 52.63 23.46 53.83

-9 9 9 8 8 8

40 27 13 59 45 31

54.5 03.0 10.4 16.9 22.6 27.7

1.029 698 1.022 914 1.016 156 1.009 422 1.002 714 0.996 030

8.54 8.60 8.65 8.71 8.77 8.83

4.55 4.58 4.61 4.64 4.67 4.70

6 6 6 6 6 6

23 22 21 19 18 16

60 36 11 46 20 54

4 5 6 7 8 9

23 23 23 23 23 23

07 09 12 14 17 19

23.74 53.17 22.15 50.64 18.65 46.17

-8 8 7 7 7 7

17 03 49 35 21 07

32.3 36.6 40.8 45.0 49.4 54.4

0.989 370 0.982 734 0.976 122 0.969 533 0.962 966 0.956 422

8.89 8.95 9.01 9.07 9.13 9.19

4.73 4.76 4.79 4.83 4.86 4.89

6 6 6 6 6 6

15 13 12 11 09 08

27 60 32 04 35 06

10 11 12 13 14 15

23 23 23 23 23 23

22 24 27 29 31 34

13.19 39.70 05.68 31.14 56.06 20.42

-6 6 6 6 5 5

53 40 26 12 58 44

59.9 06.3 13.8 22.5 32.7 44.6

0.949 900 0.943 400 0.936 922 0.930 465 0.924 030 0.917 617

9.26 9.32 9.39 9.45 9.52 9.58

4.93 4.96 5.00 5.03 5.06 5.10

6 6 6 6 6 5

06 05 03 02 00 59

37 07 36 05 33 01

16 17 18 19 20 21

23 23 23 23 23 23

36 39 41 43 46 48

44.23 07.47 30.12 52.19 13.65 34.49

-5 5 5 4 4 4

30 17 03 49 36 22

58.3 14.1 32.2 52.8 16.1 42.3

0.911 225 0.904 854 0.898 506 0.892 179 0.885 875 0.879 593

9.65 9.72 9.79 9.86 9.93 10.00

5.14 5.17 5.21 5.25 5.28 5.32

5 5 5 5 5 5

57 55 54 52 51 49

28 55 21 46 11 35

22 23 24 25 26 27

23 23 23 23 0 0

50 53 55 57 00 02

54.71 14.30 33.23 51.50 09.10 26.02

-4 3 3 3 3 3

09 55 42 29 15 02

11.6 44.2 20.3 00.1 43.7 31.4

0.873 334 0.867 097 0.860 884 0.854 694 0.848 529 0.842 387

10.07 10.14 10.22 10.29 10.36 10.44

5.36 5.40 5.44 5.48 5.52 5.56

5 5 5 5 5 5

47 46 44 43 41 39

59 22 44 06 27 47

28 29 30 July 1 2

0 0 0 0 0

04 06 09 11 13

42.26 57.82 12.67 26.82 40.26

-2 2 2 2 -1

49 36 23 10 57

23.3 19.4 20.0 25.2 35.2

0.836 269 0.830 175 0.824 105 0.818 059 0.812 036

10.52 10.59 10.67 10.75 10.83

5.60 5.64 5.68 5.72 5.76

5 5 5 5 5

38 36 34 33 31

07 26 44 02 19

136

MARS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

July 1 2 3 4 5 6

h 0 0 0 0 0 0

m 11 13 15 18 20 22

s 26.82 40.26 52.98 04.96 16.18 26.63

º -2 1 1 1 1 1

' 10 57 44 32 19 07

" 25.2 35.2 50.0 09.9 35.0 05.5

0.818 059 0.812 036 0.806 037 0.800 061 0.794 108 0.788 177

" 10.75 10.83 10.91 10.99 11.07 11.16

" 5.72 5.76 5.81 5.85 5.89 5.94

h 5 5 5 5 5 5

m 33 31 29 27 26 24

s 02 19 35 50 05 19

7 8 9 10 11 12

0 0 0 0 0 0

24 26 28 31 33 35

36.28 45.11 53.11 00.25 06.50 11.84

0 0 0 0 -0 +0

54 42 30 18 06 05

41.7 23.6 11.6 05.8 06.5 46.2

0.782 267 0.776 380 0.770 514 0.764 670 0.758 847 0.753 045

11.24 11.33 11.41 11.50 11.59 11.68

5.98 6.03 6.07 6.12 6.17 6.21

5 5 5 5 5 5

22 20 18 17 15 13

32 44 55 06 15 24

13 14 15 16 17 18

0 0 0 0 0 0

37 39 41 43 45 47

16.24 19.68 22.13 23.56 23.94 23.25

+0 0 0 0 1 1

17 29 40 52 03 14

32.1 11.0 42.5 06.7 23.2 31.8

0.747 265 0.741 507 0.735 770 0.730 056 0.724 364 0.718 695

11.77 11.86 11.95 12.05 12.14 12.24

6.26 6.31 6.36 6.41 6.46 6.51

5 5 5 5 5 5

11 09 07 05 03 01

32 39 45 49 53 56

19 20 21 22 23 24

0 0 0 0 0 0

49 51 53 55 57 58

21.44 18.50 14.38 09.07 02.52 54.71

+1 1 1 1 2 2

25 36 47 57 08 18

32.4 24.7 08.5 43.7 10.1 27.5

0.713 049 0.707 427 0.701 829 0.696 256 0.690 708 0.685 186

12.33 12.43 12.53 12.63 12.73 12.83

6.56 6.62 6.67 6.72 6.78 6.83

4 4 4 4 4 4

59 57 55 53 51 49

57 58 57 55 52 47

25 26 27 28 29 30

1 1 1 1 1 1

00 02 04 06 07 09

45.61 35.20 23.46 10.35 55.86 39.94

+2 2 2 2 3 3

28 38 48 58 07 16

35.8 34.9 24.7 05.1 35.9 57.0

0.679 691 0.674 223 0.668 783 0.663 370 0.657 986 0.652 629

12.94 13.04 13.15 13.26 13.37 13.47

6.89 6.94 7.00 7.05 7.11 7.17

4 4 4 4 4 4

47 45 43 41 39 36

42 35 26 17 05 53

31 Aug. 1 2 3 4 5

1 1 1 1 1 1

11 13 14 16 17 19

22.56 03.69 43.30 21.32 57.74 32.49

+3 3 3 3 4 4

26 35 44 52 01 09

08.4 09.8 01.1 42.2 12.9 33.0

0.647 301 0.642 002 0.636 731 0.631 489 0.626 276 0.621 092

13.59 13.70 13.81 13.93 14.04 14.16

7.23 7.29 7.35 7.41 7.47 7.54

4 4 4 4 4 4

34 32 30 27 25 23

39 23 06 48 27 06

6 7 8 9 10 11

1 1 1 1 1 1

21 22 24 25 26 28

05.53 36.81 06.29 33.90 59.61 23.35

+4 4 4 4 4 4

17 25 33 41 48 55

42.3 40.7 28.0 03.9 28.4 41.2

0.615 938 0.610 814 0.605 721 0.600 659 0.595 629 0.590 632

14.28 14.40 14.52 14.64 14.76 14.89

7.60 7.66 7.73 7.79 7.86 7.92

4 4 4 4 4 4

20 18 15 13 10 08

42 17 50 21 50 17

12 13 14 15 16

1 1 1 1 1

29 31 32 33 34

45.08 04.72 22.24 37.56 50.64

+5 5 5 5 +5

02 09 16 22 28

42.1 31.1 07.8 32.1 43.8

0.585 669 0.580 741 0.575 848 0.570 993 0.566 175

15.02 15.14 15.27 15.40 15.53

7.99 8.06 8.13 8.20 8.27

4 4 4 3 3

05 03 00 57 55

42 05 26 44 01

137

MARS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Aug. 16 17 18 19 20 21

h 1 1 1 1 1 1

m 34 36 37 38 39 40

s 50.64 01.40 09.80 15.78 19.28 20.26

º +5 5 5 5 5 5

' 28 34 40 46 51 56

" 43.8 42.9 29.0 02.1 22.1 28.8

0.566 175 0.561 398 0.556 662 0.551 969 0.547 320 0.542 718

" 15.53 15.66 15.80 15.93 16.07 16.20

" 8.27 8.34 8.41 8.48 8.55 8.62

h 3 3 3 3 3 3

m 55 52 49 46 43 40

s 01 15 27 36 43 47

22 23 24 25 26 27

1 1 1 1 1 1

41 42 43 43 44 45

18.67 14.46 07.60 58.03 45.72 30.61

+6 6 6 6 6 6

01 06 10 14 18 22

22.2 02.3 28.9 42.2 42.1 28.4

0.538 163 0.533 658 0.529 204 0.524 802 0.520 454 0.516 162

16.34 16.48 16.62 16.76 16.90 17.04

8.70 8.77 8.84 8.92 8.99 9.07

3 3 3 3 3 3

37 34 31 28 25 22

49 49 45 39 30 18

28 29 30 31 Sept. 1 2

1 1 1 1 1 1

46 46 47 48 48 48

12.66 51.82 28.05 01.28 31.47 58.57

+6 6 6 6 6 6

26 29 32 35 37 40

01.3 20.5 26.2 18.1 56.2 20.5

0.511 926 0.507 749 0.503 631 0.499 575 0.495 581 0.491 653

17.18 17.32 17.46 17.60 17.75 17.89

9.14 9.22 9.29 9.37 9.44 9.52

3 3 3 3 3 3

19 15 12 09 05 02

04 47 26 03 37 08

3 4 5 6 7 8

1 1 1 1 1 1

49 49 50 50 50 50

22.54 43.32 00.88 15.16 26.13 33.75

+6 6 6 6 6 6

42 44 46 47 48 49

30.9 27.3 09.7 38.1 52.3 52.5

0.487 790 0.483 997 0.480 274 0.476 624 0.473 049 0.469 552

18.03 18.17 18.31 18.45 18.59 18.73

9.59 9.67 9.74 9.82 9.89 9.97

2 2 2 2 2 2

58 54 51 47 43 40

35 59 21 39 53 04

9 10 11 12 13 14

1 1 1 1 1 1

50 50 50 50 50 50

37.99 38.82 36.21 30.15 20.62 07.61

+6 6 6 6 6 6

50 51 51 51 51 50

38.5 10.5 28.4 32.3 22.2 58.4

0.466 135 0.462 801 0.459 553 0.456 393 0.453 325 0.450 352

18.87 19.00 19.14 19.27 19.40 19.53

10.04 10.11 10.18 10.25 10.32 10.39

2 2 2 2 2 2

36 32 28 24 20 16

12 17 18 16 10 01

15 16 17 18 19 20

1 1 1 1 1 1

49 49 49 48 48 47

51.14 31.20 07.83 41.07 10.95 37.55

+6 6 6 6 6 6

50 49 48 47 45 43

20.8 29.8 25.6 08.4 38.6 56.7

0.447 477 0.444 703 0.442 034 0.439 473 0.437 022 0.434 686

19.65 19.78 19.89 20.01 20.12 20.23

10.46 10.52 10.59 10.65 10.71 10.77

2 2 2 1 1 1

11 07 03 58 54 49

48 32 13 50 24 55

21 22 23 24 25 26

1 1 1 1 1 1

47 46 45 44 44 43

00.93 21.17 38.34 52.54 03.85 12.38

+6 6 6 6 6 6

42 39 37 35 32 29

03.1 58.2 42.7 16.9 41.4 56.7

0.432 467 0.430 368 0.428 392 0.426 541 0.424 817 0.423 223

20.33 20.43 20.53 20.62 20.70 20.78

10.82 10.87 10.92 10.97 11.02 11.06

1 1 1 1 1 1

45 40 36 31 26 21

22 46 08 26 42 54

27 28 29 30 Oct. 1

1 1 1 1 1

42 41 40 39 38

18.23 21.50 22.33 20.84 17.16

+6 6 6 6 +6

27 24 20 17 14

03.3 01.9 53.1 37.4 15.4

0.421 762 0.420 435 0.419 246 0.418 196 0.417 287

20.85 20.92 20.98 21.03 21.07

11.10 11.13 11.16 11.19 11.22

1 1 1 1 0

17 12 07 02 57

04 12 17 20 21

138

MARS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Oct. 1 2 3 4 5 6

h 1 1 1 1 1 1

m 38 37 36 34 33 32

s 17.16 11.44 03.82 54.45 43.51 31.14

º +6 6 6 6 5 5

' 14 10 07 03 59 56

" 15.4 48.0 15.6 39.2 59.3 16.8

0.417 287 0.416 522 0.415 903 0.415 433 0.415 112 0.414 943

" 21.07 21.11 21.14 21.17 21.19 21.19

" 11.22 11.24 11.25 11.27 11.27 11.28

h 0 0 0 0 0 0

m 57 52 47 42 37 31

s 21 20 16 11 05 57

7 8 9 10 11 12

1 1 1 1 1 1

31 30 28 27 26 24

17.54 02.87 47.31 31.06 14.30 57.24

+5 5 5 5 5 5

52 48 45 41 37 33

32.4 46.9 01.2 16.0 32.3 50.9

0.414 928 0.415 069 0.415 367 0.415 824 0.416 441 0.417 220

21.19 21.19 21.17 21.15 21.12 21.08

11.28 11.28 11.27 11.25 11.24 11.22

0 0 0 0 0 0

26 21 16 11 06 00

48 38 27 15 03 51

13 14 15 16 17 18

1 1 1 1 1 1

23 22 21 19 18 17

40.06 22.96 06.17 49.87 34.27 19.59

+5 5 5 5 5 5

30 26 23 19 16 13

12.6 38.3 09.0 45.6 29.0 20.1

0.418 161 0.419 267 0.420 536 0.421 971 0.423 570 0.425 335

21.03 20.98 20.91 20.84 20.76 20.68

11.19 11.16 11.13 11.09 11.05 11.00

23 23 23 23 23 23

50 45 40 34 29 24

26 13 02 51 40 31

19 20 21 22 23 24

1 1 1 1 1 1

16 14 13 12 11 10

06.02 53.73 42.92 33.74 26.35 20.89

+5 5 5 5 5 4

10 07 04 02 00 57

19.8 29.0 48.3 18.6 00.5 54.6

0.427 264 0.429 357 0.431 613 0.434 029 0.436 606 0.439 342

20.58 20.48 20.38 20.26 20.14 20.02

10.95 10.90 10.84 10.78 10.72 10.65

23 23 23 23 22 22

19 14 09 04 59 54

24 17 13 10 09 10

25 26 27 28 29 30

1 1 1 1 1 1

09 08 07 06 05 04

17.49 16.28 17.38 20.88 26.89 35.48

+4 4 4 4 4 4

56 54 52 51 50 50

01.3 21.1 54.6 42.0 43.8 00.2

0.442 234 0.445 281 0.448 481 0.451 834 0.455 335 0.458 985

19.89 19.75 19.61 19.46 19.31 19.16

10.58 10.51 10.44 10.36 10.28 10.20

22 22 22 22 22 22

49 44 39 34 29 25

13 18 26 36 49 05

31 Nov. 1 2 3 4 5

1 1 1 1 1 1

03 03 02 01 00 00

46.75 00.75 17.55 37.21 59.77 25.26

+4 4 4 4 4 4

49 49 49 49 50 50

31.4 17.7 19.2 36.1 08.5 56.5

0.462 780 0.466 720 0.470 801 0.475 023 0.479 382 0.483 878

19.00 18.84 18.68 18.51 18.34 18.17

10.11 10.03 9.94 9.85 9.76 9.67

22 22 22 22 22 21

20 15 11 06 02 57

23 44 07 34 04 36

6 7 8 9 10 11

0 0 0 0 0 0

59 59 58 58 58 58

53.73 25.20 59.70 37.23 17.82 01.48

+4 4 4 4 4 5

52 53 54 56 58 01

00.0 19.2 54.0 44.4 50.4 11.9

0.488 509 0.493 271 0.498 164 0.503 186 0.508 334 0.513 606

18.00 17.83 17.65 17.48 17.30 17.12

9.58 9.49 9.39 9.30 9.21 9.11

21 21 21 21 21 21

53 48 44 40 36 31

12 50 32 16 04 54

12 13 14 15 16

0 0 0 0 0

57 57 57 57 57

48.22 38.04 30.94 26.92 25.98

+5 5 5 5 +5

03 06 09 13 16

48.9 41.4 49.2 12.4 50.9

0.519 001 0.524 517 0.530 150 0.535 899 0.541 761

16.94 16.77 16.59 16.41 16.23

9.02 8.92 8.83 8.73 8.64

21 21 21 21 21

27 23 19 15 11

48 45 44 47 53

139

MARS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Nov. 16 17 18 19 20 21

h 0 0 0 0 0 0

m 57 57 57 57 57 58

s 25.98 28.08 33.22 41.35 52.44 06.45

º +5 5 5 5 5 5

' 16 20 24 29 33 38

" 50.9 44.4 52.8 16.0 53.5 45.3

0.541 761 0.547 734 0.553 814 0.560 000 0.566 288 0.572 676

" 16.23 16.06 15.88 15.70 15.53 15.36

" 8.64 8.54 8.45 8.36 8.26 8.17

h 21 21 21 21 20 20

m 11 08 04 00 56 53

s 53 02 14 28 46 06

22 23 24 25 26 27

0 0 0 0 0 1

58 58 59 59 59 00

23.33 43.05 05.55 30.78 58.71 29.27

+5 5 5 6 6 6

43 49 54 00 06 12

50.9 10.1 42.6 28.1 26.2 36.6

0.579 162 0.585 743 0.592 417 0.599 182 0.606 035 0.612 975

15.18 15.01 14.84 14.68 14.51 14.35

8.08 7.99 7.90 7.81 7.72 7.63

20 20 20 20 20 20

49 45 42 38 35 32

30 56 25 56 30 07

28 29 30 Dec. 1 2 3

1 1 1 1 1 1

01 01 02 02 03 04

02.42 38.10 16.28 56.89 39.89 25.23

+6 6 6 6 6 6

18 25 32 39 46 53

59.1 33.2 18.7 15.2 22.4 40.0

0.620 001 0.627 109 0.634 298 0.641 567 0.648 914 0.656 338

14.18 14.02 13.86 13.71 13.55 13.40

7.55 7.46 7.38 7.29 7.21 7.13

20 20 20 20 20 20

28 25 22 18 15 12

46 28 12 59 48 39

4 5 6 7 8 9

1 1 1 1 1 1

05 06 06 07 08 09

12.86 02.74 54.81 49.04 45.39 43.82

+7 7 7 7 7 7

01 08 16 24 32 40

07.8 45.2 32.2 28.4 33.5 47.3

0.663 837 0.671 410 0.679 056 0.686 772 0.694 559 0.702 414

13.25 13.10 12.95 12.81 12.66 12.52

7.05 6.97 6.89 6.81 6.74 6.66

20 20 20 20 19 19

09 06 03 00 57 54

32 28 25 25 27 31

10 11 12 13 14 15

1 1 1 1 1 1

10 11 12 13 15 16

44.29 46.77 51.23 57.64 05.95 16.13

+7 7 8 8 8 8

49 57 06 15 23 32

09.5 40.0 18.5 04.8 58.6 59.8

0.710 336 0.718 325 0.726 377 0.734 493 0.742 670 0.750 906

12.38 12.24 12.11 11.97 11.84 11.71

6.59 6.52 6.44 6.37 6.30 6.23

19 19 19 19 19 19

51 48 45 43 40 37

37 45 55 06 20 35

16 17 18 19 20 21

1 1 1 1 1 1

17 18 19 21 22 23

28.14 41.95 57.50 14.77 33.70 54.27

+8 8 9 9 9 9

42 51 00 10 19 29

08.0 23.1 44.7 12.6 46.4 25.9

0.759 200 0.767 550 0.775 954 0.784 410 0.792 918 0.801 475

11.58 11.46 11.33 11.21 11.09 10.97

6.16 6.10 6.03 5.97 5.90 5.84

19 19 19 19 19 19

34 32 29 26 24 21

53 12 32 55 19 44

22 23 24 25 26 27

1 1 1 1 1 1

25 26 28 29 31 32

16.43 40.15 05.40 32.13 00.31 29.90

+9 9 9 10 10 10

39 49 58 08 18 29

10.9 01.0 56.1 55.7 59.7 07.8

0.810 081 0.818 733 0.827 430 0.836 172 0.844 957 0.853 785

10.86 10.74 10.63 10.52 10.41 10.30

5.78 5.72 5.66 5.60 5.54 5.48

19 19 19 19 19 19

19 16 14 11 09 06

11 40 10 42 15 49

28 29 30 31 32

1 1 1 1 1

34 35 37 38 40

00.89 +10 33.23 10 06.89 10 41.85 11 18.07 +11

39 49 59 10 20

19.7 35.2 54.0 15.9 40.7

0.862 653 0.871 562 0.880 510 0.889 496 0.898 521

10.19 10.09 9.99 9.89 9.79

5.43 5.37 5.32 5.26 5.21

19 19 18 18 18

04 02 59 57 55

25 02 40 20 01

140

JUPITER, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 276 276 276 276 276 276

' 03 13 23 32 42 52

" º ' " 21.3 +0 06 18.6 13.4 0 06 05.2 05.7 0 05 51.8 58.2 0 05 38.3 50.8 0 05 24.9 43.6 0 05 11.4

º 5.227 578 Apr. 2 283 5.226 849 4 283 5.226 120 6 284 5.225 391 8 284 5.224 662 10 284 5.223 932 12 284

' 40 50 00 10 20 30

" º ' " 12.4 -0 04 04.1 12.3 0 04 17.7 12.3 0 04 31.4 12.5 0 04 45.0 12.9 0 04 58.6 13.4 0 05 12.3

5.193 861 5.193 126 5.192 391 5.191 655 5.190 920 5.190 185

13 15 17 19 21 23

277 277 277 277 277 277

02 12 22 32 42 52

36.6 +0 04 58.0 29.7 0 04 44.5 23.0 0 04 31.1 16.5 0 04 17.6 10.1 0 04 04.1 03.9 0 03 50.6

5.223 202 5.222 472 5.221 741 5.221 011 5.220 280 5.219 549

40 50 00 10 20 30

14.1 -0 05 25.9 15.0 0 05 39.5 16.1 0 05 53.1 17.3 0 06 06.8 18.7 0 06 20.4 20.3 0 06 34.0

5.189 449 5.188 714 5.187 979 5.187 244 5.186 508 5.185 773

25 27 29 31 Feb. 2 4

278 278 278 278 278 278

01 11 21 31 41 51

57.9 +0 03 37.1 52.0 0 03 23.6 46.3 0 03 10.1 40.7 0 02 56.6 35.4 0 02 43.1 30.2 0 02 29.6

5.218 817 26 285 40 22.0 -0 06 47.6 5.218 086 28 285 50 23.9 0 07 01.3 5.217 354 30 286 00 26.0 0 07 14.9 5.216 622 May 2 286 10 28.2 0 07 28.5 5.215 890 4 286 20 30.7 0 07 42.2 5.215 157 6 286 30 33.3 0 07 55.8

5.185 038 5.184 303 5.183 568 5.182 834 5.182 099 5.181 364

6 8 10 12 14 16

279 279 279 279 279 279

01 11 21 31 41 51

25.2 +0 02 16.1 20.3 0 02 02.6 15.6 0 01 49.0 11.0 0 01 35.5 06.6 0 01 21.9 02.5 0 01 08.4

5.214 424 5.213 692 5.212 959 5.212 226 5.211 492 5.210 759

8 10 12 14 16 18

286 286 287 287 287 287

40 50 00 10 20 30

36.0 -0 08 09.5 38.9 0 08 23.1 42.1 0 08 36.7 45.4 0 08 50.3 48.8 0 09 04.0 52.4 0 09 17.6

5.180 630 5.179 895 5.179 161 5.178 426 5.177 692 5.176 958

18 20 22 24 26 28

280 280 280 280 280 280

00 10 20 30 40 50

58.4 +0 00 54.9 54.6 0 00 41.3 50.8 0 00 27.7 47.3 0 00 14.2 44.0 +0 00 00.6 40.8 -0 00 13.0

5.210 025 5.209 292 5.208 558 5.207 824 5.207 090 5.206 355

20 22 24 26 28 30

287 287 288 288 288 288

40 51 01 11 21 31

56.2 -0 09 31.2 00.2 0 09 44.8 04.3 0 09 58.5 08.6 0 10 12.1 13.1 0 10 25.7 17.8 0 10 39.3

5.176 224 5.175 491 5.174 757 5.174 023 5.173 290 5.172 557

1 3 5 7 9 11

281 281 281 281 281 281

00 10 20 30 40 50

37.8 -0 00 26.5 34.9 0 00 40.1 32.2 0 00 53.7 29.7 0 01 07.3 27.4 0 01 20.9 25.2 0 01 34.4

5.205 621 June 1 5.204 887 3 5.204 152 5 5.203 417 7 5.202 683 9 5.201 948 11

288 288 289 289 289 289

41 51 01 11 21 31

22.6 -0 10 53.0 27.6 0 11 06.6 32.8 0 11 20.2 38.1 0 11 33.8 43.6 0 11 47.4 49.3 0 12 01.0

5.171 824 5.171 091 5.170 358 5.169 626 5.168 894 5.168 162

13 15 17 19 21 23

282 282 282 282 282 282

00 10 20 30 40 50

23.2 -0 01 48.0 21.3 0 02 01.6 19.7 0 02 15.3 18.1 0 02 28.9 16.8 0 02 42.5 15.7 0 02 56.1

5.201 213 5.200 478 5.199 743 5.199 008 5.198 273 5.197 538

289 289 290 290 290 290

41 52 02 12 22 32

55.2 -0 12 14.6 01.2 0 12 28.3 07.4 0 12 41.9 13.8 0 12 55.5 20.4 0 13 09.1 27.1 0 13 22.7

5.167 430 5.166 698 5.165 967 5.165 235 5.164 504 5.163 774

25 27 29 31 Apr. 2

283 283 283 283 283

00 10 20 30 40

14.7 -0 03 09.7 13.9 0 03 23.3 13.2 0 03 36.9 12.7 0 03 50.5 12.4 -0 04 04.1

5.196 802 25 290 42 34.0 -0 5.196 067 27 290 52 41.1 0 5.195 332 29 291 02 48.3 0 5.194 597 July 1 291 12 55.7 0 5.193 861 3 291 23 03.3 -0

Jan.

Mar.

14 16 18 20 22 24

13 15 17 19 21 23

284 284 285 285 285 285

13 13 14 14 14

36.2 49.8 03.4 17.0 30.6

5.163 043 5.162 313 5.161 583 5.160 853 5.160 123

141

JUPITER, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 291 291 291 291 291 292

' 12 23 33 43 53 03

" º ' " 55.7 -0 14 17.0 03.3 0 14 30.6 11.0 0 14 44.1 19.0 0 14 57.7 27.1 0 15 11.3 35.3 0 15 24.9

5.160 853 Oct. 1 5.160 123 3 5.159 394 5 5.158 665 7 5.157 936 9 5.157 208 11

º 299 299 299 299 299 299

' 01 11 22 32 42 53

" º ' " 42.3 -0 24 35.8 57.8 0 24 49.1 13.5 0 25 02.4 29.3 0 25 15.6 45.3 0 25 28.9 01.4 0 25 42.1

5.127 677 5.126 967 5.126 258 5.125 549 5.124 840 5.124 133

13 15 17 19 21 23

292 292 292 292 292 293

13 23 34 44 54 04

43.8 -0 15 38.4 52.4 0 15 52.0 01.2 0 16 05.5 10.1 0 16 19.0 19.3 0 16 32.6 28.5 0 16 46.1

5.156 480 5.155 752 5.155 025 5.154 298 5.153 571 5.152 844

13 15 17 19 21 23

300 300 300 300 300 300

03 13 23 34 44 54

17.8 -0 25 55.3 34.3 0 26 08.6 51.0 0 26 21.8 07.8 0 26 34.9 24.8 0 26 48.1 42.0 0 27 01.3

5.123 426 5.122 719 5.122 013 5.121 308 5.120 603 5.119 899

25 27 29 31 Aug. 2 4

293 293 293 293 293 294

14 24 34 45 55 05

38.0 -0 16 59.7 47.7 0 17 13.2 57.5 0 17 26.7 07.5 0 17 40.2 17.7 0 17 53.7 28.0 0 18 07.2

5.152 118 5.151 392 5.150 667 5.149 942 5.149 217 Nov. 5.148 492

25 27 29 31 2 4

301 301 301 301 301 301

04 15 25 35 46 56

59.3 -0 27 14.5 16.9 0 27 27.6 34.5 0 27 40.8 52.4 0 27 53.9 10.4 0 28 07.0 28.7 0 28 20.1

5.119 196 5.118 493 5.117 791 5.117 090 5.116 389 5.115 689

6 8 10 12 14 16

294 294 294 294 294 295

15 25 36 46 56 06

38.5 -0 18 20.7 49.2 0 18 34.2 00.0 0 18 47.7 11.0 0 19 01.2 22.2 0 19 14.6 33.6 0 19 28.1

5.147 768 5.147 045 5.146 322 5.145 599 5.144 876 5.144 154

6 8 10 12 14 16

302 302 302 302 302 302

06 17 27 37 48 58

47.0 -0 28 33.2 05.6 0 28 46.3 24.3 0 28 59.4 43.1 0 29 12.4 02.2 0 29 25.5 21.4 0 29 38.5

5.114 990 5.114 291 5.113 593 5.112 896 5.112 200 5.111 504

18 20 22 24 26 28

295 295 295 295 295 296

16 26 37 47 57 07

45.1 -0 19 41.6 56.9 0 19 55.0 08.7 0 20 08.5 20.8 0 20 21.9 33.0 0 20 35.4 45.4 0 20 48.8

5.143 433 5.142 712 5.141 991 5.141 271 5.140 551 5.139 831

18 20 22 24 26 28

303 303 303 303 303 304

08 19 29 39 50 00

40.8 -0 29 51.5 00.4 0 30 04.5 20.1 0 30 17.5 40.0 0 30 30.5 00.0 0 30 43.5 20.3 0 30 56.4

5.110 809 5.110 114 5.109 421 5.108 728 5.108 036 5.107 345

30 1 3 5 7 9

296 296 296 296 296 297

17 28 38 48 58 09

58.0 -0 21 02.2 10.7 0 21 15.6 23.6 0 21 29.0 36.7 0 21 42.4 49.9 0 21 55.8 03.4 0 22 09.2

5.139 112 30 5.138 394 Dec. 2 5.137 676 4 5.136 958 6 5.136 241 8 5.135 525 10

304 304 304 304 304 305

10 21 31 41 52 02

40.7 -0 31 09.4 01.2 0 31 22.3 22.0 0 31 35.2 42.9 0 31 48.1 04.0 0 32 01.0 25.2 0 32 13.9

5.106 654 5.105 964 5.105 275 5.104 587 5.103 899 5.103 213

11 13 15 17 19 21

297 297 297 297 298 298

19 29 39 49 00 10

17.0 -0 22 22.6 30.7 0 22 35.9 44.7 0 22 49.3 58.8 0 23 02.6 13.1 0 23 16.0 27.5 0 23 29.3

5.134 809 5.134 093 5.133 378 5.132 664 5.131 950 5.131 236

12 14 16 18 20 22

305 305 305 305 305 306

12 23 33 43 54 04

46.6 -0 32 26.8 08.1 0 32 39.6 29.9 0 32 52.4 51.8 0 33 05.3 13.9 0 33 18.1 36.1 0 33 30.8

5.102 527 5.101 842 5.101 158 5.100 474 5.099 792 5.099 110

23 25 27 29 1

298 298 298 298 299

20 30 41 51 01

42.2 -0 23 42.6 56.9 0 23 55.9 11.9 0 24 09.2 27.0 0 24 22.5 42.3 -0 24 35.8

5.130 523 5.129 811 5.129 099 5.128 388 5.127 677

24 26 28 30 32

306 306 306 306 306

14 25 35 46 56

58.6 -0 33 43.6 21.1 0 33 56.4 43.9 0 34 09.1 06.8 0 34 21.9 29.9 -0 34 34.6

5.098 429 5.097 749 5.097 070 5.096 391 5.095 714

July

Sept.

Oct.

142

JUPITER, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Jan.

Feb.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

0 1 2 3 4 5

º 276 276 276 277 277 277

' 26 40 54 07 21 35

" 22.9 12.6 02.0 51.0 39.6 27.7

º +0 0 0 0 0 0

' 05 05 05 05 05 04

" 24.5 18.9 13.3 07.7 02.1 56.6

6 7 8 9 10 11

277 278 278 278 278 278

49 03 16 30 44 58

15.2 02.0 48.2 33.6 18.0 01.6

+0 0 0 0 0 0

04 04 04 04 04 04

12 13 14 15 16 17

279 279 279 279 280 280

11 25 39 52 06 19

44.0 25.3 05.4 44.1 21.5 57.5

+0 0 0 0 0 0

18 19 20 21 22 23

280 280 281 281 281 281

33 47 00 14 27 40

32.1 05.1 36.5 06.1 34.0 59.9

24 25 26 27 28 29

281 282 282 282 282 283

54 07 21 34 47 00

30 31 1 2 3 4

283 283 283 283 284 284

5 6 7 8 9 10 11 12 13 14 15

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

15 16 17 18 19 20

º 286 286 287 287 287 287

' 37 49 01 13 25 37

" 27.8 40.6 49.3 53.8 54.0 49.8

º +0 0 0 0 0 0

' 01 01 00 00 00 00

" 06.3 00.4 54.5 48.6 42.7 36.8

51.0 45.4 39.9 34.4 28.8 23.3

21 22 23 24 25 26

287 288 288 288 288 288

49 01 13 24 36 47

41.0 27.6 09.5 46.5 18.5 45.5

+0 0 0 0 0 +0

00 00 00 00 00 00

30.8 24.8 18.8 12.8 06.8 00.7

04 04 04 04 03 03

17.8 12.2 06.7 01.2 55.6 50.1

27 28 29 1 2 3

288 289 289 289 289 289

59 10 21 32 43 54

07.4 24.1 35.5 41.6 42.1 37.2

-0 0 0 0 0 0

00 00 00 00 00 00

05.4 11.5 17.6 23.8 29.9 36.1

+0 0 0 0 0 0

03 03 03 03 03 03

44.5 39.0 33.4 27.8 22.2 16.7

4 5 6 7 8 9

290 290 290 290 290 290

05 16 26 37 47 58

26.6 10.2 48.1 19.9 45.7 05.4

-0 0 0 0 0 0

00 00 00 01 01 01

42.4 48.6 54.9 01.2 07.6 14.0

23.7 45.4 04.8 21.8 36.3 48.4

+0 0 0 0 0 0

03 03 02 02 02 02

11.1 05.5 59.9 54.3 48.7 43.1

10 11 12 13 14 15

291 291 291 291 291 291

08 18 28 38 48 57

18.8 26.0 26.8 21.2 09.1 50.4

-0 0 0 0 0 0

01 01 01 01 01 01

20.4 26.9 33.4 39.9 46.5 53.1

13 27 40 53 06 19

57.7 04.5 08.4 09.5 07.7 02.9

+0 0 0 0 0 0

02 02 02 02 02 02

37.4 31.8 26.2 20.6 14.9 09.3

16 17 18 19 20 21

292 292 292 292 292 292

07 16 26 35 44 53

25.0 52.7 13.5 27.1 33.5 32.5

-0 0 0 0 0 0

01 02 02 02 02 02

59.8 06.5 13.2 20.0 26.8 33.6

284 284 284 285 285 285

31 44 57 10 22 35

55.0 44.0 29.8 12.1 51.1 26.5

+0 0 0 0 0 0

02 01 01 01 01 01

03.7 58.0 52.3 46.6 40.9 35.2

22 23 24 25 26 27

293 293 293 293 293 293

02 11 19 28 36 44

24.0 08.0 44.3 12.8 33.5 46.3

-0 0 0 0 0 0

02 02 02 03 03 03

40.5 47.4 54.4 01.4 08.4 15.5

285 286 286 286 286

47 00 12 25 37

58.2 26.3 50.6 11.2 27.8

+0 0 0 0 +0

01 01 01 01 01

29.5 23.7 17.9 12.1 06.3

28 29 30 31 1

293 294 294 294 294

52 00 08 16 23

51.0 47.7 36.1 16.2 48.0

-0 0 0 0 -0

03 03 03 03 03

22.6 29.7 36.9 44.1 51.4

Feb.

Mar.

Apr.

143

JUPITER, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Apr.

May

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 294 294 294 294 294 294

' 23 31 38 45 52 59

" 48.0 11.2 25.8 31.7 28.8 17.0

º -0 0 0 0 0 0

' 03 03 04 04 04 04

" 51.4 58.7 06.0 13.4 20.9 28.4

7 8 9 10 11 12

295 295 295 295 295 295

05 12 18 24 31 36

56.2 26.5 47.6 59.7 02.5 56.0

-0 0 0 0 0 0

04 04 04 04 05 05

13 14 15 16 17 18

295 295 295 295 296 296

42 48 53 58 03 08

40.0 14.4 39.1 54.0 59.0 53.9

-0 0 0 0 0 0

19 20 21 22 23 24

296 296 296 296 296 296

13 18 22 26 30 34

38.6 13.2 37.5 51.5 55.0 48.1

25 26 27 28 29 30

296 296 296 296 296 296

38 42 45 48 51 54

1 2 3 4 5 6

296 296 297 297 297 297

7 8 9 10 11 12 13 14 15 16 17

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

17 18 19 20 21 22

º 297 297 297 297 297 297

' 13 13 12 11 10 09

" 52.4 19.2 34.6 38.6 31.3 12.6

º -0 0 0 0 0 0

' 10 10 10 10 10 11

" 18.9 28.4 38.0 47.5 57.2 06.8

36.0 43.6 51.3 59.0 06.7 14.6

23 24 25 26 27 28

297 297 297 297 296 296

07 06 04 02 59 57

42.6 01.4 09.0 05.4 50.7 25.0

-0 0 0 0 0 0

11 11 11 11 11 12

16.5 26.2 35.9 45.6 55.4 05.2

05 05 05 05 05 06

22.5 30.4 38.4 46.4 54.4 02.6

29 30 31 1 2 3

296 296 296 296 296 296

54 52 49 45 42 39

48.4 00.8 02.5 53.5 34.0 04.2

-0 0 0 0 0 0

12 12 12 12 12 13

15.1 25.0 34.8 44.8 54.7 04.7

-0 0 0 0 0 0

06 06 06 06 06 06

10.7 18.9 27.2 35.5 43.8 52.2

4 5 6 7 8 9

296 296 296 296 296 296

35 31 27 23 19 14

24.1 33.9 33.7 23.6 03.6 34.0

-0 0 0 0 0 0

13 13 13 13 13 14

14.7 24.7 34.7 44.7 54.8 04.8

30.6 02.6 23.8 34.3 34.0 22.9

-0 0 0 0 0 0

07 07 07 07 07 07

00.6 09.1 17.7 26.2 34.9 43.5

10 11 12 13 14 15

296 296 296 295 295 295

09 05 00 55 49 44

54.7 06.0 08.0 00.9 44.8 20.0

-0 0 0 0 0 0

14 14 14 14 14 15

14.8 24.8 34.8 44.8 54.8 04.8

57 59 01 03 05 07

00.7 27.6 43.5 48.2 41.9 24.6

-0 0 0 0 0 0

07 08 08 08 08 08

52.3 01.0 09.9 18.8 27.7 36.7

16 17 18 19 20 21

295 295 295 295 295 295

38 33 27 21 15 09

46.7 05.0 15.3 17.7 12.5 00.0

-0 0 0 0 0 0

15 15 15 15 15 16

14.7 24.7 34.6 44.4 54.3 04.1

297 297 297 297 297 297

08 10 11 12 13 13

56.1 16.6 25.9 24.0 10.8 46.3

-0 0 0 0 0 0

08 08 09 09 09 09

45.8 54.9 04.1 13.3 22.5 31.8

22 23 24 25 26 27

295 294 294 294 294 294

02 56 49 43 36 29

40.3 13.7 40.4 00.8 15.0 23.4

-0 0 0 0 0 0

16 16 16 16 16 17

13.9 23.6 33.3 43.0 52.7 02.3

297 297 297 297 297

14 14 14 14 13

10.4 23.1 24.3 14.1 52.4

-0 0 0 0 -0

09 09 10 10 10

41.2 50.5 00.0 09.4 18.9

28 29 30 1 2

294 294 294 294 293

22 15 08 01 53

26.4 24.1 17.0 05.4 49.5

-0 0 0 0 -0

17 17 17 17 17

11.9 21.4 30.9 40.4 49.8

May

June

July

144

JUPITER, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

July

Aug.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 294 293 293 293 293 293

' 01 53 46 39 31 24

" 05.4 49.5 29.7 06.2 39.3 09.3

º -0 0 0 0 0 0

' 17 17 17 18 18 18

" 40.4 49.8 59.1 08.4 17.6 26.8

7 8 9 10 11 12

293 293 293 292 292 292

16 09 01 53 46 38

36.4 00.9 23.2 43.6 02.3 19.8

-0 0 0 0 0 0

18 18 18 19 19 19

13 14 15 16 17 18

292 292 292 292 291 291

30 22 15 07 59 51

36.4 52.4 08.1 24.0 40.4 57.5

-0 0 0 0 0 0

19 20 21 22 23 24

291 291 291 291 291 291

44 36 28 21 13 06

15.8 35.5 57.0 20.6 46.7 15.6

25 26 27 28 29 30

290 290 290 290 290 290

58 51 44 36 29 22

31 1 2 3 4 5

290 290 290 289 289 289

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 288 288 288 288 288 288

' 37 32 27 23 18 14

" 42.2 43.9 54.9 15.4 45.5 25.5

º -0 0 0 0 0 0

' 23 23 23 23 23 23

" 23.4 28.4 33.4 38.3 43.1 47.8

35.9 44.9 53.8 02.7 11.4 20.1

22 23 24 25 26 27

288 288 288 287 287 287

10 06 02 58 55 52

15.4 15.6 26.2 47.3 19.0 01.4

-0 0 0 0 0 0

23 23 24 24 24 24

52.4 56.9 01.4 05.7 10.0 14.2

19 19 19 19 20 20

28.7 37.2 45.6 54.0 02.2 Sept. 10.3

28 29 30 31 1 2

287 287 287 287 287 287

48 45 43 40 38 36

54.7 58.8 13.8 39.7 16.7 04.8

-0 0 0 0 0 0

24 24 24 24 24 24

18.3 22.3 26.2 30.0 33.8 37.4

-0 0 0 0 0 0

20 20 20 20 20 20

18.4 26.3 34.2 42.0 49.6 57.2

3 4 5 6 7 8

287 287 287 287 287 287

34 32 30 29 27 26

04.1 14.5 36.3 09.5 54.0 50.1

-0 0 0 0 0 0

24 24 24 24 24 24

41.0 44.5 47.9 51.2 54.5 57.7

47.6 23.1 02.4 45.9 34.0 26.8

-0 0 0 0 0 0

21 21 21 21 21 21

04.7 12.1 19.4 26.6 33.7 40.7

9 10 11 12 13 14

287 287 287 287 287 287

25 25 24 24 24 24

57.6 16.7 47.4 29.7 23.6 29.0

-0 0 0 0 0 0

25 25 25 25 25 25

00.8 03.8 06.8 09.7 12.6 15.4

15 08 01 54 48 41

24.7 27.9 36.6 51.2 11.8 38.6

-0 0 0 0 0 0

21 21 22 22 22 22

47.7 54.5 01.2 07.7 14.2 20.6

15 16 17 18 19 20

287 287 287 287 287 287

24 25 25 26 27 29

46.1 14.7 54.9 46.8 50.3 05.4

-0 0 0 0 0 0

25 25 25 25 25 25

18.1 20.8 23.4 26.0 28.6 31.1

289 289 289 289 289 289

35 28 22 16 10 04

12.1 52.3 39.6 34.2 36.5 46.5

-0 0 0 0 0 0

22 22 22 22 22 22

26.9 33.0 39.0 45.0 50.8 56.5

21 22 23 24 25 26

287 287 287 287 287 287

30 32 34 36 38 40

32.2 10.6 00.5 01.9 14.6 38.7

-0 0 0 0 0 0

25 25 25 25 25 25

33.6 36.0 38.4 40.7 43.0 45.3

288 288 288 288 288

59 53 48 42 37

04.6 31.0 06.0 49.6 42.2

-0 0 0 0 -0

23 23 23 23 23

02.1 07.5 12.9 18.2 23.4

27 28 29 30 1

287 287 287 287 287

43 46 48 52 55

14.0 00.4 57.9 06.4 25.8

-0 0 0 0 -0

25 25 25 25 25

47.5 49.6 51.8 53.9 55.9

Aug.

Oct.

145

JUPITER, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Oct.

Nov.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 287 287 288 288 288 288

' 55 58 02 06 10 14

" 25.8 56.2 37.4 29.4 32.1 45.6

º -0 0 0 0 0 0

' 25 25 26 26 26 26

" 55.9 58.0 00.0 01.9 03.8 05.7

7 8 9 10 11 12

288 288 288 288 288 288

19 23 28 33 38 43

09.6 44.2 29.2 24.6 30.2 46.1

-0 0 0 0 0 0

26 26 26 26 26 26

13 14 15 16 17 18

288 288 289 289 289 289

49 54 00 06 12 18

12.1 48.1 34.0 29.9 35.6 51.1

-0 0 0 0 0 0

19 20 21 22 23 24

289 289 289 289 289 289

25 31 38 45 52 59

16.3 51.1 35.4 29.0 31.8 43.6

25 26 27 28 29 30

290 290 290 290 290 290

07 14 22 29 37 45

31 1 2 3 4 5

290 291 291 291 291 291

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 293 293 293 293 294 294

' 23 33 43 54 05 15

" 06.9 26.9 53.5 26.5 06.0 51.6

º -0 0 0 0 0 0

' 27 27 27 27 27 27

" 19.4 21.4 23.4 25.5 27.6 29.7

07.6 09.5 11.3 13.1 14.9 16.7

22 23 24 25 26 27

294 294 294 294 295 295

26 37 48 59 11 22

43.3 41.0 44.6 54.1 09.2 30.0

-0 0 0 0 0 0

27 27 27 27 27 27

31.8 33.9 36.1 38.3 40.5 42.7

26 26 26 26 26 26

18.5 20.3 22.0 23.8 25.6 27.3

28 29 30 1 2 3

295 295 295 296 296 296

33 45 57 08 20 32

56.4 28.2 05.4 47.9 35.5 28.3

-0 0 0 0 0 0

27 27 27 27 27 27

45.0 47.3 49.6 51.9 54.3 56.7

-0 0 0 0 0 0

26 26 26 26 26 26

29.1 30.8 32.6 34.3 36.1 37.8

4 5 6 7 8 9

296 296 297 297 297 297

44 56 08 20 33 45

26.0 28.6 36.0 48.0 04.7 25.9

-0 0 0 0 0 0

27 28 28 28 28 28

59.2 01.6 04.1 06.7 09.3 11.9

04.4 34.0 12.3 59.3 54.8 58.7

-0 0 0 0 0 0

26 26 26 26 26 26

39.6 41.3 43.0 44.8 46.5 48.2

10 11 12 13 14 15

297 298 298 298 298 299

57 10 22 35 48 01

51.6 21.7 56.2 34.9 17.8 04.8

-0 0 0 0 0 0

28 28 28 28 28 28

14.6 17.3 20.1 22.9 25.7 28.6

54 02 11 19 28 37

11.0 31.6 00.4 37.2 22.0 14.8

-0 0 0 0 0 0

26 26 26 26 26 26

50.0 51.7 53.4 55.2 56.9 58.7

16 17 18 19 20 21

299 299 299 299 300 300

13 26 39 52 05 19

55.7 50.3 48.6 50.5 55.8 04.4

-0 0 0 0 0 0

28 28 28 28 28 28

31.5 34.5 37.4 40.5 43.5 46.7

291 291 292 292 292 292

46 55 04 14 23 33

15.3 23.5 39.2 02.4 33.0 10.9

-0 0 0 0 0 0

27 27 27 27 27 27

00.5 02.3 04.1 05.9 07.8 09.7

22 23 24 25 26 27

300 300 300 301 301 301

32 45 58 12 25 39

16.3 31.4 49.6 10.9 35.1 02.3

-0 0 0 0 0 0

28 28 28 28 29 29

49.8 53.0 56.2 59.5 02.8 06.1

292 292 293 293 293

42 52 02 12 23

55.9 48.1 47.4 53.7 06.9

-0 0 0 0 -0

27 27 27 27 27

11.5 13.5 15.4 17.4 19.4

28 29 30 31 32

301 302 302 302 302

52 06 19 33 46

32.2 04.8 40.1 17.8 58.0

-0 0 0 0 -0

29 29 29 29 29

09.5 12.9 16.4 19.9 23.5

Nov.

Dec.

146

JUPITER, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Jan. 0 1 2 3 4 5

h 18 18 18 18 18 18

m 28 29 30 31 32 33

s º 02.02 -23 02.14 23 02.23 23 02.28 23 02.29 23 02.26 23

' 11 10 10 09 08 08

" 22.3 47.0 10.2 32.0 52.4 11.4

6.210 104 6.208 890 6.207 460 6.205 813 6.203 951 6.201 874

" 1.42 1.42 1.42 1.42 1.42 1.42

" 14.82 14.83 14.83 14.83 14.84 14.84

h 11 11 11 11 11 11

m 50 47 44 41 38 35

s 03 07 11 15 19 23

6 7 8 9 10 11

18 18 18 18 18 18

34 35 36 37 38 39

02.17 -23 02.02 23 01.81 23 01.54 23 01.19 23 00.75 23

07 06 05 05 04 03

28.9 45.0 59.8 13.2 25.3 36.1

6.199 583 6.197 078 6.194 359 6.191 428 6.188 285 6.184 931

1.42 1.42 1.42 1.42 1.42 1.42

14.85 14.86 14.86 14.87 14.88 14.88

11 11 11 11 11 11

32 29 26 23 20 17

26 30 33 37 40 44

12 13 14 15 16 17

18 18 18 18 18 18

40 40 41 42 43 44

00.23 -23 59.61 23 58.89 23 58.06 23 57.12 22 56.07 22

02 01 01 00 59 58

45.6 53.7 00.6 06.2 10.5 13.5

6.181 366 6.177 590 6.173 604 6.169 408 6.165 003 6.160 389

1.42 1.42 1.42 1.43 1.43 1.43

14.89 14.90 14.91 14.92 14.93 14.94

11 11 11 11 11 11

14 11 08 05 02 00

47 50 53 56 59 01

18 19 20 21 22 23

18 18 18 18 18 18

45 46 47 48 49 50

54.89 -22 53.60 22 52.16 22 50.60 22 48.88 22 47.01 22

57 56 55 54 53 52

15.2 15.7 15.0 13.1 10.0 05.8

6.155 566 6.150 534 6.145 294 6.139 847 6.134 193 6.128 333

1.43 1.43 1.43 1.43 1.43 1.43

14.96 14.97 14.98 14.99 15.01 15.02

10 10 10 10 10 10

57 54 51 48 45 42

04 07 09 11 13 15

24 25 26 27 28 29

18 18 18 18 18 18

51 52 53 54 55 56

44.98 -22 42.77 22 40.38 22 37.81 22 35.05 22 32.08 22

51 49 48 47 46 45

00.5 54.1 46.6 38.0 28.4 17.8

6.122 268 6.116 000 6.109 528 6.102 856 6.095 983 6.088 911

1.44 1.44 1.44 1.44 1.44 1.44

15.04 15.05 15.07 15.08 15.10 15.12

10 10 10 10 10 10

39 36 33 30 27 24

17 18 19 21 22 22

30 31 Feb. 1 2 3 4

18 18 18 19 19 19

57 58 59 00 01 02

28.91 -22 25.53 22 21.93 22 18.12 22 14.07 22 09.80 22

44 42 41 40 39 37

06.1 53.4 39.8 25.2 09.6 53.2

6.081 642 6.074 178 6.066 519 6.058 668 6.050 626 6.042 395

1.45 1.45 1.45 1.45 1.45 1.46

15.14 15.16 15.18 15.19 15.21 15.24

10 10 10 10 10 10

21 18 15 12 09 06

23 23 23 23 23 22

5 6 7 8 9 10

19 19 19 19 19 19

03 04 04 05 06 07

05.29 -22 00.53 22 55.52 22 50.26 22 44.73 22 38.93 22

36 35 33 32 31 29

36.0 17.9 59.0 39.4 19.0 58.0

6.033 975 6.025 370 6.016 581 6.007 609 5.998 456 5.989 123

1.46 1.46 1.46 1.46 1.47 1.47

15.26 15.28 15.30 15.32 15.35 15.37

10 10 9 9 9 9

03 00 57 54 51 48

22 21 19 18 16 14

11 12 13 14 15

19 19 19 19 19

08 09 10 11 12

32.85 -22 26.49 22 19.84 22 12.91 22 05.68 -22

28 27 25 24 23

36.2 13.7 50.6 26.9 02.5

5.979 611 5.969 923 5.960 059 5.950 020 5.939 809

1.47 1.47 1.48 1.48 1.48

15.40 15.42 15.45 15.47 15.50

9 9 9 9 9

45 42 39 36 32

12 09 06 03 59

147

JUPITER, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Feb. 15 16 17 18 19 20

h 19 19 19 19 19 19

m 12 12 13 14 15 16

s º 05.68 -22 58.15 22 50.31 22 42.16 22 33.69 22 24.88 22

' 23 21 20 18 17 15

" 02.5 37.6 12.2 46.3 19.9 53.2

5.939 809 5.929 425 5.918 872 5.908 150 5.897 261 5.886 207

" 1.48 1.48 1.49 1.49 1.49 1.49

" 15.50 15.53 15.55 15.58 15.61 15.64

h 9 9 9 9 9 9

m 32 29 26 23 20 17

s 59 55 51 47 42 37

21 22 23 24 25 26

19 19 19 19 19 19

17 18 18 19 20 21

15.73 -22 06.22 22 56.37 22 46.15 22 35.56 22 24.59 22

14 12 11 10 08 07

26.1 58.6 30.8 02.8 34.5 05.9

5.874 990 5.863 613 5.852 077 5.840 385 5.828 539 5.816 541

1.50 1.50 1.50 1.51 1.51 1.51

15.67 15.70 15.73 15.76 15.79 15.83

9 9 9 9 9 8

14 11 08 05 02 58

32 26 20 13 06 59

27 28 29 Mar. 1 2 3

19 19 19 19 19 19

22 23 23 24 25 26

13.24 -22 01.50 22 49.37 22 36.84 22 23.91 21 10.57 21

05 04 02 01 59 58

37.2 08.3 39.3 10.2 41.0 11.9

5.804 394 5.792 101 5.779 663 5.767 085 5.754 367 5.741 513

1.52 1.52 1.52 1.52 1.53 1.53

15.86 15.89 15.93 15.96 16.00 16.03

8 8 8 8 8 8

55 52 49 46 43 40

51 43 35 26 17 07

4 5 6 7 8 9

19 19 19 19 19 19

26 27 28 29 29 30

56.81 -21 42.63 21 28.01 21 12.96 21 57.46 21 41.52 21

56 55 53 52 50 49

42.8 13.8 44.9 16.2 47.7 19.4

5.728 526 5.715 408 5.702 161 5.688 789 5.675 294 5.661 678

1.54 1.54 1.54 1.55 1.55 1.55

16.07 16.11 16.14 16.18 16.22 16.26

8 8 8 8 8 8

36 33 30 27 24 21

57 47 36 24 13 00

10 11 12 13 14 15

19 19 19 19 19 19

31 32 32 33 34 34

25.11 -21 08.25 21 50.92 21 33.12 21 14.85 21 56.10 21

47 46 44 43 42 40

51.4 23.7 56.3 29.2 02.5 36.3

5.647 943 5.634 092 5.620 127 5.606 051 5.591 865 5.577 572

1.56 1.56 1.56 1.57 1.57 1.58

16.30 16.34 16.38 16.42 16.46 16.51

8 8 8 8 8 8

17 14 11 08 04 01

48 35 21 07 52 37

16 17 18 19 20 21

19 19 19 19 19 19

35 36 36 37 38 38

36.86 -21 17.12 21 56.87 21 36.11 21 14.82 21 53.00 21

39 37 36 34 33 32

10.6 45.4 20.8 56.8 33.5 10.9

5.563 174 5.548 674 5.534 075 5.519 380 5.504 591 5.489 713

1.58 1.58 1.59 1.59 1.60 1.60

16.55 16.59 16.64 16.68 16.72 16.77

7 7 7 7 7 7

58 55 51 48 45 41

22 06 49 32 15 57

22 23 24 25 26 27

19 19 19 19 19 19

39 40 40 41 41 42

30.64 -21 07.74 21 44.28 21 20.26 21 55.68 21 30.53 21

30 29 28 26 25 24

49.1 28.0 07.7 48.3 29.8 12.1

5.474 747 5.459 697 5.444 566 5.429 359 5.414 077 5.398 725

1.61 1.61 1.62 1.62 1.62 1.63

16.82 16.86 16.91 16.96 17.00 17.05

7 7 7 7 7 7

38 35 31 28 25 21

38 19 59 39 18 57

28 29 30 31 Apr. 1

19 19 19 19 19

43 43 44 44 45

04.81 -21 38.50 21 11.61 21 44.12 21 16.04 -21

22 21 20 19 17

55.5 39.9 25.3 11.8 59.5

5.383 306 5.367 824 5.352 282 5.336 684 5.321 033

1.63 1.64 1.64 1.65 1.65

17.10 17.15 17.20 17.25 17.30

7 7 7 7 7

18 15 11 08 05

35 12 49 25 01

148

JUPITER, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Apr. 1 2 3 4 5 6

h 19 19 19 19 19 19

m 45 45 46 46 47 47

s º 16.04 -21 47.34 21 18.03 21 48.11 21 17.55 21 46.36 21

' 17 16 15 14 13 12

" 59.5 48.4 38.5 29.9 22.5 16.5

5.321 033 5.305 333 5.289 587 5.273 798 5.257 971 5.242 109

" 1.65 1.66 1.66 1.67 1.67 1.68

" 17.30 17.35 17.40 17.46 17.51 17.56

h 7 7 6 6 6 6

m 05 01 58 54 51 47

s 01 36 10 44 17 50

7 8 9 10 11 12

19 19 19 19 19 19

48 48 49 49 50 50

14.54 -21 42.07 21 08.97 21 35.21 21 00.80 21 25.74 21

11 10 09 08 07 06

11.9 08.6 06.8 06.4 07.4 10.0

5.226 214 5.210 289 5.194 339 5.178 365 5.162 372 5.146 362

1.68 1.69 1.69 1.70 1.70 1.71

17.62 17.67 17.72 17.78 17.83 17.89

6 6 6 6 6 6

44 40 37 33 30 26

22 53 24 54 23 52

13 14 15 16 17 18

19 19 19 19 19 19

50 51 51 51 52 52

50.00 -21 13.59 21 36.48 21 58.69 21 20.20 21 40.99 21

05 04 03 02 01 01

14.2 20.1 27.6 36.8 47.7 00.4

5.130 339 5.114 306 5.098 267 5.082 226 5.066 186 5.050 152

1.71 1.72 1.72 1.73 1.74 1.74

17.94 18.00 18.06 18.11 18.17 18.23

6 6 6 6 6 6

23 19 16 12 09 05

20 47 14 40 05 30

19 20 21 22 23 24

19 19 19 19 19 19

53 53 53 53 54 54

01.08 -21 20.45 20 39.09 20 57.00 20 14.19 20 30.64 20

00 59 58 58 57 56

14.9 31.2 49.4 09.4 31.3 55.1

5.034 128 5.018 117 5.002 125 4.986 154 4.970 209 4.954 296

1.75 1.75 1.76 1.76 1.77 1.78

18.29 18.35 18.40 18.46 18.52 18.58

6 5 5 5 5 5

01 58 54 51 47 43

54 17 40 01 22 43

25 26 27 28 29 30

19 19 19 19 19 19

54 55 55 55 55 55

46.34 -20 01.31 20 15.52 20 28.98 20 41.69 20 53.63 20

56 55 55 54 54 54

20.9 48.6 18.4 50.3 24.2 00.2

4.938 417 4.922 577 4.906 781 4.891 032 4.875 336 4.859 696

1.78 1.79 1.79 1.80 1.80 1.81

18.64 18.70 18.76 18.82 18.88 18.94

5 5 5 5 5 5

40 36 32 28 25 21

02 21 39 56 13 29

May 1 2 3 4 5 6

19 19 19 19 19 19

56 56 56 56 56 56

04.80 -20 15.21 20 24.84 20 33.70 20 41.78 20 49.09 20

53 53 53 52 52 52

38.4 18.7 01.1 45.7 32.4 21.3

4.844 117 4.828 602 4.813 156 4.797 783 4.782 486 4.767 269

1.82 1.82 1.83 1.83 1.84 1.84

19.00 19.07 19.13 19.19 19.25 19.31

5 5 5 5 5 4

17 13 10 06 02 58

44 58 11 24 36 47

7 8 9 10 11 12

19 19 19 19 19 19

56 57 57 57 57 57

55.62 -20 01.38 20 06.35 20 10.55 20 13.95 20 16.57 20

52 52 52 51 51 52

12.4 05.7 01.1 58.8 58.7 01.0

4.752 137 4.737 092 4.722 139 4.707 282 4.692 523 4.677 869

1.85 1.86 1.86 1.87 1.87 1.88

19.37 19.43 19.50 19.56 19.62 19.68

4 4 4 4 4 4

54 51 47 43 39 35

58 07 16 24 32 38

13 14 15 16 17

19 19 19 19 19

57 57 57 57 57

18.38 -20 19.40 20 19.62 20 19.03 20 17.65 -20

52 52 52 52 52

05.4 12.2 21.2 32.5 46.0

4.663 322 4.648 888 4.634 570 4.620 374 4.606 302

1.89 1.89 1.90 1.90 1.91

19.74 19.80 19.86 19.92 19.99

4 4 4 4 4

31 27 23 19 15

44 49 53 56 59

149

JUPITER, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

May 17 18 19 20 21 22

h 19 19 19 19 19 19

m 57 57 57 57 57 56

s º 17.65 -20 15.46 20 12.47 20 08.68 20 04.10 20 58.73 20

' 52 53 53 53 54 54

" 46.0 01.8 19.9 40.1 02.6 27.3

4.606 302 4.592 361 4.578 555 4.564 888 4.551 364 4.537 989

" 1.91 1.91 1.92 1.93 1.93 1.94

" 19.99 20.05 20.11 20.17 20.23 20.29

h 4 4 4 4 4 3

m 15 12 08 04 00 56

s 59 01 02 02 01 00

23 24 25 26 27 28

19 19 19 19 19 19

56 56 56 56 56 56

52.56 -20 45.61 20 37.87 20 29.35 20 20.06 20 09.99 20

54 55 55 56 57 57

54.3 23.4 54.7 28.2 03.9 41.7

4.524 767 4.511 703 4.498 800 4.486 063 4.473 498 4.461 107

1.94 1.95 1.95 1.96 1.97 1.97

20.35 20.40 20.46 20.52 20.58 20.64

3 3 3 3 3 3

51 47 43 39 35 31

58 55 51 47 41 35

29 30 31 June 1 2 3

19 19 19 19 19 19

55 55 55 55 55 54

59.15 -20 47.54 20 35.18 20 22.08 21 08.23 21 53.65 21

58 59 59 00 01 02

21.6 03.6 47.6 33.7 21.7 11.6

4.448 895 4.436 866 4.425 024 4.413 373 4.401 916 4.390 657

1.98 1.98 1.99 1.99 2.00 2.00

20.69 20.75 20.80 20.86 20.91 20.97

3 3 3 3 3 3

27 23 19 15 10 06

29 21 13 04 54 43

4 5 6 7 8 9

19 19 19 19 19 19

54 54 54 53 53 53

38.36 -21 22.35 21 05.64 21 48.23 21 30.12 21 11.33 21

03 03 04 05 06 07

03.3 57.0 52.4 49.7 48.8 49.5

4.379 599 4.368 746 4.358 102 4.347 668 4.337 450 4.327 451

2.01 2.01 2.02 2.02 2.03 2.03

21.02 21.07 21.12 21.17 21.22 21.27

3 2 2 2 2 2

02 58 54 49 45 41

32 20 08 54 40 26

10 11 12 13 14 15

19 19 19 19 19 19

52 52 52 51 51 51

51.87 -21 31.73 21 10.94 21 49.50 21 27.42 21 04.73 21

08 09 11 12 13 14

52.0 56.1 01.8 09.0 17.7 27.7

4.317 675 4.308 124 4.298 804 4.289 717 4.280 868 4.272 259

2.04 2.04 2.05 2.05 2.05 2.06

21.32 21.37 21.42 21.46 21.50 21.55

2 2 2 2 2 2

37 32 28 24 20 15

10 54 38 20 02 44

16 17 18 19 20 21

19 19 19 19 19 19

50 50 49 49 49 48

41.43 -21 17.54 21 53.07 21 28.04 21 02.48 21 36.38 21

15 16 18 19 20 21

39.2 51.9 05.9 21.0 37.3 54.7

4.263 895 4.255 778 4.247 913 4.240 302 4.232 950 4.225 858

2.06 2.07 2.07 2.07 2.08 2.08

21.59 21.63 21.67 21.71 21.75 21.78

2 2 2 1 1 1

11 07 02 58 54 49

25 05 45 24 03 41

22 23 24 25 26 27

19 19 19 19 19 19

48 47 47 46 46 45

09.77 -21 42.67 21 15.09 21 47.06 21 18.58 21 49.69 21

23 24 25 27 28 29

13.1 32.5 52.8 13.9 35.8 58.4

4.219 030 4.212 470 4.206 178 4.200 159 4.194 413 4.188 944

2.08 2.09 2.09 2.09 2.10 2.10

21.82 21.85 21.89 21.92 21.95 21.98

1 1 1 1 1 1

45 40 36 32 27 23

18 55 32 08 44 19

28 29 30 July 1 2

19 19 19 19 19

45 44 44 43 43

20.39 -21 50.72 21 20.70 21 50.35 21 19.69 -21

31 32 34 35 36

21.6 45.4 09.6 34.2 59.1

4.183 754 4.178 843 4.174 213 4.169 866 4.165 803

2.10 2.10 2.11 2.11 2.11

22.00 22.03 22.05 22.08 22.10

1 1 1 1 1

18 14 10 05 01

54 29 03 37 10

150

JUPITER, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

July 1 2 3 4 5 6

h 19 19 19 19 19 19

m 43 43 42 42 41 41

s º 50.35 -21 19.69 21 48.74 21 17.52 21 46.04 21 14.34 21

' 35 36 38 39 41 42

" 34.2 59.1 24.3 49.8 15.4 41.2

4.169 866 4.165 803 4.162 025 4.158 534 4.155 331 4.152 416

" 2.11 2.11 2.11 2.11 2.12 2.12

" 22.08 22.10 22.12 22.14 22.15 22.17

h 1 1 0 0 0 0

m 05 01 56 52 47 43

s 37 10 44 17 50 22

7 8 9 10 11 12

19 19 19 19 19 19

40 40 39 39 38 38

42.42 -21 10.31 21 38.03 21 05.60 21 33.04 21 00.39 21

44 45 46 48 49 51

07.0 32.8 58.6 24.1 49.5 14.6

4.149 791 4.147 457 4.145 415 4.143 666 4.142 211 4.141 051

2.12 2.12 2.12 2.12 2.12 2.12

22.18 22.20 22.21 22.22 22.22 22.23

0 0 0 0 0 0

38 34 29 25 21 16

55 27 59 31 02 34

13 14 15 16 17 18

19 19 19 19 19 19

37 36 36 35 35 34

27.65 -21 54.86 21 22.05 21 49.23 21 16.43 21 43.68 21

52 54 55 56 58 59

39.3 03.6 27.5 50.8 13.6 35.8

4.140 186 4.139 617 4.139 345 4.139 369 4.139 691 4.140 309

2.12 2.12 2.12 2.12 2.12 2.12

22.24 22.24 22.24 22.24 22.24 22.24

0 0 0 23 23 23

12 07 03 54 49 45

05 37 08 11 43 14

19 20 21 22 23 24

19 19 19 19 19 19

34 33 33 32 32 31

10.99 -22 38.40 22 05.93 22 33.59 22 01.42 22 29.43 22

00 02 03 04 06 07

57.3 18.1 38.2 57.4 15.8 33.3

4.141 225 4.142 436 4.143 944 4.145 747 4.147 845 4.150 235

2.12 2.12 2.12 2.12 2.12 2.12

22.23 22.22 22.22 22.21 22.19 22.18

23 23 23 23 23 23

40 36 31 27 22 18

46 18 50 22 54 27

25 26 27 28 29 30

19 19 19 19 19 19

30 30 29 29 28 28

57.66 -22 26.12 22 54.85 22 23.87 22 53.19 22 22.85 22

08 10 11 12 13 14

49.9 05.3 19.8 33.1 45.2 56.2

4.152 917 4.155 889 4.159 149 4.162 695 4.166 525 4.170 638

2.12 2.12 2.11 2.11 2.11 2.11

22.17 22.15 22.13 22.12 22.10 22.07

23 23 23 23 22 22

13 09 05 00 56 51

59 32 06 39 13 47

31 Aug. 1 2 3 4 5

19 19 19 19 19 19

27 27 26 26 25 25

52.86 -22 23.24 22 54.00 22 25.17 22 56.76 22 28.79 22

16 17 18 19 20 21

06.0 14.6 22.0 28.1 32.9 36.4

4.175 030 4.179 700 4.184 645 4.189 864 4.195 354 4.201 113

2.11 2.10 2.10 2.10 2.10 2.09

22.05 22.03 22.00 21.97 21.94 21.91

22 22 22 22 22 22

47 42 38 34 29 25

22 57 32 08 45 21

6 7 8 9 10 11

19 19 19 19 19 19

25 24 24 23 23 22

01.28 -22 34.25 22 07.72 22 41.70 22 16.21 22 51.28 22

22 23 24 25 26 27

38.5 39.3 38.6 36.5 33.0 28.0

4.207 138 4.213 428 4.219 980 4.226 791 4.233 859 4.241 182

2.09 2.09 2.08 2.08 2.08 2.07

21.88 21.85 21.82 21.78 21.74 21.71

22 22 22 22 22 21

20 16 12 07 03 59

58 36 14 53 32 12

12 13 14 15 16

19 19 19 19 19

22 22 21 21 20

26.92 -22 03.14 22 39.97 22 17.41 22 55.49 -22

28 29 30 30 31

21.5 13.5 04.0 53.0 40.5

4.248 756 4.256 579 4.264 647 4.272 958 4.281 509

2.07 2.07 2.06 2.06 2.05

21.67 21.63 21.59 21.54 21.50

21 21 21 21 21

54 50 46 41 37

53 34 15 57 40

151

JUPITER, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Aug. 16 17 18 19 20 21

h 19 19 19 19 19 19

m 20 20 20 19 19 19

s º 55.49 -22 34.22 22 13.60 22 53.66 22 34.40 22 15.84 22

' 31 32 33 33 34 35

" 40.5 26.6 11.0 54.0 35.4 15.3

4.281 509 4.290 296 4.299 315 4.308 564 4.318 038 4.327 733

" 2.05 2.05 2.05 2.04 2.04 2.03

" 21.50 21.46 21.41 21.37 21.32 21.27

h 21 21 21 21 21 21

m 37 33 29 24 20 16

s 40 24 08 53 38 25

22 23 24 25 26 27

19 19 19 19 19 19

18 18 18 18 17 17

58.00 -22 40.88 22 24.50 22 08.88 22 54.01 22 39.90 22

35 36 37 37 38 38

53.5 30.2 05.2 38.7 10.5 40.8

4.337 646 4.347 771 4.358 105 4.368 643 4.379 381 4.390 315

2.03 2.02 2.02 2.01 2.01 2.00

21.22 21.17 21.12 21.07 21.02 20.97

21 21 21 20 20 20

12 07 03 59 55 51

12 59 48 37 27 18

28 29 30 31 Sept. 1 2

19 19 19 19 19 19

17 17 17 16 16 16

26.57 -22 14.01 22 02.23 22 51.23 22 41.03 22 31.61 22

39 39 40 40 40 41

09.6 36.7 02.3 26.4 48.8 09.7

4.401 440 4.412 752 4.424 248 4.435 922 4.447 771 4.459 791

2.00 1.99 1.99 1.98 1.98 1.97

20.92 20.86 20.81 20.75 20.70 20.64

20 20 20 20 20 20

47 43 38 34 30 26

09 02 55 48 43 38

3 4 5 6 7 8

19 19 19 19 19 19

16 16 16 16 15 15

23.00 -22 15.18 22 08.18 22 01.99 22 56.61 22 52.06 22

41 41 42 42 42 42

29.1 46.8 02.9 17.5 30.5 41.9

4.471 978 4.484 328 4.496 838 4.509 502 4.522 317 4.535 280

1.97 1.96 1.96 1.95 1.94 1.94

20.59 20.53 20.47 20.41 20.36 20.30

20 20 20 20 20 20

22 18 14 10 06 02

35 32 29 28 28 28

9 10 11 12 13 14

19 19 19 19 19 19

15 15 15 15 15 15

48.33 -22 45.43 22 43.35 22 42.11 22 41.69 22 42.11 22

42 43 43 43 43 43

51.7 00.0 06.7 11.9 15.6 17.7

4.548 385 4.561 629 4.575 008 4.588 518 4.602 154 4.615 912

1.93 1.93 1.92 1.92 1.91 1.91

20.24 20.18 20.12 20.06 20.00 19.94

19 19 19 19 19 19

58 54 50 46 42 38

29 31 33 37 41 46

15 16 17 18 19 20

19 19 19 19 19 19

15 15 15 15 15 16

43.36 -22 45.44 22 48.35 22 52.09 22 56.66 22 02.07 22

43 43 43 43 43 42

18.2 17.3 14.7 10.6 05.0 57.7

4.629 788 4.643 777 4.657 875 4.672 076 4.686 377 4.700 772

1.90 1.89 1.89 1.88 1.88 1.87

19.88 19.82 19.76 19.70 19.64 19.58

19 19 19 19 19 19

34 30 27 23 19 15

52 59 07 15 25 35

21 22 23 24 25 26

19 19 19 19 19 19

16 16 16 16 16 16

08.31 -22 15.38 22 23.28 22 32.00 22 41.53 22 51.88 22

42 42 42 42 41 41

48.9 38.4 26.5 13.0 57.9 41.4

4.715 256 4.729 826 4.744 475 4.759 199 4.773 995 4.788 858

1.87 1.86 1.85 1.85 1.84 1.84

19.52 19.46 19.40 19.34 19.28 19.22

19 19 19 19 18 18

11 07 04 00 56 52

46 58 10 24 38 53

27 28 29 30 Oct. 1

19 19 19 19 19

17 17 17 17 17

03.02 -22 14.96 22 27.69 22 41.21 22 55.52 -22

41 41 40 40 39

23.2 03.6 42.4 19.6 55.2

4.803 783 4.818 767 4.833 805 4.848 893 4.864 029

1.83 1.82 1.82 1.81 1.81

19.16 19.10 19.05 18.99 18.93

18 18 18 18 18

49 45 41 38 34

09 25 43 01 20

152

JUPITER, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Oct. 1 2 3 4 5 6

h 19 19 19 19 19 19

m 17 18 18 18 19 19

s º 55.52 -22 10.60 22 26.45 22 43.08 22 00.47 22 18.63 22

' 39 39 39 38 38 37

" 55.2 29.3 01.8 32.7 02.0 29.7

4.864 029 4.879 207 4.894 424 4.909 676 4.924 959 4.940 270

" 1.81 1.80 1.80 1.79 1.79 1.78

" 18.93 18.87 18.81 18.75 18.69 18.63

h 18 18 18 18 18 18

m 34 30 26 23 19 16

s 20 39 60 21 43 06

7 8 9 10 11 12

19 19 19 19 19 19

19 19 20 20 21 21

37.54 -22 57.20 22 17.61 22 38.76 22 00.63 22 23.24 22

36 36 35 35 34 33

55.8 20.4 43.3 04.7 24.5 42.8

4.955 605 4.970 959 4.986 330 5.001 713 5.017 105 5.032 501

1.77 1.77 1.76 1.76 1.75 1.75

18.58 18.52 18.46 18.41 18.35 18.29

18 18 18 18 17 17

12 08 05 01 58 54

29 53 18 44 11 38

13 14 15 16 17 18

19 19 19 19 19 19

21 22 22 23 23 23

46.56 -22 10.59 22 35.33 22 00.78 22 26.92 22 53.75 22

32 32 31 30 29 28

59.4 14.4 27.8 39.5 49.5 57.9

5.047 898 5.063 291 5.078 677 5.094 052 5.109 410 5.124 748

1.74 1.74 1.73 1.73 1.72 1.72

18.24 18.18 18.13 18.07 18.02 17.96

17 17 17 17 17 17

51 47 44 40 37 33

05 34 03 33 04 35

19 20 21 22 23 24

19 19 19 19 19 19

24 24 25 25 26 26

21.28 -22 49.48 22 18.36 22 47.89 22 18.07 22 48.89 22

28 27 26 25 24 23

04.6 09.6 13.0 14.7 14.8 13.2

5.140 063 5.155 348 5.170 602 5.185 820 5.200 997 5.216 132

1.71 1.71 1.70 1.70 1.69 1.69

17.91 17.86 17.80 17.75 17.70 17.65

17 17 17 17 17 17

30 26 23 19 16 12

07 40 13 47 21 57

25 26 27 28 29 30

19 19 19 19 19 19

27 27 28 28 29 30

20.34 -22 52.41 22 25.09 22 58.38 22 32.27 22 06.75 22

22 21 19 18 17 16

09.9 05.0 58.3 49.9 39.8 28.0

5.231 220 5.246 258 5.261 244 5.276 172 5.291 042 5.305 849

1.68 1.68 1.67 1.67 1.66 1.66

17.60 17.55 17.50 17.45 17.40 17.35

17 17 17 16 16 16

09 06 02 59 56 52

32 09 46 24 02 41

31 Nov. 1 2 3 4 5

19 19 19 19 19 19

30 31 31 32 33 33

41.81 -22 17.45 22 53.67 22 30.45 22 07.78 22 45.67 22

15 13 12 11 10 08

14.4 59.1 42.0 23.2 02.7 40.4

5.320 591 5.335 264 5.349 866 5.364 394 5.378 845 5.393 215

1.65 1.65 1.64 1.64 1.63 1.63

17.30 17.26 17.21 17.16 17.12 17.07

16 16 16 16 16 16

49 45 42 39 36 32

20 60 40 22 03 45

6 7 8 9 10 11

19 19 19 19 19 19

34 35 35 36 37 37

24.10 -22 03.05 22 42.54 22 22.54 22 03.05 22 44.06 21

07 05 04 02 01 59

16.3 50.5 23.0 53.7 22.6 49.7

5.407 503 5.421 704 5.435 817 5.449 837 5.463 763 5.477 590

1.63 1.62 1.62 1.61 1.61 1.61

17.02 16.98 16.94 16.89 16.85 16.81

16 16 16 16 16 16

29 26 22 19 16 13

28 11 55 39 24 09

12 13 14 15 16

19 19 19 19 19

38 39 39 40 41

25.56 -21 07.56 21 50.05 21 33.01 21 16.44 -21

58 56 55 53 51

15.0 38.4 00.1 19.9 37.8

5.491 316 5.504 938 5.518 451 5.531 854 5.545 143

1.60 1.60 1.59 1.59 1.59

16.76 16.72 16.68 16.64 16.60

16 16 16 16 15

09 06 03 00 57

55 41 28 15 03

153

JUPITER, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Nov. 16 17 18 19 20 21

h 19 19 19 19 19 19

m 41 42 42 43 44 45

s º 16.44 -21 00.34 21 44.69 21 29.48 21 14.70 21 00.35 21

' 51 49 48 46 44 42

" 37.8 53.9 08.3 20.8 31.5 40.4

5.545 143 5.558 314 5.571 365 5.584 293 5.597 095 5.609 769

" 1.59 1.58 1.58 1.57 1.57 1.57

" 16.60 16.56 16.52 16.49 16.45 16.41

h 15 15 15 15 15 15

m 57 53 50 47 44 41

s 03 51 39 28 17 07

22 23 24 25 26 27

19 19 19 19 19 19

45 46 47 48 48 49

46.40 -21 32.85 21 19.71 21 06.95 21 54.57 21 42.57 21

40 38 36 34 32 30

47.5 52.7 56.1 57.7 57.4 55.3

5.622 312 5.634 723 5.646 998 5.659 137 5.671 136 5.682 993

1.56 1.56 1.56 1.55 1.55 1.55

16.37 16.34 16.30 16.27 16.23 16.20

15 15 15 15 15 15

37 34 31 28 25 22

57 48 39 30 22 14

28 29 30 Dec. 1 2 3

19 19 19 19 19 19

50 51 52 52 53 54

30.93 -21 19.66 21 08.75 21 58.18 21 47.96 21 38.06 21

28 26 24 22 20 18

51.3 45.4 37.8 28.3 16.9 03.8

5.694 708 5.706 277 5.717 699 5.728 972 5.740 093 5.751 062

1.54 1.54 1.54 1.54 1.53 1.53

16.17 16.13 16.10 16.07 16.04 16.01

15 15 15 15 15 15

19 15 12 09 06 03

07 59 52 46 40 34

4 5 6 7 8 9

19 19 19 19 19 19

55 56 57 58 58 59

28.50 -21 19.25 21 10.31 21 01.67 21 53.33 21 45.28 21

15 13 11 08 06 04

48.8 32.0 13.5 53.1 30.9 06.8

5.761 876 5.772 532 5.783 030 5.793 367 5.803 542 5.813 551

1.53 1.52 1.52 1.52 1.52 1.51

15.98 15.95 15.92 15.89 15.86 15.84

15 14 14 14 14 14

00 57 54 51 48 45

28 23 18 14 09 05

10 11 12 13 14 15

20 20 20 20 20 20

00 01 02 03 04 05

37.51 -21 30.03 20 22.82 20 15.89 20 09.21 20 02.79 20

01 59 56 54 51 49

40.9 13.2 43.6 12.2 39.0 04.0

5.823 392 5.833 065 5.842 566 5.851 893 5.861 044 5.870 017

1.51 1.51 1.51 1.50 1.50 1.50

15.81 15.78 15.76 15.73 15.71 15.68

14 14 14 14 14 14

42 38 35 32 29 26

02 58 55 52 49 47

16 17 18 19 20 21

20 20 20 20 20 20

05 06 07 08 09 10

56.62 -20 50.67 20 44.95 20 39.45 20 34.15 20 29.06 20

46 43 41 38 35 32

27.2 48.7 08.4 26.4 42.7 57.2

5.878 810 5.887 422 5.895 851 5.904 095 5.912 154 5.920 025

1.50 1.49 1.49 1.49 1.49 1.49

15.66 15.64 15.61 15.59 15.57 15.55

14 14 14 14 14 14

23 20 17 14 11 08

45 43 41 39 38 37

22 23 24 25 26 27

20 20 20 20 20 20

11 12 13 14 15 16

24.16 -20 19.45 20 14.92 20 10.57 20 06.39 20 02.38 20

30 27 24 21 18 15

09.9 20.9 30.2 37.8 43.7 48.0

5.927 708 5.935 202 5.942 505 5.949 617 5.956 537 5.963 263

1.48 1.48 1.48 1.48 1.48 1.47

15.53 15.51 15.49 15.47 15.46 15.44

14 14 13 13 13 13

05 02 59 56 53 50

36 35 34 34 34 34

28 29 30 31 32

20 20 20 20 20

16 17 18 19 20

58.53 -20 54.83 20 51.28 20 47.86 20 44.58 -20

12 09 06 03 00

50.5 51.4 50.7 48.4 44.5

5.969 796 5.976 133 5.982 275 5.988 220 5.993 967

1.47 1.47 1.47 1.47 1.47

15.42 15.40 15.39 15.37 15.36

13 13 13 13 13

47 44 41 38 35

34 34 34 35 35

154

SATURN, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 292 292 292 292 292 292

' 30 34 38 41 45 49

" º ' " 56.0 +0 03 24.0 34.0 0 03 14.6 11.9 0 03 05.1 49.9 0 02 55.7 27.9 0 02 46.2 05.9 0 02 36.8

º 10.034 334 Apr. 2 295 10.034 133 4 295 10.033 931 6 295 10.033 729 8 295 10.033 526 10 295 10.033 322 12 295

' 18 21 25 29 32 36

" º ' " 12.1 -0 03 51.1 50.5 0 04 00.5 28.9 0 04 10.0 07.3 0 04 19.5 45.8 0 04 28.9 24.2 0 04 38.4

10.024 425 10.024 194 10.023 963 10.023 732 10.023 500 10.023 267

13 15 17 19 21 23

292 292 292 293 293 293

52 56 59 03 07 10

44.0 +0 02 27.3 22.0 0 02 17.9 60.0 0 02 08.4 38.0 0 01 58.9 16.1 0 01 49.5 54.1 0 01 40.0

10.033 118 10.032 913 10.032 707 10.032 501 10.032 294 10.032 086

40 43 47 50 54 58

02.6 -0 04 47.9 41.1 0 04 57.3 19.6 0 05 06.8 58.1 0 05 16.3 36.6 0 05 25.7 15.1 0 05 35.2

10.023 034 10.022 800 10.022 565 10.022 330 10.022 094 10.021 857

25 27 29 31 Feb. 2 4

293 293 293 293 293 293

14 18 21 25 29 32

32.2 +0 01 30.6 10.3 0 01 21.1 48.4 0 01 11.7 26.5 0 01 02.2 04.6 0 00 52.8 42.7 0 00 43.3

10.031 878 26 296 01 53.6 -0 05 44.6 10.031 669 28 296 05 32.1 0 05 54.1 10.031 460 30 296 09 10.7 0 06 03.6 10.031 250 May 2 296 12 49.2 0 06 13.0 10.031 039 4 296 16 27.7 0 06 22.5 10.030 828 6 296 20 06.3 0 06 32.0

10.021 620 10.021 382 10.021 144 10.020 904 10.020 665 10.020 424

6 8 10 12 14 16

293 293 293 293 293 293

36 39 43 47 50 54

20.8 +0 00 33.9 58.9 0 00 24.4 37.1 0 00 15.0 15.2 +0 00 05.5 53.4 -0 00 04.0 31.6 0 00 13.4

10.030 616 10.030 403 10.030 190 10.029 976 10.029 762 10.029 546

8 10 12 14 16 18

296 296 296 296 296 296

23 27 31 34 38 41

44.9 -0 06 41.4 23.5 0 06 50.9 02.1 0 07 00.4 40.7 0 07 09.8 19.3 0 07 19.3 57.9 0 07 28.8

10.020 183 10.019 942 10.019 699 10.019 456 10.019 213 10.018 969

18 20 22 24 26 28

293 294 294 294 294 294

58 01 05 09 12 16

09.7 -0 00 22.9 47.9 0 00 32.3 26.1 0 00 41.8 04.3 0 00 51.3 42.6 0 01 00.7 20.8 0 01 10.2

10.029 331 10.029 114 10.028 897 10.028 680 10.028 461 10.028 242

20 22 24 26 28 30

296 296 296 296 297 297

45 49 52 56 00 03

36.6 -0 07 38.3 15.2 0 07 47.7 53.9 0 07 57.2 32.6 0 08 06.7 11.3 0 08 16.1 50.0 0 08 25.6

10.018 724 10.018 478 10.018 232 10.017 986 10.017 738 10.017 490

1 3 5 7 9 11

294 294 294 294 294 294

19 23 27 30 34 38

59.0 -0 01 19.7 37.2 0 01 29.1 15.5 0 01 38.6 53.8 0 01 48.0 32.0 0 01 57.5 10.3 0 02 06.9

10.028 023 June 1 10.027 803 3 10.027 582 5 10.027 361 7 10.027 138 9 10.026 916 11

297 297 297 297 297 297

07 11 14 18 22 25

28.7 -0 08 35.1 07.4 0 08 44.5 46.1 0 08 54.0 24.9 0 09 03.4 03.7 0 09 12.9 42.4 0 09 22.4

10.017 242 10.016 992 10.016 742 10.016 492 10.016 241 10.015 989

13 15 17 19 21 23

294 294 294 294 294 295

41 45 49 52 56 00

48.6 -0 02 16.4 26.9 0 02 25.9 05.2 0 02 35.3 43.5 0 02 44.8 21.9 0 02 54.3 00.2 0 03 03.7

10.026 692 10.026 469 10.026 244 10.026 019 10.025 793 10.025 566

297 297 297 297 297 297

29 32 36 40 43 47

21.2 -0 09 31.8 60.0 0 09 41.3 38.8 0 09 50.8 17.6 0 10 00.2 56.4 0 10 09.7 35.2 0 10 19.2

10.015 736 10.015 483 10.015 230 10.014 975 10.014 720 10.014 465

25 27 29 31 Apr. 2

295 295 295 295 295

03 07 10 14 18

38.6 -0 03 13.2 16.9 0 03 22.7 55.3 0 03 32.1 33.7 0 03 41.6 12.1 -0 03 51.1

10.025 339 25 297 51 14.1 -0 10.025 112 27 297 54 52.9 0 10.024 883 29 297 58 31.8 0 10.024 654 July 1 298 02 10.7 0 10.024 425 3 298 05 49.6 -0

Jan.

Mar.

14 16 18 20 22 24

13 15 17 19 21 23

295 295 295 295 295 295

10 10 10 10 11

28.6 38.1 47.6 57.0 06.5

10.014 208 10.013 951 10.013 694 10.013 436 10.013 177

155

SATURN, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 298 298 298 298 298 298

' 02 05 09 13 16 20

" º ' " 10.7 -0 10 57.0 49.6 0 11 06.5 28.5 0 11 16.0 07.4 0 11 25.4 46.3 0 11 34.9 25.2 0 11 44.3

10.013 436 Oct. 1 10.013 177 3 10.012 917 5 10.012 657 7 10.012 396 9 10.012 135 11

º 300 300 300 301 301 301

' 50 53 57 01 04 08

" º ' " 11.7 -0 18 11.9 51.2 0 18 21.3 30.6 0 18 30.8 10.0 0 18 40.2 49.5 0 18 49.7 29.0 0 18 59.1

10.000 876 10.000 588 10.000 300 10.000 011 9.999 721 9.999 431

13 15 17 19 21 23

298 298 298 298 298 298

24 27 31 35 38 42

04.2 -0 11 53.8 43.1 0 12 03.3 22.1 0 12 12.7 01.1 0 12 22.2 40.1 0 12 31.6 19.1 0 12 41.1

10.011 873 10.011 610 10.011 347 10.011 083 10.010 819 10.010 553

13 15 17 19 21 23

301 301 301 301 301 301

12 15 19 23 26 30

08.5 -0 19 08.6 48.0 0 19 18.0 27.5 0 19 27.4 07.1 0 19 36.9 46.7 0 19 46.3 26.2 0 19 55.7

9.999 141 9.998 849 9.998 557 9.998 265 9.997 971 9.997 678

25 27 29 31 Aug. 2 4

298 298 298 298 299 299

45 49 53 56 00 04

58.1 -0 12 50.6 37.1 0 13 00.0 16.2 0 13 09.5 55.2 0 13 19.0 34.3 0 13 28.4 13.4 0 13 37.8

10.010 288 10.010 021 10.009 754 10.009 486 10.009 218 Nov. 10.008 949

25 27 29 31 2 4

301 301 301 301 301 301

34 37 41 45 48 52

05.8 -0 20 05.2 45.4 0 20 14.6 25.0 0 20 24.0 04.6 0 20 33.4 44.2 0 20 42.9 23.9 0 20 52.3

9.997 383 9.997 088 9.996 793 9.996 496 9.996 199 9.995 902

6 8 10 12 14 16

299 299 299 299 299 299

07 11 15 18 22 26

52.4 -0 13 47.3 31.6 0 13 56.8 10.6 0 14 06.2 49.8 0 14 15.7 28.9 0 14 25.1 08.0 0 14 34.6

10.008 679 10.008 409 10.008 138 10.007 867 10.007 595 10.007 322

6 8 10 12 14 16

301 301 302 302 302 302

56 59 03 07 10 14

03.5 -0 21 01.7 43.2 0 21 11.2 22.9 0 21 20.6 02.6 0 21 30.0 42.3 0 21 39.4 22.0 0 21 48.9

9.995 604 9.995 305 9.995 006 9.994 706 9.994 406 9.994 104

18 20 22 24 26 28

299 299 299 299 299 299

29 33 37 40 44 48

47.2 -0 14 44.1 26.4 0 14 53.5 05.5 0 15 03.0 44.7 0 15 12.4 24.0 0 15 21.8 03.1 0 15 31.3

10.007 048 10.006 774 10.006 500 10.006 224 10.005 949 10.005 672

18 20 22 24 26 28

302 302 302 302 302 302

18 21 25 29 32 36

01.7 -0 21 58.3 41.5 0 22 07.7 21.2 0 22 17.1 01.0 0 22 26.5 40.8 0 22 36.0 20.6 0 22 45.4

9.993 803 9.993 500 9.993 198 9.992 894 9.992 590 9.992 285

30 1 3 5 7 9

299 299 299 300 300 300

51 55 59 02 06 09

42.4 -0 15 40.8 21.6 0 15 50.2 00.9 0 15 59.7 40.1 0 16 09.1 19.4 0 16 18.6 58.7 0 16 28.0

10.005 395 30 10.005 117 Dec. 2 10.004 839 4 10.004 560 6 10.004 280 8 10.004 000 10

302 302 302 302 302 302

40 43 47 50 54 58

00.4 -0 22 54.8 40.3 0 23 04.2 20.1 0 23 13.6 60.0 0 23 23.0 39.9 0 23 32.5 19.7 0 23 41.9

9.991 980 9.991 674 9.991 368 9.991 060 9.990 753 9.990 444

11 13 15 17 19 21

300 300 300 300 300 300

13 17 20 24 28 31

38.0 -0 16 37.5 17.3 0 16 46.9 56.7 0 16 56.3 36.0 0 17 05.8 15.3 0 17 15.2 54.7 0 17 24.7

10.003 719 10.003 437 10.003 155 10.002 872 10.002 589 10.002 305

12 14 16 18 20 22

303 303 303 303 303 303

01 05 09 12 16 20

59.6 -0 23 51.3 39.5 0 24 00.7 19.5 0 24 10.1 59.4 0 24 19.5 39.4 0 24 28.9 19.3 0 24 38.3

9.990 135 9.989 826 9.989 516 9.989 205 9.988 894 9.988 582

23 25 27 29 1

300 300 300 300 300

35 39 42 46 50

34.1 -0 17 34.1 13.5 0 17 43.6 52.9 0 17 53.0 32.3 0 18 02.5 11.7 -0 18 11.9

10.002 021 10.001 735 10.001 449 10.001 163 10.000 876

24 26 28 30 32

303 303 303 303 303

23 27 31 34 38

59.3 -0 24 47.7 39.3 0 24 57.1 19.3 0 25 06.5 59.4 0 25 15.9 39.4 -0 25 25.3

9.988 269 9.987 956 9.987 642 9.987 328 9.987 013

July

Sept.

Oct.

156

SATURN, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Jan.

Feb.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

0 1 2 3 4 5

º 291 291 291 291 291 291

' 16 23 30 37 44 51

" 40.9 41.6 43.1 45.4 48.4 52.1

º +0 0 0 0 0 0

' 03 03 03 02 02 02

" 10.8 06.4 02.0 57.7 53.3 49.0

6 7 8 9 10 11

291 292 292 292 292 292

58 06 13 20 27 34

56.4 01.3 06.6 12.4 18.6 25.0

+0 0 0 0 0 0

02 02 02 02 02 02

12 13 14 15 16 17

292 292 292 293 293 293

41 48 55 02 09 17

31.7 38.8 43.3 50.9 57.5 03.9

+0 0 0 0 0 0

18 19 20 21 22 23

293 293 293 293 293 293

24 31 38 45 52 59

10.2 16.2 21.9 27.2 32.1 36.4

24 25 26 27 28 29

294 294 294 294 294 294

06 13 20 27 34 41

30 31 1 2 3 4

294 294 295 295 295 295

5 6 7 8 9 10 11 12 13 14 15

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

15 16 17 18 19 20

º 296 296 296 296 297 297

' 36 43 49 56 02 08

" 53.6 23.4 51.1 16.4 39.3 59.8

º -0 0 0 0 0 0

' 00 00 00 00 00 00

" 07.7 12.1 16.4 20.8 25.2 29.6

44.6 40.3 36.0 31.7 27.4 23.1

21 22 23 24 25 26

297 297 297 297 297 297

15 21 27 33 40 46

17.7 33.0 45.6 55.3 02.3 06.3

-0 0 0 0 0 0

00 00 00 00 00 00

34.1 38.5 42.9 47.4 51.8 56.3

02 02 02 02 02 01

18.8 14.5 10.3 05.9 01.6 57.3

27 28 29 1 2 3

297 297 298 298 298 298

52 58 04 09 15 21

07.3 05.4 00.4 52.3 41.0 26.5

-0 0 0 0 0 0

01 01 01 01 01 01

00.7 05.2 09.7 14.1 18.6 23.1

+0 0 0 0 0 0

01 01 01 01 01 01

53.0 48.7 44.4 40.1 35.8 31.5

4 5 6 7 8 9

298 298 298 298 298 298

27 32 38 43 49 54

08.7 47.6 23.0 54.9 23.2 47.8

-0 0 0 0 0 0

01 01 01 01 01 01

27.7 32.2 36.7 41.3 45.8 50.4

40.1 43.1 45.2 46.4 46.6 45.8

+0 0 0 0 0 0

01 01 01 01 01 01

27.2 22.9 18.6 14.3 10.0 05.7

10 11 12 13 14 15

299 299 299 299 299 299

00 05 10 15 20 25

08.7 25.9 39.3 49.0 54.9 56.8

-0 0 0 0 0 0

01 01 02 02 02 02

55.0 59.6 04.2 08.9 13.5 18.2

48 55 02 09 16 23

43.9 40.9 36.7 31.1 24.3 16.1

+0 0 0 0 0 0

01 00 00 00 00 00

01.4 57.1 52.8 48.5 44.2 39.9

16 17 18 19 20 21

299 299 299 299 299 299

30 35 40 45 50 54

54.8 48.8 38.6 24.2 05.5 42.5

-0 0 0 0 0 0

02 02 02 02 02 02

22.9 27.6 32.3 37.1 41.8 46.6

295 295 295 295 295 296

30 36 43 50 57 03

06.4 55.3 42.5 28.0 11.8 53.6

+0 0 0 0 0 0

00 00 00 00 00 00

35.6 31.3 27.0 22.7 18.4 14.1

22 23 24 25 26 27

299 300 300 300 300 300

59 03 08 12 16 20

15.1 43.2 06.8 25.8 40.3 50.1

-0 0 0 0 0 0

02 02 03 03 03 03

51.3 56.1 00.9 05.7 10.6 15.4

296 296 296 296 296

10 17 23 30 36

33.6 11.6 47.7 21.7 53.6

+0 0 +0 -0 -0

00 00 00 00 00

09.7 05.4 01.0 03.3 07.7

28 29 30 31 1

300 300 300 300 300

24 28 32 36 40

55.2 55.7 51.3 42.2 28.2

-0 0 0 0 -0

03 03 03 03 03

20.3 25.1 30.0 34.9 39.9

Feb.

Mar.

Apr.

157

SATURN, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Apr.

May

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 300 300 300 300 300 300

' 40 44 47 51 54 58

" 28.2 09.3 45.3 16.4 42.3 03.1

º -0 0 0 0 0 0

' 03 03 03 03 03 04

" 39.9 44.8 49.7 54.7 59.7 04.7

7 8 9 10 11 12

301 301 301 301 301 301

01 04 07 10 13 16

18.8 29.2 34.6 34.7 29.7 19.4

-0 0 0 0 0 0

04 04 04 04 04 04

13 14 15 16 17 18

301 301 301 301 301 301

19 21 24 26 29 31

03.7 42.7 16.2 44.2 06.6 23.4

-0 0 0 0 0 0

19 20 21 22 23 24

301 301 301 301 301 301

33 35 37 39 41 43

34.6 40.2 40.1 34.3 22.8 05.6

25 26 27 28 29 30

301 301 301 301 301 301

44 46 47 48 50 51

1 2 3 4 5 6

301 301 301 301 301 301

7 8 9 10 11 12 13 14 15 16 17

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

17 18 19 20 21 22

º 301 301 301 301 301 301

' 55 55 54 53 52 51

" 45.1 08.0 25.0 36.4 42.0 42.0

º -0 0 0 0 0 0

' 07 07 07 08 08 08

" 45.3 51.0 56.7 02.5 08.2 13.9

09.7 14.8 19.9 25.0 30.1 35.2

23 24 25 26 27 28

301 301 301 301 301 301

50 49 48 46 45 43

36.3 24.9 08.0 45.6 17.6 44.1

-0 0 0 0 0 0

08 08 08 08 08 08

19.7 25.4 31.2 37.0 42.8 48.5

04 04 04 04 05 05

40.4 45.5 50.7 55.9 01.1 06.4

29 30 31 1 2 3

301 301 301 301 301 301

42 40 38 36 34 32

05.1 20.7 30.9 35.9 35.6 30.3

-0 0 0 0 0 0

08 09 09 09 09 09

54.3 00.2 06.0 11.8 17.6 23.5

-0 0 0 0 0 0

05 05 05 05 05 05

11.6 16.9 22.2 27.5 32.8 38.1

4 5 6 7 8 9

301 301 301 301 301 301

30 28 25 23 20 18

19.9 04.6 44.3 19.2 49.2 14.4

-0 0 0 0 0 0

09 09 09 09 09 09

29.3 35.2 41.1 46.9 52.8 58.7

42.7 14.0 39.6 59.4 13.4 21.5

-0 0 0 0 0 0

05 05 05 05 06 06

43.5 48.8 54.2 59.6 05.0 10.4

10 11 12 13 14 15

301 301 301 301 301 301

15 12 10 07 04 01

34.8 50.5 01.6 08.1 10.1 07.8

-0 0 0 0 0 0

10 10 10 10 10 10

04.5 10.4 16.3 22.1 28.0 33.8

52 53 54 54 55 56

23.8 20.2 10.7 55.3 34.0 07.0

-0 0 0 0 0 0

06 06 06 06 06 06

15.9 21.3 26.8 32.3 37.8 43.4

16 17 18 19 20 21

300 300 300 300 300 300

58 54 51 48 44 41

01.3 50.5 35.7 16.9 54.3 27.9

-0 0 0 0 0 0

10 10 10 10 11 11

39.7 45.5 51.3 57.1 02.9 08.7

301 301 301 301 301 301

56 56 57 57 57 57

34.1 55.5 11.1 20.8 24.8 22.9

-0 0 0 0 0 0

06 06 07 07 07 07

48.9 54.5 00.1 05.7 11.3 17.0

22 23 24 25 26 27

300 300 300 300 300 300

37 34 30 27 23 19

57.7 24.0 46.8 06.1 22.2 35.0

-0 0 0 0 0 0

11 11 11 11 11 11

14.5 20.3 26.1 31.9 37.6 43.4

301 301 301 301 301

57 57 56 56 55

15.1 01.4 41.8 16.4 45.1

-0 0 0 0 -0

07 07 07 07 07

22.6 28.3 33.9 39.6 45.3

28 29 30 1 2

300 300 300 300 299

15 11 07 03 59

44.8 51.7 55.8 57.3 56.3

-0 0 0 0 -0

11 11 12 12 12

49.1 54.8 00.6 06.3 12.0

May

June

July

158

SATURN, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

July

Aug.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 300 299 299 299 299 299

' 03 59 55 51 47 43

" 57.3 56.3 53.0 47.3 39.4 29.5

º -0 0 0 0 0 0

' 12 12 12 12 12 12

" 06.3 12.0 17.7 23.3 29.0 34.6

7 8 9 10 11 12

299 299 299 299 299 299

39 35 30 26 22 17

17.5 03.6 47.9 30.6 11.7 51.5

-0 0 0 0 0 0

12 12 12 12 13 13

13 14 15 16 17 18

299 299 299 299 298 298

13 09 04 00 55 51

30.0 07.4 43.9 19.6 54.6 29.1

-0 0 0 0 0 0

19 20 21 22 23 24

298 298 298 298 298 298

47 42 38 33 29 24

03.2 37.0 10.7 44.3 18.0 51.9

25 26 27 28 29 30

298 298 298 298 298 297

20 16 11 07 02 58

31 1 2 3 4 5

297 297 297 297 297 297

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 296 296 296 296 296 296

' 49 45 41 38 34 31

" 16.2 35.9 59.0 25.5 55.6 29.4

º -0 0 0 0 0 0

' 16 16 16 16 16 16

" 02.3 06.7 11.0 15.3 19.6 23.9

40.2 45.8 51.4 56.9 02.5 08.0

22 23 24 25 26 27

296 296 296 296 296 296

28 24 21 18 15 12

07.1 48.7 34.5 24.4 18.7 17.3

-0 0 0 0 0 0

16 16 16 16 16 16

28.1 32.2 36.4 40.5 44.6 48.6

13 13 13 13 13 13

13.4 18.9 24.3 29.7 35.1 Sept. 40.4

28 29 30 31 1 2

296 296 296 296 295 295

09 06 03 00 58 55

20.4 27.9 40.1 56.8 18.1 44.2

-0 0 0 0 0 0

16 16 17 17 17 17

52.6 56.6 00.6 04.5 08.3 12.2

-0 0 0 0 0 0

13 13 13 14 14 14

45.7 51.0 56.3 01.5 06.7 11.9

3 4 5 6 7 8

295 295 295 295 295 295

53 50 48 46 44 42

15.2 51.0 31.8 17.6 08.6 04.8

-0 0 0 0 0 0

17 17 17 17 17 17

16.0 19.7 23.5 27.1 30.8 34.4

26.2 01.1 36.7 13.3 50.8 29.5

-0 0 0 0 0 0

14 14 14 14 14 14

17.0 22.2 27.3 32.3 37.4 42.4

9 10 11 12 13 14

295 295 295 295 295 295

40 38 36 34 33 31

06.3 13.1 25.3 43.0 06.1 34.7

-0 0 0 0 0 0

17 17 17 17 17 17

38.0 41.6 45.1 48.6 52.1 55.5

54 49 45 41 37 32

09.5 50.9 33.8 18.2 04.4 52.3

-0 0 0 0 0 0

14 14 14 15 15 15

47.4 52.3 57.3 02.1 07.0 11.8

15 16 17 18 19 20

295 295 295 295 295 295

30 28 27 26 25 24

08.8 48.5 33.9 24.9 21.7 24.4

-0 0 0 0 0 0

17 18 18 18 18 18

58.9 02.3 05.7 09.0 12.3 15.6

297 297 297 297 297 297

28 24 20 16 12 08

42.2 34.1 28.2 24.7 23.6 25.2

-0 0 0 0 0 0

15 15 15 15 15 15

16.6 21.3 26.0 30.7 35.3 39.9

21 22 23 24 25 26

295 295 295 295 295 295

23 22 22 21 21 20

32.9 47.3 07.7 34.0 06.2 44.3

-0 0 0 0 0 0

18 18 18 18 18 18

18.9 22.1 25.3 28.5 31.7 34.8

297 297 296 296 296

04 00 56 52 49

29.4 36.6 46.7 59.9 16.2

-0 0 0 0 -0

15 15 15 15 16

44.5 49.0 53.5 57.9 02.3

27 28 29 30 1

295 295 295 295 295

20 20 20 20 20

28.2 18.1 13.9 15.6 23.2

-0 0 0 0 -0

18 18 18 18 18

38.0 41.1 44.1 47.2 50.2

Aug.

Oct.

159

SATURN, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Oct.

Nov.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 295 295 295 295 295 295

' 20 20 20 21 21 22

" 23.2 36.7 56.2 21.7 53.2 30.7

º -0 0 0 0 0 0

' 18 18 18 18 19 19

" 50.2 53.2 56.2 59.2 02.1 05.0

7 8 9 10 11 12

295 295 295 295 295 295

23 24 24 26 27 28

14.2 03.7 59.1 00.5 07.9 21.1

-0 0 0 0 0 0

19 19 19 19 19 19

13 14 15 16 17 18

295 295 295 295 295 295

29 31 32 34 35 37

40.3 05.3 36.2 13.0 55.7 44.4

-0 0 0 0 0 0

19 20 21 22 23 24

295 295 295 295 295 295

39 41 43 45 48 50

38.9 39.3 45.6 57.6 15.2 38.6

25 26 27 28 29 30

295 295 295 296 296 296

53 55 58 01 03 06

31 1 2 3 4 5

296 296 296 296 296 296

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 297 297 297 297 297 297

' 10 14 19 23 28 33

" 04.2 31.2 02.9 39.0 19.6 04.4

º -0 0 0 0 0 0

' 20 21 21 21 21 21

" 57.3 00.0 02.8 05.5 08.3 11.0

07.9 10.8 13.7 16.5 19.4 22.2

22 23 24 25 26 27

297 297 297 297 297 298

37 42 47 52 57 03

53.5 46.8 44.3 45.8 51.4 01.0

-0 0 0 0 0 0

21 21 21 21 21 21

13.8 16.6 19.4 22.2 25.0 27.8

19 19 19 19 19 19

25.0 27.8 30.6 33.4 36.2 39.0

28 29 30 1 2 3

298 298 298 298 298 298

08 13 18 24 29 35

14.5 32.0 53.3 18.3 47.1 19.5

-0 0 0 0 0 0

21 21 21 21 21 21

30.6 33.4 36.3 39.1 42.0 44.9

-0 0 0 0 0 0

19 19 19 19 19 19

41.8 44.5 47.3 50.0 52.7 55.5

4 5 6 7 8 9

298 298 298 298 299 299

40 46 52 58 03 09

55.5 35.0 17.8 04.1 53.6 46.4

-0 0 0 0 0 0

21 21 21 21 21 22

47.8 50.7 53.7 56.6 59.6 02.6

07.4 41.9 21.8 07.2 58.1 54.4

-0 0 0 0 0 0

19 20 20 20 20 20

58.2 00.9 03.6 06.3 09.0 11.7

10 11 12 13 14 15

299 299 299 299 299 299

15 21 27 33 39 46

42.3 41.5 43.7 49.1 57.5 08.8

-0 0 0 0 0 0

22 22 22 22 22 22

05.6 08.7 11.7 14.8 17.9 21.0

09 13 16 19 22 26

56.1 03.2 15.7 33.4 56.4 24.6

-0 0 0 0 0 0

20 20 20 20 20 20

14.3 17.0 19.7 22.3 25.0 27.7

16 17 18 19 20 21

299 299 300 300 300 300

52 58 04 11 17 24

23.0 39.8 59.2 21.2 45.6 12.5

-0 0 0 0 0 0

22 22 22 22 22 22

24.2 27.3 30.5 33.7 36.9 40.2

296 296 296 296 296 296

29 33 37 41 45 49

58.0 36.5 20.0 08.4 01.8 00.1

-0 0 0 0 0 0

20 20 20 20 20 20

30.3 33.0 35.7 38.4 41.0 43.7

22 23 24 25 26 27

300 300 300 300 300 301

30 37 43 50 57 03

41.6 13.0 46.7 22.5 00.5 40.5

-0 0 0 0 0 0

22 22 22 22 22 23

43.5 46.7 50.0 53.4 56.7 00.1

296 296 297 297 297

53 57 01 05 10

03.3 11.3 24.1 41.8 04.2

-0 0 0 0 -0

20 20 20 20 20

46.4 49.1 51.8 54.6 57.3

28 29 30 31 32

301 301 301 301 301

10 17 23 30 37

22.5 06.4 52.1 39.6 28.7

-0 0 0 0 -0

23 23 23 23 23

03.5 06.9 10.4 13.9 17.4

Nov.

Dec.

160

SATURN, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Jan. 0 1 2 3 4 5

h 19 19 19 19 19 19

m 31 32 32 33 33 34

s º 57.68 -21 27.54 21 57.46 21 27.42 21 57.43 21 27.48 21

' 42 41 40 38 37 36

" 04.3 03.1 01.5 59.3 56.8 53.7

10.993 032 10.996 391 10.999 491 11.002 334 11.004 917 11.007 241

" 0.80 0.80 0.80 0.80 0.80 0.80

" 6.72 6.71 6.71 6.71 6.71 6.71

h 12 12 12 12 12 12

m 53 50 46 43 39 36

s 35 09 43 17 51 25

6 7 8 9 10 11

19 19 19 19 19 19

34 35 35 36 36 37

57.56 -21 27.68 21 57.82 21 27.99 21 58.17 21 28.37 21

35 34 33 32 31 30

50.2 46.2 41.9 37.1 31.9 26.4

11.009 306 11.011 111 11.012 657 11.013 943 11.014 969 11.015 735

0.80 0.80 0.80 0.80 0.80 0.80

6.71 6.70 6.70 6.70 6.70 6.70

12 12 12 12 12 12

32 29 26 22 19 15

59 33 07 41 15 49

12 13 14 15 16 17

19 19 19 19 19 19

37 38 38 39 39 40

58.58 -21 28.80 21 58.84 21 29.09 21 59.26 21 29.42 21

29 28 27 26 24 23

20.5 14.2 07.8 00.9 53.7 46.1

11.016 242 11.016 488 11.016 474 11.016 200 11.015 665 11.014 869

0.80 0.80 0.80 0.80 0.80 0.80

6.70 6.70 6.70 6.70 6.70 6.70

12 12 12 12 11 11

12 08 05 02 58 55

23 57 31 06 40 14

18 19 20 21 22 23

19 19 19 19 19 19

40 41 41 42 42 43

59.54 -21 29.65 21 59.72 21 29.77 21 59.77 21 29.73 21

22 21 20 19 18 16

38.2 29.9 21.4 12.7 03.7 54.4

11.013 811 11.012 493 11.010 913 11.009 072 11.006 969 11.004 606

0.80 0.80 0.80 0.80 0.80 0.80

6.70 6.70 6.70 6.71 6.71 6.71

11 11 11 11 11 11

51 48 44 41 38 34

48 22 56 30 04 38

24 25 26 27 28 29

19 19 19 19 19 19

43 44 44 45 45 46

59.63 -21 29.47 21 59.25 21 28.95 21 58.58 21 28.13 21

15 14 13 12 11 09

45.0 35.4 25.6 15.6 05.5 55.3

11.001 983 10.999 100 10.995 958 10.992 558 10.988 901 10.984 988

0.80 0.80 0.80 0.80 0.80 0.80

6.71 6.71 6.71 6.72 6.72 6.72

11 11 11 11 11 11

31 27 24 20 17 13

11 45 19 52 26 59

30 31 Feb. 1 2 3 4

19 19 19 19 19 19

46 47 47 48 48 49

57.59 -21 26.97 21 56.25 21 25.43 21 54.52 21 23.50 21

08 07 06 05 04 02

44.8 34.3 23.7 12.9 02.1 51.2

10.980 820 10.976 399 10.971 726 10.966 802 10.961 629 10.956 208

0.80 0.80 0.80 0.80 0.80 0.80

6.72 6.73 6.73 6.73 6.73 6.74

11 11 11 11 10 10

10 07 03 00 56 53

33 06 39 12 45 18

5 6 7 8 9 10

19 19 19 19 19 19

49 50 50 51 51 52

52.37 -21 21.12 21 49.76 20 18.27 20 46.65 20 14.89 20

01 00 59 58 56 55

40.3 29.4 18.5 07.7 56.9 46.1

10.950 541 10.944 630 10.938 476 10.932 081 10.925 446 10.918 573

0.80 0.80 0.80 0.80 0.80 0.81

6.74 6.74 6.75 6.75 6.76 6.76

10 10 10 10 10 10

49 46 42 39 36 32

51 24 56 28 01 33

11 12 13 14 15

19 19 19 19 19

52 53 53 54 54

42.99 -20 10.95 20 38.75 20 06.41 20 33.92 -20

54 53 52 51 49

35.5 24.9 14.4 04.0 53.6

10.911 464 10.904 119 10.896 541 10.888 730 10.880 689

0.81 0.81 0.81 0.81 0.81

6.77 6.77 6.77 6.78 6.78

10 10 10 10 10

29 25 22 18 15

05 37 08 40 11

161

SATURN, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Feb. 15 16 17 18 19 20

h 19 19 19 19 19 19

m 54 55 55 55 56 56

s º 33.92 -20 01.27 20 28.46 20 55.48 20 22.34 20 49.01 20

' 49 48 47 46 45 44

" 53.6 43.5 33.5 23.6 14.1 04.7

10.880 689 10.872 417 10.863 918 10.855 193 10.846 244 10.837 072

" 0.81 0.81 0.81 0.81 0.81 0.81

" 6.78 6.79 6.79 6.80 6.81 6.81

h 10 10 10 10 10 9

m 15 11 08 04 01 57

s 11 43 14 45 15 46

21 22 23 24 25 26

19 19 19 19 19 19

57 57 58 58 58 59

15.49 -20 41.79 20 07.88 20 33.78 20 59.47 20 24.96 20

42 41 40 39 38 37

55.6 46.8 38.3 30.1 22.2 14.6

10.827 681 10.818 071 10.808 247 10.798 209 10.787 961 10.777 506

0.81 0.81 0.81 0.81 0.82 0.82

6.82 6.82 6.83 6.84 6.84 6.85

9 9 9 9 9 9

54 50 47 43 40 36

16 46 16 46 16 45

27 28 29 Mar. 1 2 3

19 20 20 20 20 20

59 00 00 01 01 01

50.22 -20 15.28 20 40.11 20 04.72 20 29.11 20 53.26 20

36 35 33 32 31 30

07.4 00.5 54.1 48.0 42.4 37.2

10.766 846 10.755 984 10.744 924 10.733 667 10.722 217 10.710 577

0.82 0.82 0.82 0.82 0.82 0.82

6.86 6.86 6.87 6.88 6.88 6.89

9 9 9 9 9 9

33 29 26 22 19 15

14 43 12 40 09 37

4 5 6 7 8 9

20 20 20 20 20 20

02 02 03 03 03 04

17.18 -20 40.86 20 04.30 20 27.48 20 50.41 20 13.08 20

29 28 27 26 25 24

32.5 28.3 24.6 21.5 18.9 17.0

10.698 751 10.686 741 10.674 550 10.662 181 10.649 639 10.636 925

0.82 0.82 0.82 0.82 0.83 0.83

6.90 6.91 6.92 6.92 6.93 6.94

9 9 9 9 8 8

12 08 04 01 57 54

04 32 59 26 53 20

10 11 12 13 14 15

20 20 20 20 20 20

04 04 05 05 06 06

35.49 -20 57.63 20 19.51 20 41.11 20 02.45 20 23.52 20

23 22 21 20 19 18

15.6 14.8 14.5 14.9 16.0 17.7

10.624 042 10.610 993 10.597 782 10.584 410 10.570 880 10.557 196

0.83 0.83 0.83 0.83 0.83 0.83

6.95 6.96 6.97 6.97 6.98 6.99

8 8 8 8 8 8

50 47 43 40 36 32

46 12 38 03 28 53

16 17 18 19 20 21

20 20 20 20 20 20

06 07 07 07 08 08

44.30 -20 04.80 20 25.01 20 44.93 20 04.54 20 23.84 20

17 16 15 14 13 12

20.0 23.2 27.0 31.7 37.1 43.3

10.543 361 10.529 377 10.515 248 10.500 978 10.486 569 10.472 027

0.83 0.84 0.84 0.84 0.84 0.84

7.00 7.01 7.02 7.03 7.04 7.05

8 8 8 8 8 8

29 25 22 18 14 11

18 42 07 30 54 17

22 23 24 25 26 27

20 20 20 20 20 20

08 09 09 09 09 10

42.84 -20 01.52 20 19.89 20 37.94 20 55.66 20 13.06 20

11 10 10 09 08 07

50.3 58.2 06.9 16.4 26.8 38.1

10.457 353 10.442 552 10.427 629 10.412 586 10.397 429 10.382 161

0.84 0.84 0.84 0.84 0.85 0.85

7.06 7.07 7.08 7.09 7.10 7.11

8 8 8 7 7 7

07 04 00 56 53 49

40 02 25 47 08 30

28 29 30 31 Apr. 1

20 20 20 20 20

10 10 11 11 11

30.14 -20 46.88 20 03.30 20 19.37 20 35.11 -20

06 06 05 04 03

50.3 03.4 17.5 32.5 48.5

10.366 786 10.351 308 10.335 732 10.320 063 10.304 303

0.85 0.85 0.85 0.85 0.85

7.12 7.13 7.14 7.15 7.16

7 7 7 7 7

45 42 38 34 31

51 11 32 52 11

162

SATURN, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Apr. 1 2 3 4 5 6

h 20 20 20 20 20 20

m 11 11 12 12 12 12

s º 35.11 -20 50.51 20 05.55 20 20.25 20 34.59 20 48.57 20

' 03 03 02 01 01 00

" 48.5 05.6 23.6 42.7 02.9 24.1

10.304 303 10.288 457 10.272 531 10.256 527 10.240 449 10.224 303

" 0.85 0.85 0.86 0.86 0.86 0.86

" 7.16 7.18 7.19 7.20 7.21 7.22

h 7 7 7 7 7 7

m 31 27 23 20 16 12

s 11 30 49 08 26 44

7 8 9 10 11 12

20 20 20 20 20 20

13 13 13 13 13 14

02.20 -19 15.46 19 28.37 19 40.92 19 53.10 19 04.92 19

59 59 58 57 57 56

46.4 09.8 34.2 59.7 26.2 54.0

10.208 092 10.191 818 10.175 488 10.159 103 10.142 668 10.126 187

0.86 0.86 0.86 0.87 0.87 0.87

7.23 7.24 7.25 7.27 7.28 7.29

7 7 7 6 6 6

09 05 01 57 54 50

02 19 36 52 08 24

13 14 15 16 17 18

20 20 20 20 20 20

14 14 14 14 14 15

16.37 -19 27.45 19 38.15 19 48.47 19 58.40 19 07.94 19

56 55 55 54 54 54

22.8 52.9 24.2 56.6 30.3 05.2

10.109 664 10.093 102 10.076 507 10.059 882 10.043 232 10.026 562

0.87 0.87 0.87 0.87 0.88 0.88

7.30 7.31 7.33 7.34 7.35 7.36

6 6 6 6 6 6

46 42 39 35 31 27

39 54 09 23 37 51

19 20 21 22 23 24

20 20 20 20 20 20

15 15 15 15 15 15

17.10 -19 25.86 19 34.23 19 42.21 19 49.79 19 56.98 19

53 53 52 52 52 52

41.3 18.6 57.2 37.0 18.0 00.3

10.009 876 9.993 178 9.976 475 9.959 769 9.943 066 9.926 372

0.88 0.88 0.88 0.88 0.88 0.89

7.37 7.39 7.40 7.41 7.42 7.44

6 6 6 6 6 6

24 20 16 12 08 05

04 16 29 41 52 03

25 26 27 28 29 30

20 20 20 20 20 20

16 16 16 16 16 16

03.77 -19 10.17 19 16.16 19 21.76 19 26.96 19 31.75 19

51 51 51 51 50 50

43.9 28.8 14.9 02.4 51.1 41.2

9.909 690 9.893 026 9.876 384 9.859 770 9.843 187 9.826 642

0.89 0.89 0.89 0.89 0.89 0.89

7.45 7.46 7.47 7.49 7.50 7.51

6 5 5 5 5 5

01 57 53 49 45 42

14 24 34 44 53 02

May 1 2 3 4 5 6

20 20 20 20 20 20

16 16 16 16 16 16

36.14 -19 40.13 19 43.70 19 46.87 19 49.64 19 52.00 19

50 50 50 50 50 50

32.7 25.4 19.5 14.9 11.6 09.6

9.810 138 9.793 681 9.777 274 9.760 923 9.744 631 9.728 402

0.90 0.90 0.90 0.90 0.90 0.90

7.52 7.54 7.55 7.56 7.58 7.59

5 5 5 5 5 5

38 34 30 26 22 18

10 18 26 33 40 46

7 8 9 10 11 12

20 20 20 20 20 20

16 16 16 16 16 16

53.96 -19 55.52 19 56.69 19 57.45 19 57.81 19 57.77 19

50 50 50 50 50 50

08.9 09.5 11.4 14.7 19.3 25.2

9.712 242 9.696 153 9.680 140 9.664 208 9.648 360 9.632 602

0.91 0.91 0.91 0.91 0.91 0.91

7.60 7.61 7.63 7.64 7.65 7.66

5 5 5 5 4 4

14 10 07 03 59 55

52 58 03 07 12 16

13 14 15 16 17

20 20 20 20 20

16 16 16 16 16

57.32 -19 56.47 19 55.20 19 53.54 19 51.47 -19

50 50 50 51 51

32.5 41.1 51.0 02.3 14.8

9.616 937 9.601 370 9.585 906 9.570 549 9.555 305

0.91 0.92 0.92 0.92 0.92

7.68 7.69 7.70 7.71 7.73

4 4 4 4 4

51 47 43 39 35

19 22 25 28 30

163

SATURN, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

May 17 18 19 20 21 22

h 20 20 20 20 20 20

m 16 16 16 16 16 16

s º 51.47 -19 48.99 19 46.12 19 42.85 19 39.18 19 35.12 19

' 51 51 51 52 52 52

" 14.8 28.7 43.8 00.3 17.9 36.9

9.555 305 9.540 178 9.525 172 9.510 293 9.495 545 9.480 933

" 0.92 0.92 0.92 0.92 0.93 0.93

" 7.73 7.74 7.75 7.76 7.77 7.79

h 4 4 4 4 4 4

m 35 31 27 23 19 15

s 30 31 32 33 33 33

23 24 25 26 27 28

20 20 20 20 20 20

16 16 16 16 16 16

30.67 -19 25.83 19 20.61 19 15.00 19 09.01 19 02.64 19

52 53 53 54 54 54

57.1 18.6 41.4 05.4 30.6 57.1

9.466 462 9.452 136 9.437 961 9.423 940 9.410 078 9.396 379

0.93 0.93 0.93 0.93 0.93 0.94

7.80 7.81 7.82 7.83 7.84 7.86

4 4 4 3 3 3

11 07 03 59 55 51

33 32 31 29 28 25

29 30 31 June 1 2 3

20 20 20 20 20 20

15 15 15 15 15 15

55.89 -19 48.76 19 41.26 19 33.40 19 25.17 19 16.59 19

55 55 56 56 57 58

24.8 53.7 23.8 55.0 27.3 00.8

9.382 849 9.369 490 9.356 307 9.343 304 9.330 484 9.317 851

0.94 0.94 0.94 0.94 0.94 0.94

7.87 7.88 7.89 7.90 7.91 7.92

3 3 3 3 3 3

47 43 39 35 31 27

23 19 16 12 08 04

4 5 6 7 8 9

20 20 20 20 20 20

15 14 14 14 14 14

07.67 -19 58.39 19 48.78 19 38.83 20 28.54 20 17.92 20

58 59 59 00 01 01

35.3 10.8 47.5 25.2 04.0 43.8

9.305 409 9.293 160 9.281 110 9.269 260 9.257 615 9.246 178

0.95 0.95 0.95 0.95 0.95 0.95

7.93 7.94 7.95 7.96 7.97 7.98

3 3 3 3 3 3

22 18 14 10 06 02

59 54 48 42 36 30

10 11 12 13 14 15

20 20 20 20 20 20

14 13 13 13 13 13

06.96 -20 55.68 20 44.08 20 32.15 20 19.92 20 07.38 20

02 03 03 04 05 06

24.7 06.5 49.3 33.0 17.6 03.2

9.234 953 9.223 944 9.213 154 9.202 588 9.192 248 9.182 138

0.95 0.95 0.95 0.96 0.96 0.96

7.99 8.00 8.01 8.02 8.03 8.04

2 2 2 2 2 2

58 54 50 46 41 37

23 16 08 00 52 44

16 17 18 19 20 21

20 20 20 20 20 20

12 12 12 12 12 11

54.54 -20 41.42 20 28.00 20 14.31 20 00.35 20 46.13 20

06 07 08 09 10 10

49.5 36.8 24.8 13.6 03.2 53.5

9.172 262 9.162 624 9.153 228 9.144 075 9.135 171 9.126 517

0.96 0.96 0.96 0.96 0.96 0.96

8.05 8.06 8.06 8.07 8.08 8.09

2 2 2 2 2 2

33 29 25 21 16 12

35 26 17 07 57 47

22 23 24 25 26 27

20 20 20 20 20 20

11 11 11 10 10 10

31.65 -20 16.91 20 01.93 20 46.71 20 31.25 20 15.57 20

11 12 13 14 15 16

44.6 36.3 28.8 21.9 15.7 10.0

9.118 118 9.109 977 9.102 095 9.094 477 9.087 124 9.080 039

0.96 0.97 0.97 0.97 0.97 0.97

8.10 8.10 8.11 8.12 8.12 8.13

2 2 2 1 1 1

08 04 00 56 51 47

37 26 16 04 53 42

28 29 30 July 1 2

20 20 20 20 20

09 09 09 09 08

59.68 -20 43.58 20 27.28 20 10.80 20 54.14 -20

17 18 18 19 20

04.9 00.3 56.1 52.4 49.1

9.073 223 9.066 680 9.060 411 9.054 416 9.048 699

0.97 0.97 0.97 0.97 0.97

8.14 8.14 8.15 8.15 8.16

1 1 1 1 1

43 39 35 30 26

30 18 06 54 41

164

SATURN, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

July 1 2 3 4 5 6

h 20 20 20 20 20 20

m 09 08 08 08 08 07

s º 10.80 -20 54.14 20 37.32 20 20.33 20 03.18 20 45.89 20

' 19 20 21 22 23 24

" 52.4 49.1 46.2 43.7 41.5 39.7

9.054 416 9.048 699 9.043 261 9.038 103 9.033 227 9.028 634

" 0.97 0.97 0.97 0.97 0.97 0.97

" 8.15 8.16 8.16 8.17 8.17 8.18

h 1 1 1 1 1 1

m 30 26 22 18 14 09

s 54 41 28 16 03 49

7 8 9 10 11 12

20 20 20 20 20 20

07 07 06 06 06 05

28.45 -20 10.87 20 53.16 20 35.34 20 17.40 20 59.37 20

25 26 27 28 29 30

38.2 37.0 36.0 35.2 34.6 34.2

9.024 325 9.020 304 9.016 570 9.013 126 9.009 972 9.007 111

0.97 0.97 0.98 0.98 0.98 0.98

8.18 8.18 8.19 8.19 8.19 8.20

1 1 0 0 0 0

05 01 57 52 48 44

36 23 09 56 42 28

13 14 15 16 17 18

20 20 20 20 20 20

05 05 05 04 04 04

41.24 -20 23.04 20 04.76 20 46.42 20 28.04 20 09.61 20

31 32 33 34 35 36

33.8 33.5 33.3 33.0 32.8 32.5

9.004 544 9.002 271 9.000 294 8.998 615 8.997 233 8.996 150

0.98 0.98 0.98 0.98 0.98 0.98

8.20 8.20 8.20 8.20 8.20 8.21

0 0 0 0 0 0

40 36 31 27 23 19

14 00 46 32 18 03

19 20 21 22 23 24

20 20 20 20 20 20

03 03 03 02 02 02

51.15 -20 32.66 20 14.16 20 55.65 20 37.15 20 18.65 20

37 38 39 40 41 42

32.2 31.8 31.3 30.7 30.0 29.0

8.995 366 8.994 882 8.994 698 8.994 815 8.995 231 8.995 948

0.98 0.98 0.98 0.98 0.98 0.98

8.21 8.21 8.21 8.21 8.21 8.21

0 0 0 0 23 23

14 10 06 02 53 49

49 35 21 06 38 23

25 26 27 28 29 30

20 20 20 20 20 20

02 01 01 01 00 00

00.18 -20 41.75 20 23.36 20 05.03 20 46.77 20 28.58 20

43 44 45 46 47 48

27.8 26.3 24.5 22.3 19.8 16.9

8.996 965 8.998 280 8.999 893 9.001 803 9.004 009 9.006 510

0.98 0.98 0.98 0.98 0.98 0.98

8.20 8.20 8.20 8.20 8.20 8.20

23 23 23 23 23 23

45 40 36 32 28 23

09 55 41 27 13 59

31 Aug. 1 2 3 4 5

20 19 19 19 19 19

00 59 59 59 58 58

10.48 -20 52.48 20 34.57 20 16.77 20 59.08 20 41.52 20

49 50 51 52 52 53

13.6 09.9 05.8 01.2 56.2 50.7

9.009 304 9.012 391 9.015 769 9.019 437 9.023 394 9.027 637

0.98 0.98 0.98 0.98 0.97 0.97

8.19 8.19 8.19 8.18 8.18 8.18

23 23 23 23 23 22

19 15 11 07 02 58

45 31 18 04 51 38

6 7 8 9 10 11

19 19 19 19 19 19

58 58 57 57 57 56

24.08 -20 06.79 20 49.64 20 32.66 20 15.84 20 59.21 20

54 55 56 57 58 59

44.6 38.0 30.8 22.9 14.5 05.4

9.032 168 9.036 983 9.042 081 9.047 461 9.053 122 9.059 062

0.97 0.97 0.97 0.97 0.97 0.97

8.17 8.17 8.16 8.16 8.15 8.15

22 22 22 22 22 22

54 50 45 41 37 33

24 11 59 46 34 21

12 13 14 15 16

19 19 19 19 19

56 56 56 55 55

42.76 -20 26.51 21 10.46 21 54.62 21 39.01 -21

59 00 01 02 03

55.6 45.1 33.9 22.0 09.4

9.065 279 9.071 771 9.078 536 9.085 573 9.092 878

0.97 0.97 0.97 0.97 0.97

8.14 8.14 8.13 8.12 8.12

22 22 22 22 22

29 24 20 16 12

09 57 46 34 23

165

SATURN, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Aug. 16 17 18 19 20 21

h 19 19 19 19 19 19

m 55 55 55 54 54 54

s º 39.01 -21 23.62 21 08.47 21 53.56 21 38.90 21 24.49 21

' 03 03 04 05 06 06

" 09.4 56.1 42.0 27.1 11.5 55.0

9.092 878 9.100 451 9.108 288 9.116 386 9.124 743 9.133 356

" 0.97 0.97 0.97 0.96 0.96 0.96

" 8.12 8.11 8.10 8.10 8.09 8.08

h 22 22 22 21 21 21

m 12 08 04 59 55 51

s 23 12 01 51 40 31

22 23 24 25 26 27

19 19 19 19 19 19

54 53 53 53 53 53

10.35 -21 56.49 21 42.91 21 29.63 21 16.64 21 03.97 21

07 08 09 09 10 10

37.6 19.4 00.3 40.3 19.3 57.5

9.142 222 9.151 336 9.160 696 9.170 297 9.180 137 9.190 212

0.96 0.96 0.96 0.96 0.96 0.96

8.07 8.07 8.06 8.05 8.04 8.03

21 21 21 21 21 21

47 43 39 34 30 26

21 11 02 53 45 37

28 29 30 31 Sept. 1 2

19 19 19 19 19 19

52 52 52 52 52 51

51.60 -21 39.54 21 27.80 21 16.38 21 05.29 21 54.53 21

11 12 12 13 13 14

34.7 11.0 46.5 20.9 54.4 27.0

9.200 518 9.211 051 9.221 807 9.232 785 9.243 979 9.255 386

0.96 0.95 0.95 0.95 0.95 0.95

8.02 8.01 8.00 8.00 7.99 7.98

21 21 21 21 21 21

22 18 14 10 06 01

29 21 14 07 00 54

3 4 5 6 7 8

19 19 19 19 19 19

51 51 51 51 51 50

44.10 -21 34.02 21 24.29 21 14.91 21 05.88 21 57.23 21

14 15 15 16 16 17

58.6 29.1 58.7 27.2 54.7 21.2

9.267 003 9.278 826 9.290 852 9.303 076 9.315 496 9.328 108

0.95 0.95 0.95 0.95 0.94 0.94

7.97 7.96 7.95 7.94 7.92 7.91

20 20 20 20 20 20

57 53 49 45 41 37

48 42 37 32 27 23

9 10 11 12 13 14

19 19 19 19 19 19

50 50 50 50 50 50

48.94 -21 41.03 21 33.49 21 26.34 21 19.57 21 13.19 21

17 18 18 18 19 19

46.6 11.0 34.4 56.7 18.0 38.2

9.340 907 9.353 891 9.367 054 9.380 393 9.393 905 9.407 584

0.94 0.94 0.94 0.94 0.94 0.93

7.90 7.89 7.88 7.87 7.86 7.85

20 20 20 20 20 20

33 29 25 21 17 13

19 16 13 10 08 06

15 16 17 18 19 20

19 19 19 19 19 19

50 50 49 49 49 49

07.20 -21 01.59 21 56.39 21 51.58 21 47.17 21 43.18 21

19 20 20 20 21 21

57.4 15.6 32.6 48.6 03.5 17.2

9.421 427 9.435 428 9.449 584 9.463 890 9.478 341 9.492 931

0.93 0.93 0.93 0.93 0.93 0.93

7.84 7.82 7.81 7.80 7.79 7.78

20 20 20 19 19 19

09 05 01 57 53 49

04 03 02 02 02 03

21 22 23 24 25 26

19 19 19 19 19 19

49 49 49 49 49 49

39.60 -21 36.44 21 33.69 21 31.36 21 29.44 21 27.94 21

21 21 21 22 22 22

29.8 41.3 51.7 01.0 09.2 16.3

9.507 656 9.522 511 9.537 490 9.552 590 9.567 804 9.583 129

0.92 0.92 0.92 0.92 0.92 0.92

7.76 7.75 7.74 7.73 7.72 7.70

19 19 19 19 19 19

45 41 37 33 29 25

04 05 06 09 11 14

27 28 29 30 Oct. 1

19 19 19 19 19

49 49 49 49 49

26.86 -21 26.18 21 25.93 21 26.08 21 26.66 -21

22 22 22 22 22

22.3 27.3 31.1 33.8 35.4

9.598 559 9.614 091 9.629 718 9.645 438 9.661 246

0.92 0.91 0.91 0.91 0.91

7.69 7.68 7.67 7.65 7.64

19 19 19 19 19

21 17 13 09 05

17 21 25 30 35

166

SATURN, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Oct. 1 2 3 4 5 6

h 19 19 19 19 19 19

m 49 49 49 49 49 49

s º 26.66 -21 27.65 21 29.07 21 30.90 21 33.15 21 35.83 21

' 22 22 22 22 22 22

" 35.4 35.9 35.3 33.5 30.6 26.6

9.661 246 9.677 136 9.693 105 9.709 148 9.725 260 9.741 438

" 0.91 0.91 0.91 0.91 0.90 0.90

" 7.64 7.63 7.62 7.60 7.59 7.58

h 19 19 18 18 18 18

m 05 01 57 53 49 46

s 35 40 46 52 59 06

7 8 9 10 11 12

19 19 19 19 19 19

49 49 49 49 49 50

38.93 -21 42.45 21 46.39 21 50.75 21 55.52 21 00.72 21

22 22 22 21 21 21

21.4 15.2 07.8 59.4 49.8 39.2

9.757 676 9.773 971 9.790 317 9.806 710 9.823 146 9.839 619

0.90 0.90 0.90 0.90 0.90 0.89

7.57 7.55 7.54 7.53 7.51 7.50

18 18 18 18 18 18

42 38 34 30 26 22

14 22 30 39 48 57

13 14 15 16 17 18

19 19 19 19 19 19

50 50 50 50 50 50

06.32 -21 12.34 21 18.78 21 25.62 21 32.88 21 40.56 21

21 21 21 20 20 20

27.4 14.6 00.6 45.6 29.3 11.9

9.856 125 9.872 659 9.889 216 9.905 791 9.922 378 9.938 973

0.89 0.89 0.89 0.89 0.89 0.88

7.49 7.48 7.46 7.45 7.44 7.43

18 18 18 18 18 18

19 15 11 07 03 00

07 18 29 40 51 03

19 20 21 22 23 24

19 19 19 19 19 19

50 50 51 51 51 51

48.65 -21 57.16 21 06.07 21 15.39 21 25.11 21 35.22 21

19 19 19 18 18 18

53.4 33.8 13.1 51.3 28.4 04.5

9.955 571 9.972 165 9.988 752 10.005 326 10.021 883 10.038 417

0.88 0.88 0.88 0.88 0.88 0.88

7.41 7.40 7.39 7.38 7.37 7.35

17 17 17 17 17 17

56 52 48 44 41 37

16 29 42 56 10 24

25 26 27 28 29 30

19 19 19 19 19 19

51 51 52 52 52 52

45.72 -21 56.62 21 07.89 21 19.56 21 31.60 21 44.02 21

17 17 16 16 15 15

39.5 13.3 46.1 17.9 48.5 18.0

10.054 925 10.071 402 10.087 844 10.104 246 10.120 604 10.136 914

0.87 0.87 0.87 0.87 0.87 0.87

7.34 7.33 7.32 7.31 7.29 7.28

17 17 17 17 17 17

33 29 26 22 18 14

39 54 10 26 42 59

31 Nov. 1 2 3 4 5

19 19 19 19 19 19

52 53 53 53 53 54

56.83 -21 10.00 21 23.55 21 37.48 21 51.77 21 06.42 21

14 14 13 13 12 11

46.4 13.8 40.0 05.2 29.3 52.4

10.153 171 10.169 373 10.185 513 10.201 589 10.217 597 10.233 532

0.87 0.86 0.86 0.86 0.86 0.86

7.27 7.26 7.25 7.24 7.22 7.21

17 17 17 17 16 16

11 07 03 00 56 52

16 33 51 09 28 47

6 7 8 9 10 11

19 19 19 19 19 19

54 54 54 55 55 55

21.43 -21 36.80 21 52.52 21 08.59 21 25.00 21 41.76 21

11 10 09 09 08 07

14.5 35.5 55.4 14.4 32.3 49.2

10.249 390 10.265 167 10.280 859 10.296 461 10.311 971 10.327 382

0.86 0.86 0.86 0.85 0.85 0.85

7.20 7.19 7.18 7.17 7.16 7.15

16 16 16 16 16 16

49 45 41 38 34 30

06 26 46 06 27 48

12 13 14 15 16

19 19 19 19 19

55 56 56 56 57

58.85 -21 16.27 21 34.03 21 52.13 21 10.55 -21

07 06 05 04 03

05.0 19.8 33.5 46.1 57.7

10.342 692 10.357 895 10.372 988 10.387 965 10.402 822

0.85 0.85 0.85 0.85 0.85

7.14 7.13 7.12 7.11 7.10

16 16 16 16 16

27 23 19 16 12

09 31 53 15 38

167

SATURN, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Nov. 16 17 18 19 20 21

h 19 19 19 19 19 19

m 57 57 57 58 58 58

s º 10.55 -21 29.31 21 48.37 21 07.75 21 27.44 21 47.42 20

' 03 03 02 01 00 59

" 57.7 08.3 17.9 26.6 34.2 40.9

10.402 822 10.417 556 10.432 161 10.446 634 10.460 972 10.475 170

" 0.85 0.84 0.84 0.84 0.84 0.84

" 7.10 7.09 7.08 7.07 7.06 7.05

h 16 16 16 16 15 15

m 12 09 05 01 58 54

s 38 01 24 47 11 35

22 23 24 25 26 27

19 19 19 20 20 20

59 59 59 00 00 00

07.70 -20 28.26 20 49.12 20 10.25 20 31.66 20 53.35 20

58 57 56 55 54 54

46.6 51.3 55.1 57.8 59.6 00.5

10.489 225 10.503 133 10.516 892 10.530 498 10.543 948 10.557 238

0.84 0.84 0.84 0.84 0.83 0.83

7.04 7.03 7.02 7.01 7.00 6.99

15 15 15 15 15 15

50 47 43 40 36 33

60 25 50 15 40 06

28 29 30 Dec. 1 2 3

20 20 20 20 20 20

01 01 02 02 02 03

15.31 -20 37.53 20 00.02 20 22.77 20 45.78 20 09.03 20

53 51 50 49 48 47

00.3 59.3 57.2 54.3 50.4 45.7

10.570 366 10.583 329 10.596 123 10.608 746 10.621 194 10.633 466

0.83 0.83 0.83 0.83 0.83 0.83

6.98 6.98 6.97 6.96 6.95 6.94

15 15 15 15 15 15

29 25 22 18 15 11

32 59 25 52 19 47

4 5 6 7 8 9

20 20 20 20 20 20

03 03 04 04 05 05

32.53 -20 56.26 20 20.23 20 44.42 20 08.84 20 33.48 20

46 45 44 43 42 40

40.0 33.5 26.1 17.8 08.7 58.7

10.645 557 10.657 466 10.669 189 10.680 722 10.692 064 10.703 212

0.83 0.83 0.82 0.82 0.82 0.82

6.93 6.93 6.92 6.91 6.90 6.90

15 15 15 14 14 14

08 04 01 57 54 50

14 42 10 39 07 36

10 11 12 13 14 15

20 20 20 20 20 20

05 06 06 07 07 08

58.34 -20 23.41 20 48.70 20 14.19 20 39.88 20 05.78 20

39 38 37 36 34 33

47.8 36.0 23.3 09.8 55.5 40.3

10.714 161 10.724 909 10.735 453 10.745 791 10.755 918 10.765 832

0.82 0.82 0.82 0.82 0.82 0.82

6.89 6.88 6.88 6.87 6.86 6.86

14 14 14 14 14 14

47 43 40 36 33 29

05 34 03 33 03 33

16 17 18 19 20 21

20 20 20 20 20 20

08 08 09 09 10 10

31.86 -20 58.13 20 24.56 20 51.17 20 17.94 20 44.87 20

32 31 29 28 27 25

24.3 07.6 50.1 31.9 12.9 53.1

10.775 531 10.785 012 10.794 272 10.803 310 10.812 123 10.820 710

0.82 0.82 0.81 0.81 0.81 0.81

6.85 6.84 6.84 6.83 6.83 6.82

14 14 14 14 14 14

26 22 19 15 12 08

03 33 04 34 05 36

22 23 24 25 26 27

20 20 20 20 20 20

11 11 12 12 13 13

11.96 -20 39.19 20 06.58 20 34.10 20 01.76 20 29.56 20

24 23 21 20 19 17

32.6 11.4 49.4 26.6 03.2 39.1

10.829 069 10.837 197 10.845 094 10.852 758 10.860 187 10.867 380

0.81 0.81 0.81 0.81 0.81 0.81

6.82 6.81 6.81 6.80 6.80 6.79

14 14 13 13 13 13

05 01 58 54 51 47

07 38 10 41 13 45

28 29 30 31 32

20 20 20 20 20

13 14 14 15 15

57.49 -20 25.54 20 53.72 20 22.00 20 50.39 -20

16 14 13 11 10

14.3 48.9 22.8 56.1 28.8

10.874 335 10.881 051 10.887 527 10.893 761 10.899 752

0.81 0.81 0.81 0.81 0.81

6.79 6.78 6.78 6.78 6.77

13 13 13 13 13

44 40 37 33 30

17 49 21 53 26

168

URANUS, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 35 35 35 35 35 35

' 19 20 21 23 24 25

" º ' " 18.0 -0 29 01.2 37.3 0 29 00.4 56.6 0 28 59.6 15.9 0 28 58.7 35.2 0 28 57.9 54.5 0 28 57.1

º 19.818 61 Apr. 2 36 19.818 36 4 36 19.818 12 6 36 19.817 87 8 36 19.817 63 10 36 19.817 38 12 36

' 20 21 22 24 25 26

" º ' " 08.4 -0 28 22.8 27.8 0 28 21.9 47.2 0 28 21.1 06.6 0 28 20.2 26.0 0 28 19.4 45.4 0 28 18.6

19.807 21 19.806 96 19.806 71 19.806 46 19.806 21 19.805 96

13 15 17 19 21 23

35 35 35 35 35 35

27 28 29 31 32 33

13.8 -0 28 56.3 33.1 0 28 55.4 52.5 0 28 54.6 11.8 0 28 53.8 31.1 0 28 52.9 50.4 0 28 52.1

19.817 13 19.816 89 19.816 64 19.816 39 19.816 15 19.815 90

28 29 30 32 33 34

04.8 -0 28 17.7 24.2 0 28 16.9 43.7 0 28 16.0 03.1 0 28 15.2 22.6 0 28 14.3 42.0 0 28 13.5

19.805 71 19.805 46 19.805 20 19.804 95 19.804 70 19.804 45

25 27 29 31 Feb. 2 4

35 35 35 35 35 35

35 36 37 39 40 41

09.8 -0 28 51.3 29.1 0 28 50.4 48.4 0 28 49.6 07.7 0 28 48.7 27.1 0 28 47.9 46.4 0 28 47.1

19.815 65 26 36 36 01.4 -0 28 12.6 19.815 41 28 36 37 20.8 0 28 11.8 19.815 16 30 36 38 40.3 0 28 11.0 19.814 91 May 2 36 39 59.8 0 28 10.1 19.814 66 4 36 41 19.2 0 28 09.3 19.814 42 6 36 42 38.6 0 28 08.4

19.804 20 19.803 95 19.803 70 19.803 45 19.803 20 19.802 95

6 8 10 12 14 16

35 35 35 35 35 35

43 44 45 47 48 49

05.8 -0 28 46.2 25.1 0 28 45.4 44.5 0 28 44.6 03.8 0 28 43.7 23.2 0 28 42.9 42.5 0 28 42.1

19.814 17 19.813 92 19.813 67 19.813 43 19.813 18 19.812 93

8 10 12 14 16 18

36 36 36 36 36 36

43 45 46 47 49 50

58.1 -0 28 07.6 17.6 0 28 06.7 37.0 0 28 05.9 56.5 0 28 05.0 15.9 0 28 04.2 35.4 0 28 03.3

19.802 70 19.802 44 19.802 19 19.801 94 19.801 69 19.801 44

18 20 22 24 26 28

35 35 35 35 35 35

51 52 53 54 56 57

01.9 -0 28 41.2 21.2 0 28 40.4 40.6 0 28 39.5 60.0 0 28 38.7 19.3 0 28 37.9 38.7 0 28 37.1

19.812 68 19.812 44 19.812 19 19.811 94 19.811 69 19.811 44

20 22 24 26 28 30

36 36 36 36 36 36

51 53 54 55 57 58

54.9 -0 28 02.5 14.3 0 28 01.6 33.8 0 28 00.8 53.3 0 27 59.9 12.8 0 27 59.1 32.2 0 27 58.2

19.801 19 19.800 93 19.800 68 19.800 43 19.800 18 19.799 93

1 3 5 7 9 11

35 36 36 36 36 36

58 00 01 02 04 05

58.1 -0 28 36.2 17.4 0 28 35.4 36.8 0 28 34.6 56.2 0 28 33.7 15.6 0 28 32.9 35.0 0 28 32.0

19.811 19 June 1 19.810 95 3 19.810 70 5 19.810 45 7 19.810 20 9 19.809 95 11

36 37 37 37 37 37

59 01 02 03 05 06

51.7 -0 27 57.4 11.2 0 27 56.5 30.7 0 27 55.7 50.2 0 27 54.8 09.6 0 27 53.9 29.2 0 27 53.1

19.799 67 19.799 42 19.799 17 19.798 92 19.798 66 19.798 41

13 15 17 19 21 23

36 36 36 36 36 36

06 08 09 10 12 13

54.4 -0 28 31.2 13.8 0 28 30.4 33.1 0 28 29.5 52.5 0 28 28.7 11.9 0 28 27.8 31.3 0 28 27.0

19.809 70 19.809 45 19.809 20 19.808 95 19.808 70 19.808 45

37 37 37 37 37 37

07 09 10 11 13 14

48.6 -0 27 52.2 08.1 0 27 51.4 27.7 0 27 50.5 47.1 0 27 49.7 06.6 0 27 48.8 26.2 0 27 48.0

19.798 16 19.797 91 19.797 65 19.797 40 19.797 15 19.796 89

25 27 29 31 Apr. 2

36 36 36 36 36

14 16 17 18 20

50.7 -0 28 26.1 10.1 0 28 25.3 29.5 0 28 24.5 48.9 0 28 23.6 08.4 -0 28 22.8

19.808 21 25 37 15 45.7 -0 19.807 96 27 37 17 05.2 0 19.807 71 29 37 18 24.7 0 19.807 46 July 1 37 19 44.2 0 19.807 21 3 37 21 03.7 -0

Jan.

Mar.

14 16 18 20 22 24

13 15 17 19 21 23

36 36 36 36 36 36

27 27 27 27 27

47.1 46.3 45.4 44.6 43.7

19.796 64 19.796 39 19.796 13 19.795 88 19.795 63

169

URANUS, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 37 37 37 37 37 37

' 19 21 22 23 25 26

" º ' " 44.2 -0 27 44.6 03.7 0 27 43.7 23.3 0 27 42.9 42.8 0 27 42.0 02.3 0 27 41.2 21.9 0 27 40.3

19.795 88 Oct. 1 19.795 63 3 19.795 37 5 19.795 12 7 19.794 87 9 19.794 61 11

º 38 38 38 38 38 38

' 20 22 23 24 26 27

" º ' " 44.9 -0 27 04.9 04.5 0 27 04.1 24.2 0 27 03.2 43.8 0 27 02.4 03.5 0 27 01.5 23.1 0 27 00.6

19.784 12 19.783 86 19.783 60 19.783 35 19.783 09 19.782 83

13 15 17 19 21 23

37 37 37 37 37 37

27 29 30 31 32 34

41.4 -0 27 39.4 00.9 0 27 38.6 20.5 0 27 37.7 40.0 0 27 36.9 59.6 0 27 36.0 19.1 0 27 35.2

19.794 36 19.794 10 19.793 85 19.793 60 19.793 34 19.793 09

13 15 17 19 21 23

38 38 38 38 38 38

28 30 31 32 34 35

42.8 -0 26 59.8 02.4 0 26 58.9 22.1 0 26 58.0 41.8 0 26 57.1 01.4 0 26 56.3 21.1 0 26 55.4

19.782 57 19.782 31 19.782 05 19.781 80 19.781 54 19.781 28

25 27 29 31 Aug. 2 4

37 37 37 37 37 37

35 36 38 39 40 42

38.7 -0 27 34.3 58.2 0 27 33.4 17.8 0 27 32.6 37.3 0 27 31.7 56.9 0 27 30.9 16.4 0 27 30.0

19.792 83 19.792 58 19.792 32 19.792 07 19.791 81 Nov. 19.791 56

25 27 29 31 2 4

38 38 38 38 38 38

36 38 39 40 41 43

40.7 -0 26 54.5 00.4 0 26 53.7 20.1 0 26 52.8 39.8 0 26 51.9 59.4 0 26 51.1 19.1 0 26 50.2

19.781 02 19.780 76 19.780 50 19.780 24 19.779 98 19.779 72

6 8 10 12 14 16

37 37 37 37 37 37

43 44 46 47 48 50

36.0 -0 27 29.2 55.6 0 27 28.3 15.1 0 27 27.4 34.7 0 27 26.6 54.3 0 27 25.7 13.9 0 27 24.9

19.791 30 19.791 05 19.790 79 19.790 54 19.790 28 19.790 03

6 8 10 12 14 16

38 38 38 38 38 38

44 45 47 48 49 51

38.8 -0 26 49.3 58.5 0 26 48.4 18.1 0 26 47.6 37.8 0 26 46.7 57.5 0 26 45.8 17.2 0 26 44.9

19.779 46 19.779 20 19.778 94 19.778 68 19.778 42 19.778 16

18 20 22 24 26 28

37 37 37 37 37 37

51 52 54 55 56 58

33.5 -0 27 24.0 53.1 0 27 23.1 12.6 0 27 22.2 32.2 0 27 21.4 51.8 0 27 20.5 11.4 0 27 19.7

19.789 77 19.789 51 19.789 26 19.789 00 19.788 75 19.788 49

18 20 22 24 26 28

38 38 38 38 38 38

52 53 55 56 57 59

36.9 -0 26 44.1 56.6 0 26 43.2 16.3 0 26 42.3 36.0 0 26 41.5 55.7 0 26 40.6 15.4 0 26 39.7

19.777 90 19.777 64 19.777 38 19.777 12 19.776 86 19.776 60

30 1 3 5 7 9

37 38 38 38 38 38

59 00 02 03 04 06

31.0 -0 27 18.8 50.6 0 27 17.9 10.2 0 27 17.1 29.8 0 27 16.2 49.4 0 27 15.4 09.0 0 27 14.5

19.788 23 30 19.787 98 Dec. 2 19.787 72 4 19.787 46 6 19.787 21 8 19.786 95 10

39 39 39 39 39 39

00 01 03 04 05 07

35.2 -0 26 38.8 54.9 0 26 38.0 14.6 0 26 37.1 34.3 0 26 36.2 54.0 0 26 35.3 13.8 0 26 34.4

19.776 34 19.776 08 19.775 82 19.775 56 19.775 30 19.775 04

11 13 15 17 19 21

38 38 38 38 38 38

07 08 10 11 12 14

28.6 -0 27 13.6 48.2 0 27 12.8 07.9 0 27 11.9 27.5 0 27 11.0 47.1 0 27 10.2 06.7 0 27 09.3

19.786 69 19.786 44 19.786 18 19.785 92 19.785 67 19.785 41

12 14 16 18 20 22

39 39 39 39 39 39

08 09 11 12 13 15

33.5 -0 26 33.6 53.2 0 26 32.7 12.9 0 26 31.8 32.7 0 26 30.9 52.4 0 26 30.1 12.2 0 26 29.2

19.774 77 19.774 51 19.774 25 19.773 99 19.773 73 19.773 47

23 25 27 29 1

38 38 38 38 38

15 16 18 19 20

26.3 -0 27 08.4 46.0 0 27 07.6 05.6 0 27 06.7 25.3 0 27 05.8 44.9 -0 27 04.9

19.785 15 19.784 89 19.784 64 19.784 38 19.784 12

24 26 28 30 32

39 39 39 39 39

16 17 19 20 21

31.9 -0 26 28.3 51.7 0 26 27.4 11.4 0 26 26.6 31.1 0 26 25.7 50.9 -0 26 24.8

19.773 21 19.772 94 19.772 68 19.772 42 19.772 16

July

Sept.

Oct.

170

URANUS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Jan.

Feb.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

0 1 2 3 4 5

º 32 32 32 32 32 32

' 42 41 41 40 40 39

" 11.7 38.8 08.8 42.0 18.2 57.5

º -0 0 0 0 0 0

' 29 29 29 29 29 29

" 39.2 37.4 35.5 33.6 31.7 29.8

6 7 8 9 10 11

32 32 32 32 32 32

39 39 39 39 39 38

40.0 25.6 14.4 06.3 01.4 59.6

-0 0 0 0 0 0

29 29 29 29 29 29

12 13 14 15 16 17

32 32 32 32 32 32

39 39 39 39 39 39

00.9 05.3 12.8 23.3 37.0 53.8

-0 0 0 0 0 0

18 19 20 21 22 23

32 32 32 32 32 32

40 40 41 41 42 42

13.8 37.0 03.3 32.9 05.6 41.5

24 25 26 27 28 29

32 32 32 32 32 32

43 44 44 45 46 47

30 31 1 2 3 4

32 32 32 32 32 32

5 6 7 8 9 10 11 12 13 14 15

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

15 16 17 18 19 20

º 33 33 33 33 33 33

' 10 12 13 15 17 19

" 18.5 04.9 54.0 45.8 40.2 37.2

º -0 0 0 0 0 0

' 28 28 28 28 28 28

" 12.1 10.4 08.6 06.9 05.2 03.5

27.8 25.9 24.0 22.1 20.1 18.2

21 22 23 24 25 26

33 33 33 33 33 33

21 23 25 27 29 32

36.8 38.9 43.4 50.5 59.9 11.7

-0 0 0 0 0 0

28 28 27 27 27 27

01.8 00.2 58.5 56.9 55.3 53.7

29 29 29 29 29 29

16.2 14.3 12.3 10.4 08.4 06.5

27 28 29 1 2 3

33 33 33 33 33 33

34 36 39 41 43 46

25.9 42.5 01.4 22.6 46.0 11.8

-0 0 0 0 0 0

27 27 27 27 27 27

52.1 50.5 48.9 47.4 45.8 44.3

-0 0 0 0 0 0

29 29 29 28 28 28

04.6 02.6 00.7 58.8 56.8 54.9

4 5 6 7 8 9

33 33 33 33 33 34

48 51 53 56 58 01

39.7 09.7 41.9 16.0 52.2 30.2

-0 0 0 0 0 0

27 27 27 27 27 27

42.8 41.3 39.8 38.4 37.0 35.5

20.5 02.6 47.7 36.0 27.3 21.6

-0 0 0 0 0 0

28 28 28 28 28 28

53.0 51.0 49.1 47.2 45.3 43.4

10 11 12 13 14 15

34 34 34 34 34 34

04 06 09 12 15 17

10.1 52.0 35.6 21.2 08.7 57.9

-0 0 0 0 0 0

27 27 27 27 27 27

34.1 32.8 31.4 30.1 28.8 27.5

48 49 50 51 52 53

19.0 19.4 22.9 29.4 38.9 51.4

-0 0 0 0 0 0

28 28 28 28 28 28

41.5 39.6 37.7 35.8 33.9 32.1

16 17 18 19 20 21

34 34 34 34 34 34

20 23 26 29 32 35

48.9 41.7 36.1 32.1 29.7 28.8

-0 0 0 0 0 0

27 27 27 27 27 27

26.2 24.9 23.7 22.5 21.2 20.1

32 32 32 32 33 33

55 56 57 59 00 02

07.0 25.4 46.8 11.1 38.2 08.0

-0 0 0 0 0 0

28 28 28 28 28 28

30.2 28.3 26.5 24.6 22.8 21.0

22 23 24 25 26 27

34 34 34 34 34 34

38 41 44 47 50 53

29.3 31.3 34.7 39.4 45.5 52.9

-0 0 0 0 0 0

27 27 27 27 27 27

18.9 17.7 16.6 15.5 14.4 13.3

33 33 33 33 33

03 05 06 08 10

40.6 15.9 54.0 34.9 18.5

-0 0 0 0 -0

28 28 28 28 28

19.2 17.4 15.6 13.8 12.1

28 29 30 31 1

34 35 35 35 35

57 00 03 06 09

01.7 11.6 22.8 35.1 48.5

-0 0 0 0 -0

27 27 27 27 27

12.3 11.3 10.2 09.2 08.3

Feb.

Mar.

Apr.

171

URANUS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Apr.

May

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 35 35 35 35 35 35

' 09 13 16 19 22 26

" 48.5 03.0 18.5 34.8 52.0 10.1

º -0 0 0 0 0 0

' 27 27 27 27 27 27

" 08.3 07.3 06.4 05.5 04.6 03.7

7 8 9 10 11 12

35 35 35 35 35 35

29 32 36 39 42 46

28.9 48.5 08.9 30.0 51.9 14.6

-0 0 0 0 0 0

27 27 27 27 26 26

13 14 15 16 17 18

35 35 35 35 36 36

49 53 56 59 03 06

37.8 01.6 25.9 50.7 15.8 41.3

-0 0 0 0 0 0

19 20 21 22 23 24

36 36 36 36 36 36

10 13 16 20 23 27

07.2 33.3 59.8 26.4 53.3 20.4

25 26 27 28 29 30

36 36 36 36 36 36

30 34 37 41 44 48

1 2 3 4 5 6

36 36 36 37 37 37

7 8 9 10 11 12 13 14 15 16 17

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

17 18 19 20 21 22

º 37 37 37 37 37 38

' 45 49 52 55 58 02

" 47.3 05.6 23.0 39.5 55.2 09.8

º -0 0 0 0 0 0

' 26 26 26 26 26 26

" 46.3 46.3 46.4 46.4 46.5 46.5

02.9 02.1 01.3 00.5 59.7 59.0

23 24 25 26 27 28

38 38 38 38 38 38

05 08 11 14 18 21

23.6 36.3 47.9 58.5 07.8 15.9

-0 0 0 0 0 0

26 26 26 26 26 26

46.6 46.8 46.9 47.1 47.2 47.4

26 26 26 26 26 26

58.3 57.6 56.9 56.3 55.6 55.0

29 30 31 1 2 3

38 38 38 38 38 38

24 27 30 33 36 39

22.7 28.2 32.3 35.0 36.4 36.3

-0 0 0 0 0 0

26 26 26 26 26 26

47.6 47.9 48.1 48.4 48.7 49.0

-0 0 0 0 0 0

26 26 26 26 26 26

54.4 53.9 53.3 52.8 52.3 51.8

4 5 6 7 8 9

38 38 38 38 38 38

42 45 48 51 54 57

34.9 32.0 27.7 21.9 14.5 05.4

-0 0 0 0 0 0

26 26 26 26 26 26

49.3 49.7 50.0 50.4 50.8 51.2

47.7 15.1 41.4 08.9 36.3 03.4

-0 0 0 0 0 0

26 26 26 26 26 26

51.4 51.5 50.8 50.1 49.7 49.3

10 11 12 13 14 15

38 39 39 39 39 39

59 02 05 08 10 13

54.7 42.2 28.0 12.1 54.3 34.7

-0 0 0 0 0 0

26 26 26 26 26 26

51.7 52.1 52.6 53.0 53.5 54.0

51 54 58 01 05 08

30.4 57.0 23.4 49.5 15.2 40.6

-0 0 0 0 0 0

26 26 26 26 26 26

48.9 48.6 48.3 48.0 47.8 47.5

16 17 18 19 20 21

39 39 39 39 39 39

16 18 21 23 26 28

13.2 49.9 24.7 57.6 28.6 57.6

-0 0 0 0 0 0

26 26 26 26 26 26

54.6 55.1 55.6 56.2 56.8 57.4

37 37 37 37 37 37

12 15 18 22 25 29

05.6 30.3 54.5 18.3 41.6 04.3

-0 0 0 0 0 0

26 26 26 26 26 26

47.3 47.1 47.0 46.8 46.7 46.6

22 23 24 25 26 27

39 39 39 39 39 39

31 33 36 38 40 43

24.5 49.4 12.1 32.6 50.8 06.8

-0 0 0 0 0 0

26 26 26 26 27 27

58.0 58.6 59.2 59.9 00.6 01.2

37 37 37 37 37

32 35 39 42 45

26.4 47.8 08.4 28.3 47.3

-0 0 0 0 -0

26 26 26 26 26

46.5 46.4 46.4 46.3 46.3

28 29 30 1 2

39 39 39 39 39

45 47 49 51 53

20.6 32.1 41.3 48.2 52.9

-0 0 0 0 -0

27 27 27 27 27

01.9 02.6 03.4 04.1 04.8

May

June

July

172

URANUS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

July

Aug.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 39 39 39 39 39 40

' 51 53 55 57 59 01

" 48.2 52.9 55.3 55.4 53.0 48.2

º -0 0 0 0 0 0

' 27 27 27 27 27 27

" 04.1 04.8 05.6 06.4 07.2 08.0

7 8 9 10 11 12

40 40 40 40 40 40

03 05 07 09 10 12

41.0 31.2 18.9 04.0 46.5 26.5

-0 0 0 0 0 0

27 27 27 27 27 27

13 14 15 16 17 18

40 40 40 40 40 40

14 15 17 18 20 21

03.9 38.7 10.9 40.4 07.4 31.6

-0 0 0 0 0 0

19 20 21 22 23 24

40 40 40 40 40 40

22 24 25 26 27 28

53.1 11.9 27.9 41.1 51.4 58.8

25 26 27 28 29 30

40 40 40 40 40 40

30 31 32 33 33 34

31 1 2 3 4 5

40 40 40 40 40 40

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 40 40 40 40 40 40

' 41 41 41 41 41 40

" 30.6 27.9 22.2 13.4 01.6 46.8

º -0 0 0 0 0 0

' 27 27 27 27 27 27

" 45.9 46.8 47.8 48.7 49.6 50.6

08.8 09.6 10.4 11.2 12.1 12.9

22 23 24 25 26 27

40 40 40 40 40 40

40 40 39 39 38 38

29.0 08.3 44.7 18.2 48.8 16.6

-0 0 0 0 0 0

27 27 27 27 27 27

51.5 52.4 53.4 54.3 55.2 56.1

27 27 27 27 27 27

13.8 14.6 15.5 16.4 17.3 Sept. 18.2

28 29 30 31 1 2

40 40 40 40 40 40

37 37 36 35 34 34

41.6 03.6 22.8 39.2 52.7 03.3

-0 0 0 0 0 0

27 27 27 27 28 28

57.0 57.8 58.7 59.6 00.4 01.3

-0 0 0 0 0 0

27 27 27 27 27 27

19.1 20.0 20.9 21.8 22.7 23.7

3 4 5 6 7 8

40 40 40 40 40 40

33 32 31 30 29 28

11.1 16.2 18.5 18.1 15.1 09.3

-0 0 0 0 0 0

28 28 28 28 28 28

02.1 02.9 03.7 04.5 05.2 06.0

03.4 05.1 03.9 00.0 53.2 43.5

-0 0 0 0 0 0

27 27 27 27 27 27

24.6 25.6 26.5 27.5 28.4 29.4

9 10 11 12 13 14

40 40 40 40 40 40

27 25 24 23 22 20

01.0 50.1 36.6 20.5 01.9 40.7

-0 0 0 0 0 0

28 28 28 28 28 28

06.7 07.5 08.2 08.9 09.6 10.2

35 36 36 37 38 38

31.0 15.7 57.4 36.2 12.0 44.8

-0 0 0 0 0 0

27 27 27 27 27 27

30.4 31.3 32.3 33.3 34.3 35.2

15 16 17 18 19 20

40 40 40 40 40 40

19 17 16 14 13 11

16.9 50.7 21.9 50.7 17.2 41.3

-0 0 0 0 0 0

28 28 28 28 28 28

10.9 11.5 12.1 12.7 13.3 13.9

40 40 40 40 40 40

39 39 40 40 40 40

14.7 41.5 05.4 26.4 44.4 59.4

-0 0 0 0 0 0

27 27 27 27 27 27

36.2 37.2 38.2 39.1 40.1 41.1

21 22 23 24 25 26

40 40 40 40 40 40

10 08 06 04 03 01

03.3 23.0 40.7 56.2 09.5 20.9

-0 0 0 0 0 0

28 28 28 28 28 28

14.4 15.0 15.5 16.0 16.5 16.9

40 40 40 40 40

41 41 41 41 41

11.6 20.7 27.0 30.3 30.6

-0 0 0 0 -0

27 27 27 27 27

42.0 43.0 44.0 44.9 45.9

27 28 29 30 1

39 39 39 39 39

59 57 55 53 51

30.1 37.4 42.6 46.0 47.5

-0 0 0 0 -0

28 28 28 28 28

17.3 17.7 18.1 18.5 18.8

Aug.

Oct.

173

URANUS, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Oct.

Nov.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 39 39 39 39 39 39

' 51 49 47 45 43 41

" 47.5 47.2 45.1 41.4 36.1 29.2

º -0 0 0 0 0 0

' 28 28 28 28 28 28

" 18.8 19.1 19.4 19.7 19.9 20.2

7 8 9 10 11 12

39 39 39 39 39 39

39 37 34 32 30 28

20.8 10.9 59.6 46.9 32.8 17.5

-0 0 0 0 0 0

28 28 28 28 28 28

13 14 15 16 17 18

39 39 39 39 39 39

26 23 21 19 16 14

00.8 42.9 23.8 03.7 42.6 20.6

-0 0 0 0 0 0

19 20 21 22 23 24

39 39 39 39 39 38

11 09 07 04 02 59

57.8 34.2 10.0 45.1 19.6 53.5

25 26 27 28 29 30

38 38 38 38 38 38

57 54 52 50 47 45

31 1 2 3 4 5

38 38 38 38 38 38

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 38 38 37 37 37 37

' 03 01 59 56 54 52

" 45.6 25.4 06.2 48.2 31.4 15.7

º -0 0 0 0 0 0

' 28 28 28 28 28 28

" 06.3 05.4 04.4 03.5 02.5 01.5

20.3 20.5 20.6 20.8 20.9 20.9

22 23 24 25 26 27

37 37 37 37 37 37

50 47 45 43 41 39

01.3 48.2 36.5 26.3 17.6 10.5

-0 0 0 0 0 0

28 27 27 27 27 27

00.4 59.4 58.3 57.2 56.0 54.9

28 28 28 28 28 28

21.0 21.0 21.0 20.9 20.9 20.8

28 29 30 1 2 3

37 37 37 37 37 37

37 35 32 30 29 27

05.0 01.3 59.4 59.3 01.1 04.7

-0 0 0 0 0 0

27 27 27 27 27 27

53.7 52.4 51.2 49.9 48.7 47.4

-0 0 0 0 0 0

28 28 28 28 28 28

20.7 20.6 20.4 20.2 20.0 19.7

4 5 6 7 8 9

37 37 37 37 37 37

25 23 21 19 17 16

10.4 18.0 27.6 39.2 52.9 08.8

-0 0 0 0 0 0

27 27 27 27 27 27

46.0 44.7 43.3 41.9 40.5 39.1

26.8 59.8 32.3 04.5 36.5 08.3

-0 0 0 0 0 0

28 28 28 28 28 28

19.5 19.2 18.8 18.5 18.1 17.7

10 11 12 13 14 15

37 37 37 37 37 37

14 12 11 09 08 06

26.9 47.3 10.1 35.3 03.1 33.3

-0 0 0 0 0 0

27 27 27 27 27 27

37.7 36.2 34.7 33.2 31.7 30.2

42 40 37 35 32 30

40.0 11.7 43.5 15.3 47.4 19.7

-0 0 0 0 0 0

28 28 28 28 28 28

17.2 16.7 16.2 15.7 15.1 14.5

16 17 18 19 20 21

37 37 37 37 36 36

05 03 02 00 59 58

06.1 41.4 19.2 59.7 42.7 28.4

-0 0 0 0 0 0

27 27 27 27 27 27

28.7 27.1 25.5 23.9 22.3 20.7

38 38 38 38 38 38

27 25 22 20 18 15

52.3 25.2 58.4 32.1 06.2 40.9

-0 0 0 0 0 0

28 28 28 28 28 28

13.9 13.3 12.6 11.9 11.2 10.4

22 23 24 25 26 27

36 36 36 36 36 36

57 56 55 53 52 52

16.8 07.9 01.9 58.7 58.3 00.9

-0 0 0 0 0 0

27 27 27 27 27 27

19.1 17.4 15.7 14.1 12.4 10.7

38 38 38 38 38

13 10 08 06 03

16.2 52.2 29.0 06.8 45.6

-0 0 0 0 -0

28 28 28 28 28

09.6 08.8 08.0 07.1 06.3

28 29 30 31 32

36 36 36 36 36

51 50 49 48 47

06.3 14.7 26.1 40.4 57.6

-0 0 0 0 -0

27 27 27 27 27

09.0 07.2 05.5 03.7 02.0

Nov.

Dec.

174

URANUS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Jan. 0 1 2 3 4 5

h 2 2 2 2 2 2

m 02 02 02 02 02 02

s º 42.11 +11 39.96 11 38.00 11 36.23 11 34.67 11 33.30 11

' 56 56 56 56 56 56

" 40.5 31.0 22.5 15.1 08.8 03.5

19.402 930 19.418 725 19.434 636 19.450 658 19.466 787 19.483 016

" 0.45 0.45 0.45 0.45 0.45 0.45

" 1.80 1.80 1.80 1.80 1.80 1.80

h 19 19 19 19 19 19

m 22 19 15 11 07 03

s 58 00 02 05 07 10

6 7 8 9 10 11

2 2 2 2 2 2

02 02 02 02 02 02

32.13 +11 31.17 11 30.40 11 29.84 11 29.48 11 29.32 11

55 55 55 55 55 55

59.3 56.1 54.1 53.2 53.3 54.5

19.499 341 19.515 755 19.532 255 19.548 834 19.565 489 19.582 213

0.45 0.45 0.45 0.45 0.45 0.45

1.80 1.79 1.79 1.79 1.79 1.79

18 18 18 18 18 18

59 55 51 47 43 39

13 16 20 24 28 32

12 13 14 15 16 17

2 2 2 2 2 2

02 02 02 02 02 02

29.36 +11 29.60 11 30.03 11 30.66 11 31.49 11 32.52 11

55 56 56 56 56 56

56.8 00.2 04.6 10.1 16.6 24.2

19.599 002 19.615 851 19.632 755 19.649 709 19.666 708 19.683 748

0.45 0.45 0.45 0.45 0.45 0.45

1.79 1.79 1.78 1.78 1.78 1.78

18 18 18 18 18 18

35 31 27 23 19 16

36 40 45 50 55 00

18 19 20 21 22 23

2 2 2 2 2 2

02 02 02 02 02 02

33.75 +11 35.19 11 36.83 11 38.68 11 40.73 11 42.98 11

56 56 56 57 57 57

32.9 42.6 53.4 05.4 18.4 32.5

19.700 823 19.717 927 19.735 055 19.752 203 19.769 363 19.786 531

0.45 0.45 0.45 0.45 0.44 0.44

1.78 1.78 1.77 1.77 1.77 1.77

18 18 18 18 17 17

12 08 04 00 56 52

06 11 17 23 30 36

24 25 26 27 28 29

2 2 2 2 2 2

02 02 02 02 02 03

45.43 +11 48.08 11 50.93 11 53.97 11 57.21 11 00.65 11

57 58 58 58 58 59

47.6 03.9 21.1 39.5 58.8 19.2

19.803 702 19.820 868 19.838 026 19.855 169 19.872 291 19.889 388

0.44 0.44 0.44 0.44 0.44 0.44

1.77 1.77 1.77 1.76 1.76 1.76

17 17 17 17 17 17

48 44 40 37 33 29

43 50 57 04 11 19

30 31 Feb. 1 2 3 4

2 2 2 2 2 2

03 03 03 03 03 03

04.28 +11 08.10 12 12.12 12 16.34 12 20.75 12 25.35 12

59 00 00 00 01 01

40.6 03.1 26.5 51.0 16.5 43.1

19.906 455 19.923 485 19.940 473 19.957 415 19.974 305 19.991 139

0.44 0.44 0.44 0.44 0.44 0.44

1.76 1.76 1.76 1.75 1.75 1.75

17 17 17 17 17 17

25 21 17 13 10 06

27 35 43 52 00 09

5 6 7 8 9 10

2 2 2 2 2 2

03 03 03 03 03 03

30.15 +12 35.13 12 40.31 12 45.66 12 51.20 12 56.91 12

02 02 03 03 04 04

10.6 39.1 08.7 39.2 10.6 43.0

20.007 912 20.024 618 20.041 254 20.057 814 20.074 295 20.090 692

0.44 0.44 0.44 0.44 0.44 0.44

1.75 1.75 1.75 1.75 1.74 1.74

17 16 16 16 16 16

02 58 54 50 46 43

18 27 37 46 56 06

11 12 13 14 15

2 2 2 2 2

04 04 04 04 04

02.80 +12 08.87 12 15.12 12 21.54 12 28.14 +12

05 05 06 07 07

16.3 50.5 25.6 01.7 38.6

20.107 001 20.123 217 20.139 336 20.155 355 20.171 267

0.44 0.44 0.44 0.44 0.44

1.74 1.74 1.74 1.74 1.74

16 16 16 16 16

39 35 31 27 23

16 26 36 47 58

175

URANUS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Feb. 15 16 17 18 19 20

h 2 2 2 2 2 2

m 04 04 04 04 04 05

s º 28.14 +12 34.92 12 41.88 12 49.01 12 56.31 12 03.77 12

' 07 08 08 09 10 10

" 38.6 16.4 55.2 34.8 15.4 56.8

20.171 267 20.187 069 20.202 757 20.218 324 20.233 768 20.249 083

" 0.44 0.44 0.44 0.43 0.43 0.43

" 1.74 1.73 1.73 1.73 1.73 1.73

h 16 16 16 16 16 16

m 23 20 16 12 08 04

s 58 09 20 31 43 54

21 22 23 24 25 26

2 2 2 2 2 2

05 05 05 05 05 05

11.40 +12 19.20 12 27.15 12 35.26 12 43.52 12 51.94 12

11 12 13 13 14 15

39.0 22.1 06.0 50.7 36.2 22.4

20.264 264 20.279 308 20.294 209 20.308 963 20.323 566 20.338 014

0.43 0.43 0.43 0.43 0.43 0.43

1.73 1.73 1.73 1.72 1.72 1.72

16 15 15 15 15 15

01 57 53 49 45 42

06 18 30 42 55 07

27 28 29 Mar. 1 2 3

2 2 2 2 2 2

06 06 06 06 06 06

00.52 +12 09.25 12 18.13 12 27.16 12 36.33 12 45.66 12

16 16 17 18 19 20

09.4 57.2 45.8 35.1 25.1 15.8

20.352 303 20.366 428 20.380 386 20.394 173 20.407 786 20.421 220

0.43 0.43 0.43 0.43 0.43 0.43

1.72 1.72 1.72 1.72 1.72 1.71

15 15 15 15 15 15

38 34 30 26 23 19

20 33 46 59 13 26

4 5 6 7 8 9

2 2 2 2 2 2

06 07 07 07 07 07

55.12 +12 04.72 12 14.46 12 24.33 12 34.33 12 44.45 12

21 21 22 23 24 25

07.3 59.5 52.3 45.8 39.9 34.6

20.434 473 20.447 541 20.460 422 20.473 111 20.485 607 20.497 906

0.43 0.43 0.43 0.43 0.43 0.43

1.71 1.71 1.71 1.71 1.71 1.71

15 15 15 15 15 14

15 11 08 04 00 56

40 53 07 21 35 49

10 11 12 13 14 15

2 2 2 2 2 2

07 08 08 08 08 08

54.69 +12 05.06 12 15.55 12 26.16 12 36.90 12 47.75 12

26 27 28 29 30 31

29.9 25.8 22.3 19.3 17.0 15.1

20.510 006 20.521 904 20.533 598 20.545 084 20.556 359 20.567 421

0.43 0.43 0.43 0.43 0.43 0.43

1.71 1.71 1.71 1.70 1.70 1.70

14 14 14 14 14 14

53 49 45 41 38 34

04 18 33 48 03 17

16 17 18 19 20 21

2 2 2 2 2 2

08 09 09 09 09 09

58.72 +12 09.80 12 20.99 12 32.29 12 43.69 12 55.18 12

32 33 34 35 36 37

13.9 13.2 13.0 13.3 14.0 15.3

20.578 267 20.588 893 20.599 297 20.609 476 20.619 427 20.629 147

0.43 0.43 0.43 0.43 0.43 0.43

1.70 1.70 1.70 1.70 1.70 1.70

14 14 14 14 14 14

30 26 23 19 15 11

33 48 03 18 34 49

22 23 24 25 26 27

2 2 2 2 2 2

10 10 10 10 10 11

06.77 +12 18.46 12 30.24 12 42.11 12 54.07 12 06.12 12

38 39 40 41 42 43

17.0 19.1 21.6 24.5 27.8 31.5

20.638 634 20.647 884 20.656 896 20.665 667 20.674 195 20.682 479

0.43 0.43 0.43 0.43 0.43 0.43

1.70 1.70 1.70 1.69 1.69 1.69

14 14 14 13 13 13

08 04 00 56 53 49

05 21 37 53 09 25

28 29 30 31 Apr. 1

2 2 2 2 2

11 11 11 11 12

18.25 +12 30.46 12 42.76 12 55.13 12 07.57 +12

44 45 46 47 48

35.6 40.0 44.8 49.9 55.3

20.690 514 20.698 301 20.705 838 20.713 122 20.720 152

0.43 0.42 0.42 0.42 0.42

1.69 1.69 1.69 1.69 1.69

13 13 13 13 13

45 41 38 34 30

41 57 14 30 47

176

URANUS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Apr. 1 2 3 4 5 6

h 2 2 2 2 2 2

m 12 12 12 12 12 13

s º 07.57 +12 20.09 12 32.66 12 45.30 12 58.00 12 10.75 12

' 48 50 51 52 53 54

" 55.3 01.1 07.1 13.3 19.8 26.5

20.720 152 20.726 927 20.733 445 20.739 707 20.745 710 20.751 454

" 0.42 0.42 0.42 0.42 0.42 0.42

" 1.69 1.69 1.69 1.69 1.69 1.69

h 13 13 13 13 13 13

m 30 27 23 19 15 12

s 47 03 20 37 53 10

7 8 9 10 11 12

2 2 2 2 2 2

13 13 13 14 14 14

23.56 +12 36.42 12 49.33 12 02.30 12 15.31 13 28.38 13

55 56 57 58 00 01

33.4 40.5 47.7 55.1 02.8 10.6

20.756 937 20.762 160 20.767 121 20.771 819 20.776 254 20.780 424

0.42 0.42 0.42 0.42 0.42 0.42

1.69 1.69 1.69 1.69 1.69 1.69

13 13 13 12 12 12

08 04 01 57 53 49

27 44 01 18 35 52

13 14 15 16 17 18

2 2 2 2 2 2

14 14 15 15 15 15

41.48 +13 54.63 13 07.81 13 21.02 13 34.26 13 47.53 13

02 03 04 05 06 07

18.5 26.6 34.8 43.1 51.5 59.9

20.784 327 20.787 964 20.791 332 20.794 432 20.797 261 20.799 819

0.42 0.42 0.42 0.42 0.42 0.42

1.68 1.68 1.68 1.68 1.68 1.68

12 12 12 12 12 12

46 42 38 35 31 27

09 26 44 01 18 35

19 20 21 22 23 24

2 2 2 2 2 2

16 16 16 16 16 17

00.82 +13 14.13 13 27.46 13 40.81 13 54.18 13 07.56 13

09 10 11 12 13 14

08.3 16.8 25.3 33.9 42.4 50.9

20.802 106 20.804 121 20.805 862 20.807 331 20.808 527 20.809 449

0.42 0.42 0.42 0.42 0.42 0.42

1.68 1.68 1.68 1.68 1.68 1.68

12 12 12 12 12 12

23 20 16 12 09 05

53 10 28 45 02 20

25 26 27 28 29 30

2 2 2 2 2 2

17 17 17 18 18 18

20.96 +13 34.38 13 47.72 13 01.14 13 14.55 13 27.95 13

15 17 18 19 20 21

59.3 07.3 15.6 24.3 32.7 40.9

20.810 097 20.810 472 20.810 574 20.810 402 20.809 959 20.809 243

0.42 0.42 0.42 0.42 0.42 0.42

1.68 1.68 1.68 1.68 1.68 1.68

12 11 11 11 11 11

01 57 54 50 46 43

37 55 12 29 47 04

May 1 2 3 4 5 6

2 2 2 2 2 2

18 18 19 19 19 19

41.34 +13 54.72 13 08.08 13 21.42 13 34.74 13 48.05 13

22 23 25 26 27 28

48.9 56.8 04.6 12.1 19.5 26.7

20.808 256 20.806 999 20.805 472 20.803 677 20.801 614 20.799 285

0.42 0.42 0.42 0.42 0.42 0.42

1.68 1.68 1.68 1.68 1.68 1.68

11 11 11 11 11 11

39 35 31 28 24 20

22 39 56 14 31 48

7 8 9 10 11 12

2 2 2 2 2 2

20 20 20 20 20 21

01.33 +13 14.59 13 27.83 13 41.05 13 54.23 13 07.37 13

29 30 31 32 33 35

33.7 40.5 47.1 53.5 59.7 05.6

20.796 690 20.793 830 20.790 706 20.787 319 20.783 669 20.779 756

0.42 0.42 0.42 0.42 0.42 0.42

1.68 1.68 1.68 1.68 1.68 1.69

11 11 11 11 11 10

17 13 09 05 02 58

06 23 40 57 15 32

13 14 15 16 17

2 2 2 2 2

21 21 21 21 22

20.48 +13 33.54 13 46.56 13 59.53 13 12.45 +13

36 37 38 39 40

11.3 16.7 21.8 26.6 31.0

20.775 583 20.771 148 20.766 454 20.761 502 20.756 291

0.42 0.42 0.42 0.42 0.42

1.69 1.69 1.69 1.69 1.69

10 10 10 10 10

54 51 47 43 39

49 06 23 40 57

177

URANUS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

May 17 18 19 20 21 22

h 2 2 2 2 2 2

m 22 22 22 22 23 23

s º 12.45 +13 25.32 13 38.14 13 50.91 13 03.62 13 16.27 13

' 40 41 42 43 44 45

" 31.0 35.1 38.9 42.4 45.4 48.1

20.756 291 20.750 824 20.745 102 20.739 127 20.732 898 20.726 419

" 0.42 0.42 0.42 0.42 0.42 0.42

" 1.69 1.69 1.69 1.69 1.69 1.69

h 10 10 10 10 10 10

m 39 36 32 28 25 21

s 57 14 31 47 04 21

23 24 25 26 27 28

2 2 2 2 2 2

23 23 23 24 24 24

28.86 +13 41.38 13 53.84 13 06.23 13 18.54 13 30.78 13

46 47 48 49 50 51

50.5 52.4 54.0 55.1 55.9 56.2

20.719 692 20.712 716 20.705 496 20.698 033 20.690 328 20.682 385

0.42 0.42 0.42 0.42 0.43 0.43

1.69 1.69 1.69 1.69 1.69 1.69

10 10 10 10 10 9

17 13 10 06 02 58

37 54 10 27 43 59

29 30 31 June 1 2 3

2 2 2 2 2 2

24 24 25 25 25 25

42.93 +13 55.00 13 06.98 13 18.87 13 30.68 13 42.40 13

52 53 54 55 56 57

56.0 55.3 54.1 52.5 50.3 47.6

20.674 206 20.665 793 20.657 149 20.648 276 20.639 178 20.629 855

0.43 0.43 0.43 0.43 0.43 0.43

1.69 1.69 1.70 1.70 1.70 1.70

9 9 9 9 9 9

55 51 47 44 40 36

15 31 47 03 19 35

4 5 6 7 8 9

2 2 2 2 2 2

25 26 26 26 26 26

54.03 +13 05.57 13 17.01 14 28.36 14 39.61 14 50.75 14

58 59 00 01 02 03

44.3 40.6 36.4 31.6 26.3 20.5

20.620 311 20.610 549 20.600 569 20.590 376 20.579 970 20.569 355

0.43 0.43 0.43 0.43 0.43 0.43

1.70 1.70 1.70 1.70 1.70 1.70

9 9 9 9 9 9

32 29 25 21 17 14

50 06 21 37 52 07

10 11 12 13 14 15

2 2 2 2 2 2

27 27 27 27 27 27

01.79 +14 12.71 14 23.52 14 34.22 14 44.80 14 55.27 14

04 05 05 06 07 08

14.0 07.0 59.4 51.1 42.3 32.8

20.558 532 20.547 504 20.536 273 20.524 842 20.513 213 20.501 389

0.43 0.43 0.43 0.43 0.43 0.43

1.70 1.70 1.71 1.71 1.71 1.71

9 9 9 8 8 8

10 06 02 59 55 51

22 37 52 06 21 35

16 17 18 19 20 21

2 2 2 2 2 2

28 28 28 28 28 28

05.62 +14 15.85 14 25.95 14 35.94 14 45.80 14 55.53 14

09 10 11 11 12 13

22.6 11.8 00.4 48.4 35.6 22.3

20.489 373 20.477 167 20.464 776 20.452 201 20.439 446 20.426 514

0.43 0.43 0.43 0.43 0.43 0.43

1.71 1.71 1.71 1.71 1.71 1.71

8 8 8 8 8 8

47 44 40 36 32 28

50 04 18 32 46 60

22 23 24 25 26 27

2 2 2 2 2 2

29 29 29 29 29 29

05.13 +14 14.59 14 23.91 14 33.10 14 42.14 14 51.03 14

14 14 15 16 17 17

08.2 53.5 38.0 21.8 04.9 47.3

20.413 410 20.400 135 20.386 695 20.373 092 20.359 331 20.345 415

0.43 0.43 0.43 0.43 0.43 0.43

1.72 1.72 1.72 1.72 1.72 1.72

8 8 8 8 8 8

25 21 17 13 10 06

13 27 40 53 06 19

28 29 30 July 1 2

2 2 2 2 2

29 30 30 30 30

59.77 +14 08.37 14 16.82 14 25.13 14 33.29 +14

18 19 19 20 21

28.8 09.7 49.7 29.0 07.5

20.331 349 20.317 136 20.302 779 20.288 284 20.273 653

0.43 0.43 0.43 0.43 0.43

1.72 1.72 1.72 1.73 1.73

8 7 7 7 7

02 58 54 51 47

32 44 57 09 21

178

URANUS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

July 1 2 3 4 5 6

h 2 2 2 2 2 2

m 30 30 30 30 30 31

s º 25.13 +14 33.29 14 41.30 14 49.16 14 56.86 14 04.41 14

' 20 21 21 22 22 23

" 29.0 07.5 45.3 22.4 58.7 34.2

20.288 284 20.273 653 20.258 889 20.243 997 20.228 981 20.213 842

" 0.43 0.43 0.43 0.43 0.43 0.44

" 1.73 1.73 1.73 1.73 1.73 1.73

h 7 7 7 7 7 7

m 51 47 43 39 35 32

s 09 21 33 45 57 08

7 8 9 10 11 12

2 2 2 2 2 2

31 31 31 31 31 31

11.79 +14 19.01 14 26.06 14 32.95 14 39.67 14 46.22 14

24 24 25 25 26 26

08.9 42.8 15.8 48.1 19.5 50.1

20.198 586 20.183 215 20.167 734 20.152 145 20.136 452 20.120 660

0.44 0.44 0.44 0.44 0.44 0.44

1.73 1.74 1.74 1.74 1.74 1.74

7 7 7 7 7 7

28 24 20 16 13 09

20 31 42 53 04 14

13 14 15 16 17 18

2 2 2 2 2 2

31 31 32 32 32 32

52.61 +14 58.82 14 04.87 14 10.74 14 16.45 14 21.97 14

27 27 28 28 29 29

19.8 48.7 16.7 44.0 10.3 35.8

20.104 772 20.088 792 20.072 724 20.056 573 20.040 342 20.024 036

0.44 0.44 0.44 0.44 0.44 0.44

1.74 1.74 1.74 1.75 1.75 1.75

7 7 6 6 6 6

05 01 57 53 50 46

25 35 45 55 04 14

19 20 21 22 23 24

2 2 2 2 2 2

32 32 32 32 32 32

27.33 +14 32.50 14 37.49 14 42.29 14 46.91 14 51.34 14

30 30 30 31 31 31

00.5 24.3 47.3 09.3 30.5 50.7

20.007 660 19.991 218 19.974 714 19.958 154 19.941 542 19.924 883

0.44 0.44 0.44 0.44 0.44 0.44

1.75 1.75 1.75 1.75 1.76 1.76

6 6 6 6 6 6

42 38 34 30 26 23

23 33 42 50 59 07

25 26 27 28 29 30

2 2 2 2 2 2

32 32 33 33 33 33

55.58 +14 59.64 14 03.51 14 07.20 14 10.70 14 14.02 14

32 32 32 33 33 33

10.0 28.4 45.9 02.4 18.1 32.9

19.908 181 19.891 443 19.874 671 19.857 872 19.841 050 19.824 208

0.44 0.44 0.44 0.44 0.44 0.44

1.76 1.76 1.76 1.76 1.77 1.77

6 6 6 6 6 5

19 15 11 07 03 59

16 24 32 39 47 54

31 Aug. 1 2 3 4 5

2 2 2 2 2 2

33 33 33 33 33 33

17.15 +14 20.09 14 22.84 14 25.40 14 27.76 14 29.93 14

33 33 34 34 34 34

46.8 59.8 11.9 23.1 33.4 42.8

19.807 352 19.790 486 19.773 613 19.756 739 19.739 868 19.723 004

0.44 0.44 0.44 0.45 0.45 0.45

1.77 1.77 1.77 1.77 1.77 1.78

5 5 5 5 5 5

56 52 48 44 40 36

01 08 15 22 28 34

6 7 8 9 10 11

2 2 2 2 2 2

33 33 33 33 33 33

31.90 +14 33.68 14 35.27 14 36.66 14 37.86 14 38.86 14

34 34 35 35 35 35

51.2 58.7 05.2 10.8 15.5 19.3

19.706 151 19.689 313 19.672 496 19.655 703 19.638 939 19.622 209

0.45 0.45 0.45 0.45 0.45 0.45

1.78 1.78 1.78 1.78 1.78 1.78

5 5 5 5 5 5

32 28 24 20 17 13

40 46 52 57 02 08

12 13 14 15 16

2 2 2 2 2

33 33 33 33 33

39.68 +14 40.30 14 40.73 14 40.96 14 41.00 +14

35 35 35 35 35

22.1 24.1 25.1 25.2 24.4

19.605 518 19.588 870 19.572 270 19.555 722 19.539 233

0.45 0.45 0.45 0.45 0.45

1.79 1.79 1.79 1.79 1.79

5 5 5 4 4

09 05 01 57 53

12 17 22 26 30

179

URANUS, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Aug. 16 17 18 19 20 21

h 2 2 2 2 2 2

m 33 33 33 33 33 33

s º 41.00 +14 40.85 14 40.49 14 39.94 14 39.19 14 38.24 14

' 35 35 35 35 35 35

" 24.4 22.7 20.1 16.5 12.0 06.5

19.539 233 19.522 807 19.506 449 19.490 163 19.473 957 19.457 834

" 0.45 0.45 0.45 0.45 0.45 0.45

" 1.79 1.79 1.80 1.80 1.80 1.80

h 4 4 4 4 4 4

m 53 49 45 41 37 33

s 30 34 37 41 44 47

22 23 24 25 26 27

2 2 2 2 2 2

33 33 33 33 33 33

37.09 +14 35.76 14 34.23 14 32.51 14 30.61 14 28.52 14

35 34 34 34 34 34

00.1 52.8 44.5 35.4 25.4 14.5

19.441 799 19.425 858 19.410 016 19.394 277 19.378 647 19.363 128

0.45 0.45 0.45 0.45 0.45 0.45

1.80 1.80 1.80 1.81 1.81 1.81

4 4 4 4 4 4

29 25 21 17 14 10

50 53 56 58 00 02

28 29 30 31 Sept. 1 2

2 2 2 2 2 2

33 33 33 33 33 33

26.25 +14 23.79 14 21.13 14 18.30 14 15.27 14 12.06 14

34 33 33 33 33 32

02.7 50.0 36.5 22.1 06.8 50.7

19.347 727 19.332 447 19.317 293 19.302 268 19.287 378 19.272 625

0.45 0.45 0.46 0.46 0.46 0.46

1.81 1.81 1.81 1.81 1.82 1.82

4 4 3 3 3 3

06 02 58 54 50 46

04 05 07 08 09 10

3 4 5 6 7 8

2 2 2 2 2 2

33 33 33 32 32 32

08.66 +14 05.08 14 01.33 14 57.39 14 53.28 14 49.00 14

32 32 31 31 31 30

33.6 15.7 57.0 37.3 16.9 55.6

19.258 016 19.243 553 19.229 241 19.215 085 19.201 088 19.187 256

0.46 0.46 0.46 0.46 0.46 0.46

1.82 1.82 1.82 1.82 1.82 1.83

3 3 3 3 3 3

42 38 34 30 26 22

11 11 12 12 12 12

9 10 11 12 13 14

2 2 2 2 2 2

32 32 32 32 32 32

44.55 +14 39.92 14 35.13 14 30.17 14 25.04 14 19.75 14

30 30 29 29 28 28

33.6 10.7 47.0 22.5 57.3 31.3

19.173 592 19.160 100 19.146 786 19.133 654 19.120 708 19.107 953

0.46 0.46 0.46 0.46 0.46 0.46

1.83 1.83 1.83 1.83 1.83 1.83

3 3 3 3 3 2

18 14 10 06 02 58

11 11 10 09 08 07

15 16 17 18 19 20

2 2 2 2 2 2

32 32 32 31 31 31

14.29 +14 08.66 14 02.87 14 56.92 14 50.82 14 44.57 14

28 27 27 26 26 25

04.5 36.9 08.6 39.4 09.5 38.9

19.095 392 19.083 032 19.070 875 19.058 927 19.047 192 19.035 674

0.46 0.46 0.46 0.46 0.46 0.46

1.83 1.84 1.84 1.84 1.84 1.84

2 2 2 2 2 2

54 50 46 42 37 33

06 04 02 00 59 56

21 22 23 24 25 26

2 2 2 2 2 2

31 31 31 31 31 31

38.17 +14 31.63 14 24.95 14 18.13 14 11.18 14 04.09 14

25 24 24 23 22 22

07.6 35.6 02.9 29.6 55.7 21.1

19.024 377 19.013 305 19.002 461 18.991 849 18.981 471 18.971 332

0.46 0.46 0.46 0.46 0.46 0.46

1.84 1.84 1.84 1.84 1.84 1.85

2 2 2 2 2 2

29 25 21 17 13 09

54 52 49 46 44 41

27 28 29 30 Oct. 1

2 2 2 2 2

30 30 30 30 30

56.86 +14 49.50 14 42.02 14 34.41 14 26.68 +14

21 21 20 19 19

45.9 10.1 33.6 56.6 18.9

18.961 433 18.951 779 18.942 373 18.933 216 18.924 313

0.46 0.46 0.46 0.46 0.46

1.85 1.85 1.85 1.85 1.85

2 2 1 1 1

05 01 57 53 49

37 34 31 27 24

180

URANUS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Oct. 1 2 3 4 5 6

h 2 2 2 2 2 2

m 30 30 30 30 29 29

s º 26.68 +14 18.83 14 10.87 14 02.80 14 54.62 14 46.35 14

' 19 18 18 17 16 16

" 18.9 40.7 02.0 22.7 42.9 02.6

18.924 313 18.915 665 18.907 276 18.899 149 18.891 287 18.883 692

" 0.46 0.46 0.47 0.47 0.47 0.47

" 1.85 1.85 1.85 1.85 1.85 1.85

h 1 1 1 1 1 1

m 49 45 41 37 33 29

s 24 20 16 12 08 04

7 8 9 10 11 12

2 2 2 2 2 2

29 29 29 29 29 28

37.97 +14 29.50 14 20.93 14 12.28 14 03.54 14 54.71 14

15 14 13 13 12 11

21.8 40.6 58.9 16.9 34.4 51.5

18.876 367 18.869 314 18.862 538 18.856 039 18.849 821 18.843 887

0.47 0.47 0.47 0.47 0.47 0.47

1.86 1.86 1.86 1.86 1.86 1.86

1 1 1 1 1 1

24 20 16 12 08 04

60 56 51 47 42 37

13 14 15 16 17 18

2 2 2 2 2 2

28 28 28 28 28 28

45.79 +14 36.80 14 27.73 14 18.59 14 09.39 14 00.13 14

11 10 09 08 08 07

08.1 24.5 40.4 55.9 11.2 26.1

18.838 239 18.832 880 18.827 812 18.823 037 18.818 558 18.814 376

0.47 0.47 0.47 0.47 0.47 0.47

1.86 1.86 1.86 1.86 1.86 1.86

1 0 0 0 0 0

00 56 52 48 44 40

32 28 23 18 13 08

19 20 21 22 23 24

2 2 2 2 2 2

27 27 27 27 27 27

50.82 +14 41.47 14 32.07 14 22.62 14 13.14 14 03.61 14

06 05 05 04 03 02

40.8 55.3 09.5 23.6 37.5 51.2

18.810 494 18.806 911 18.803 631 18.800 654 18.797 980 18.795 610

0.47 0.47 0.47 0.47 0.47 0.47

1.86 1.86 1.86 1.86 1.86 1.86

0 0 0 0 0 0

36 31 27 23 19 15

02 57 52 47 41 36

25 26 27 28 29 30

2 2 2 2 2 2

26 26 26 26 26 26

54.06 +14 44.47 14 34.86 14 25.23 13 15.58 13 05.93 13

02 01 00 59 58 58

04.7 18.2 31.4 44.6 57.7 10.7

18.793 546 18.791 787 18.790 334 18.789 188 18.788 348 18.787 816

0.47 0.47 0.47 0.47 0.47 0.47

1.86 1.86 1.86 1.86 1.86 1.86

0 0 0 23 23 23

11 07 03 55 51 46

30 25 20 09 03 58

31 Nov. 1 2 3 4 5

2 2 2 2 2 2

25 25 25 25 25 25

56.27 +13 46.60 13 36.95 13 27.30 13 17.66 13 08.04 13

57 56 55 55 54 53

23.7 36.7 49.7 02.8 15.9 29.1

18.787 591 18.787 675 18.788 065 18.788 764 18.789 771 18.791 087

0.47 0.47 0.47 0.47 0.47 0.47

1.86 1.86 1.86 1.86 1.86 1.86

23 23 23 23 23 23

42 38 34 30 26 22

52 47 41 36 30 25

6 7 8 9 10 11

2 2 2 2 2 2

24 24 24 24 24 24

58.44 +13 48.86 13 39.30 13 29.77 13 20.27 13 10.80 13

52 51 51 50 49 48

42.4 55.8 09.3 23.0 36.9 50.9

18.792 710 18.794 641 18.796 879 18.799 426 18.802 279 18.805 439

0.47 0.47 0.47 0.47 0.47 0.47

1.86 1.86 1.86 1.86 1.86 1.86

23 23 23 23 23 22

18 14 10 06 01 57

19 14 08 03 58 52

12 13 14 15 16

2 2 2 2 2

24 23 23 23 23

01.38 +13 52.01 13 42.69 13 33.43 13 24.23 +13

48 47 46 45 45

05.1 19.5 34.1 49.1 04.3

18.808 906 18.812 678 18.816 755 18.821 135 18.825 817

0.47 0.47 0.47 0.47 0.47

1.86 1.86 1.86 1.86 1.86

22 22 22 22 22

53 49 45 41 37

47 42 37 32 27

181

URANUS, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Nov. 16 17 18 19 20 21

h 2 2 2 2 2 2

m 23 23 23 22 22 22

s º 24.23 +13 15.10 13 06.05 13 57.06 13 48.15 13 39.32 13

' 45 44 43 42 42 41

" 04.3 20.0 35.9 52.3 09.1 26.2

18.825 817 18.830 800 18.836 082 18.841 660 18.847 532 18.853 696

" 0.47 0.47 0.47 0.47 0.47 0.47

" 1.86 1.86 1.86 1.86 1.86 1.86

h 22 22 22 22 22 22

m 37 33 29 25 21 17

s 27 22 17 12 08 03

22 23 24 25 26 27

2 2 2 2 2 2

22 22 22 22 21 21

30.57 +13 21.90 13 13.33 13 04.85 13 56.47 13 48.20 13

40 40 39 38 37 37

43.8 01.7 20.2 39.1 58.5 18.4

18.860 150 18.866 892 18.873 918 18.881 226 18.888 814 18.896 679

0.47 0.47 0.47 0.47 0.47 0.47

1.86 1.86 1.86 1.85 1.85 1.85

22 22 22 22 21 21

12 08 04 00 56 52

58 54 50 45 41 37

28 29 30 Dec. 1 2 3

2 2 2 2 2 2

21 21 21 21 21 21

40.03 +13 31.98 13 24.04 13 16.22 13 08.53 13 00.95 13

36 35 35 34 34 33

38.8 59.9 21.5 43.7 06.5 29.9

18.904 818 18.913 229 18.921 908 18.930 854 18.940 063 18.949 532

0.47 0.46 0.46 0.46 0.46 0.46

1.85 1.85 1.85 1.85 1.85 1.85

21 21 21 21 21 21

48 44 40 36 32 28

33 29 26 22 19 15

4 5 6 7 8 9

2 2 2 2 2 2

20 20 20 20 20 20

53.51 +13 46.19 13 39.00 13 31.94 13 25.02 13 18.23 13

32 32 31 31 30 30

54.1 18.8 44.2 10.3 37.1 04.6

18.959 259 18.969 240 18.979 473 18.989 954 19.000 680 19.011 648

0.46 0.46 0.46 0.46 0.46 0.46

1.85 1.85 1.85 1.84 1.84 1.84

21 21 21 21 21 21

24 20 16 12 08 03

12 09 06 03 01 58

10 11 12 13 14 15

2 2 2 2 2 2

20 20 19 19 19 19

11.60 +13 05.11 13 58.78 13 52.60 13 46.59 13 40.74 13

29 29 28 28 27 27

32.8 01.7 31.4 01.9 33.2 05.4

19.022 856 19.034 298 19.045 972 19.057 873 19.069 998 19.082 342

0.46 0.46 0.46 0.46 0.46 0.46

1.84 1.84 1.84 1.84 1.84 1.84

20 20 20 20 20 20

59 55 51 47 43 39

56 54 51 50 48 46

16 17 18 19 20 21

2 2 2 2 2 2

19 19 19 19 19 19

35.05 +13 29.53 13 24.17 13 18.98 13 13.96 13 09.11 13

26 26 25 25 24 24

38.4 12.2 46.9 22.5 58.9 36.2

19.094 901 19.107 669 19.120 643 19.133 818 19.147 189 19.160 751

0.46 0.46 0.46 0.46 0.46 0.46

1.83 1.83 1.83 1.83 1.83 1.83

20 20 20 20 20 20

35 31 27 23 19 15

45 43 42 41 41 40

22 23 24 25 26 27

2 2 2 2 2 2

19 18 18 18 18 18

04.44 +13 59.94 13 55.62 13 51.49 13 47.55 13 43.79 13

24 23 23 23 22 22

14.4 53.4 33.4 14.3 56.2 39.0

19.174 498 19.188 428 19.202 534 19.216 812 19.231 258 19.245 865

0.46 0.46 0.46 0.46 0.46 0.46

1.83 1.83 1.82 1.82 1.82 1.82

20 20 20 19 19 19

11 07 03 59 55 51

40 39 39 40 40 40

28 29 30 31 32

2 2 2 2 2

18 18 18 18 18

40.22 +13 36.84 13 33.65 13 30.65 13 27.84 +13

22 22 21 21 21

22.7 07.5 53.2 39.9 27.6

19.260 631 19.275 549 19.290 616 19.305 826 19.321 175

0.46 0.46 0.46 0.46 0.46

1.82 1.82 1.82 1.81 1.81

19 19 19 19 19

47 43 39 35 31

41 42 43 44 46

182

NEPTUNE, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 347 348 348 348 348 348

' 59 00 01 01 02 03

" º ' " 44.9 -1 02 22.4 28.7 1 02 23.5 12.5 1 02 24.5 56.3 1 02 25.6 40.1 1 02 26.7 23.9 1 02 27.8

º 29.932 92 Apr. 2 348 29.932 89 4 348 29.932 86 6 348 29.932 83 8 348 29.932 80 10 348 29.932 76 12 348

' 33 34 34 35 36 36

" º ' " 19.5 -1 03 12.2 03.3 1 03 13.3 47.1 1 03 14.4 30.9 1 03 15.4 14.7 1 03 16.5 58.5 1 03 17.6

29.931 46 29.931 43 29.931 40 29.931 36 29.931 33 29.931 30

13 15 17 19 21 23

348 348 348 348 348 348

04 04 05 06 07 07

07.7 -1 02 28.9 51.4 1 02 30.0 35.2 1 02 31.1 19.0 1 02 32.2 02.8 1 02 33.2 46.6 1 02 34.3

29.932 73 29.932 70 29.932 67 29.932 64 29.932 61 29.932 57

37 38 39 39 40 41

42.3 -1 03 18.7 26.1 1 03 19.8 09.9 1 03 20.8 53.7 1 03 21.9 37.5 1 03 23.0 21.3 1 03 24.1

29.931 27 29.931 24 29.931 20 29.931 17 29.931 14 29.931 11

25 27 29 31 Feb. 2 4

348 348 348 348 348 348

08 09 09 10 11 12

30.4 -1 02 35.4 14.2 1 02 36.5 58.0 1 02 37.6 41.7 1 02 38.7 25.5 1 02 39.8 09.3 1 02 40.8

29.932 54 26 348 42 05.2 -1 03 25.1 29.932 51 28 348 42 49.0 1 03 26.2 29.932 48 30 348 43 32.8 1 03 27.3 29.932 45 May 2 348 44 16.6 1 03 28.4 29.932 41 4 348 45 00.4 1 03 29.4 29.932 38 6 348 45 44.2 1 03 30.5

29.931 08 29.931 04 29.931 01 29.930 98 29.930 95 29.930 92

6 8 10 12 14 16

348 348 348 348 348 348

12 13 14 15 15 16

53.1 -1 02 41.9 36.9 1 02 43.0 20.7 1 02 44.1 04.5 1 02 45.2 48.3 1 02 46.3 32.1 1 02 47.3

29.932 35 29.932 32 29.932 29 29.932 26 29.932 22 29.932 19

8 10 12 14 16 18

348 348 348 348 348 348

46 47 47 48 49 50

28.0 -1 03 31.6 11.8 1 03 32.7 55.6 1 03 33.7 39.4 1 03 34.8 23.2 1 03 35.9 07.1 1 03 37.0

29.930 88 29.930 85 29.930 82 29.930 79 29.930 76 29.930 73

18 20 22 24 26 28

348 348 348 348 348 348

17 17 18 19 20 20

15.9 -1 02 48.4 59.7 1 02 49.5 43.5 1 02 50.6 27.3 1 02 51.7 11.1 1 02 52.7 54.9 1 02 53.8

29.932 16 29.932 13 29.932 10 29.932 06 29.932 03 29.932 00

20 22 24 26 28 30

348 348 348 348 348 348

50 51 52 53 53 54

50.9 -1 03 38.1 34.7 1 03 39.1 18.5 1 03 40.2 02.3 1 03 41.3 46.1 1 03 42.4 29.9 1 03 43.4

29.930 69 29.930 66 29.930 63 29.930 60 29.930 57 29.930 53

1 3 5 7 9 11

348 348 348 348 348 348

21 22 23 23 24 25

38.7 -1 02 54.9 22.5 1 02 56.0 06.3 1 02 57.1 50.1 1 02 58.2 33.9 1 02 59.2 17.7 1 03 00.3

29.931 97 June 1 29.931 94 3 29.931 91 5 29.931 87 7 29.931 84 9 29.931 81 11

348 348 348 348 348 348

55 55 56 57 58 58

13.7 -1 03 44.5 57.6 1 03 45.6 41.4 1 03 46.6 25.2 1 03 47.7 09.0 1 03 48.8 52.8 1 03 49.9

29.930 50 29.930 47 29.930 44 29.930 40 29.930 37 29.930 34

13 15 17 19 21 23

348 348 348 348 348 348

26 26 27 28 28 29

01.5 -1 03 01.4 45.3 1 03 02.5 29.1 1 03 03.5 12.9 1 03 04.6 56.7 1 03 05.7 40.5 1 03 06.8

29.931 78 29.931 75 29.931 71 29.931 68 29.931 65 29.931 62

348 349 349 349 349 349

59 00 01 01 02 03

36.6 -1 03 51.0 20.5 1 03 52.0 04.3 1 03 53.1 48.1 1 03 54.2 31.9 1 03 55.2 15.7 1 03 56.3

29.930 31 29.930 28 29.930 24 29.930 21 29.930 18 29.930 15

25 27 29 31 Apr. 2

348 348 348 348 348

30 31 31 32 33

24.3 -1 03 07.9 08.1 1 03 09.0 51.9 1 03 10.1 35.7 1 03 11.1 19.5 -1 03 12.2

29.931 59 25 349 03 59.6 -1 29.931 55 27 349 04 43.4 1 29.931 52 29 349 05 27.2 1 29.931 49 July 1 349 06 11.0 1 29.931 46 3 349 06 54.8 -1

Jan.

Mar.

14 16 18 20 22 24

13 15 17 19 21 23

348 348 348 348 348 348

03 03 03 04 04

57.4 58.5 59.5 00.6 01.7

29.930 12 29.930 08 29.930 05 29.930 02 29.929 99

183

NEPTUNE, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 3 5 7 9 11

º 349 349 349 349 349 349

' 06 06 07 08 09 09

" º ' " 11.0 -1 04 00.6 54.8 1 04 01.7 38.7 1 04 02.7 22.5 1 04 03.8 06.3 1 04 04.9 50.2 1 04 05.9

29.930 02 Oct. 1 29.929 99 3 29.929 95 5 29.929 92 7 29.929 89 9 29.929 86 11

º 349 349 349 349 349 349

' 39 40 41 41 42 43

" º ' " 47.2 -1 04 49.7 31.1 1 04 50.8 14.9 1 04 51.8 58.7 1 04 52.9 42.6 1 04 54.0 26.4 1 04 55.0

29.928 51 29.928 48 29.928 44 29.928 41 29.928 38 29.928 34

13 15 17 19 21 23

349 349 349 349 349 349

10 11 12 12 13 14

34.0 -1 04 07.0 17.8 1 04 08.1 01.6 1 04 09.2 45.4 1 04 10.2 29.3 1 04 11.3 13.1 1 04 12.4

29.929 83 29.929 79 29.929 76 29.929 73 29.929 70 29.929 66

13 15 17 19 21 23

349 349 349 349 349 349

44 44 45 46 47 47

10.2 -1 04 56.1 54.1 1 04 57.2 37.9 1 04 58.2 21.8 1 04 59.3 05.6 1 05 00.4 49.5 1 05 01.4

29.928 31 29.928 28 29.928 24 29.928 21 29.928 18 29.928 14

25 27 29 31 Aug. 2 4

349 349 349 349 349 349

14 15 16 17 17 18

56.9 -1 04 13.5 40.7 1 04 14.5 24.6 1 04 15.6 08.4 1 04 16.7 52.2 1 04 17.7 36.1 1 04 18.8

29.929 63 29.929 60 29.929 57 29.929 53 29.929 50 Nov. 29.929 47

25 27 29 31 2 4

349 349 349 349 349 349

48 49 50 50 51 52

33.3 -1 05 02.5 17.1 1 05 03.5 01.0 1 05 04.6 44.8 1 05 05.6 28.7 1 05 06.7 12.5 1 05 07.8

29.928 11 29.928 08 29.928 04 29.928 01 29.927 98 29.927 94

6 8 10 12 14 16

349 349 349 349 349 349

19 20 20 21 22 22

19.9 -1 04 19.9 03.7 1 04 20.9 47.5 1 04 22.0 31.4 1 04 23.1 15.2 1 04 24.1 59.0 1 04 25.2

29.929 43 29.929 40 29.929 37 29.929 34 29.929 30 29.929 27

6 8 10 12 14 16

349 349 349 349 349 349

52 53 54 55 55 56

56.4 -1 05 08.8 40.2 1 05 09.9 24.0 1 05 11.0 07.9 1 05 12.0 51.7 1 05 13.1 35.6 1 05 14.2

29.927 91 29.927 87 29.927 84 29.927 81 29.927 77 29.927 74

18 20 22 24 26 28

349 349 349 349 349 349

23 24 25 25 26 27

42.8 -1 04 26.3 26.7 1 04 27.3 10.5 1 04 28.4 54.4 1 04 29.5 38.2 1 04 30.5 22.0 1 04 31.6

29.929 24 29.929 21 29.929 17 29.929 14 29.929 11 29.929 07

18 20 22 24 26 28

349 349 349 349 350 350

57 58 58 59 00 00

19.4 -1 05 15.2 03.3 1 05 16.3 47.1 1 05 17.3 31.0 1 05 18.4 14.8 1 05 19.4 58.6 1 05 20.5

29.927 71 29.927 67 29.927 64 29.927 60 29.927 57 29.927 54

30 1 3 5 7 9

349 349 349 349 349 349

28 28 29 30 31 31

05.9 -1 04 32.7 49.7 1 04 33.7 33.5 1 04 34.8 17.4 1 04 35.9 01.2 1 04 36.9 45.0 1 04 38.0

29.929 04 30 29.929 01 Dec. 2 29.928 98 4 29.928 94 6 29.928 91 8 29.928 88 10

350 350 350 350 350 350

01 02 03 03 04 05

42.5 -1 05 21.6 26.3 1 05 22.6 10.2 1 05 23.7 54.1 1 05 24.7 37.9 1 05 25.8 21.7 1 05 26.8

29.927 50 29.927 47 29.927 44 29.927 40 29.927 37 29.927 33

11 13 15 17 19 21

349 349 349 349 349 349

32 33 33 34 35 36

28.9 -1 04 39.1 12.7 1 04 40.1 56.5 1 04 41.2 40.4 1 04 42.3 24.2 1 04 43.3 08.1 1 04 44.4

29.928 84 29.928 81 29.928 78 29.928 74 29.928 71 29.928 68

12 14 16 18 20 22

350 350 350 350 350 350

06 06 07 08 09 09

05.6 -1 05 27.9 49.4 1 05 29.0 33.3 1 05 30.0 17.1 1 05 31.1 01.0 1 05 32.1 44.8 1 05 33.2

29.927 30 29.927 27 29.927 23 29.927 20 29.927 16 29.927 13

23 25 27 29 1

349 349 349 349 349

36 37 38 39 39

51.9 -1 04 45.4 35.7 1 04 46.5 19.6 1 04 47.6 03.4 1 04 48.6 47.2 -1 04 49.7

29.928 64 29.928 61 29.928 58 29.928 54 29.928 51

24 26 28 30 32

350 350 350 350 350

10 11 11 12 13

28.7 -1 05 34.2 12.6 1 05 35.3 56.4 1 05 36.4 40.3 1 05 37.4 24.1 -1 05 38.5

29.927 10 29.927 06 29.927 03 29.926 99 29.926 96

July

Sept.

Oct.

184

NEPTUNE, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Jan.

Feb.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

0 1 2 3 4 5

º 346 346 346 346 346 346

' 14 15 17 18 19 20

" 43.7 52.1 02.4 14.4 28.2 43.9

º -1 1 1 1 1 1

' 01 01 01 01 01 01

" 36.9 35.5 34.1 32.7 31.3 30.0

6 7 8 9 10 11

346 346 346 346 346 346

22 23 24 26 27 28

01.3 20.5 41.5 04.2 28.6 54.6

-1 1 1 1 1 1

01 01 01 01 01 01

12 13 14 15 16 17

346 346 346 346 346 346

30 31 33 34 36 38

22.3 51.5 22.3 54.6 28.4 03.7

-1 1 1 1 1 1

18 19 20 21 22 23

346 346 346 346 346 346

39 41 42 44 46 48

40.6 19.0 59.0 40.4 23.3 07.5

24 25 26 27 28 29

346 346 346 346 346 346

49 51 53 55 57 59

30 31 1 2 3 4

347 347 347 347 347 347

5 6 7 8 9 10 11 12 13 14 15

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

15 16 17 18 19 20

º 347 347 347 347 347 347

' 33 35 37 39 42 44

" 23.0 32.1 41.9 52.4 03.6 15.3

º -1 1 1 1 1 1

' 00 00 00 00 00 00

" 55.2 54.9 54.7 54.5 54.4 54.3

28.6 27.3 26.0 24.8 23.5 22.3

21 22 23 24 25 26

347 347 347 347 347 347

46 48 50 53 55 57

27.6 40.3 53.5 07.1 21.2 35.6

-1 1 1 1 1 1

00 00 00 00 00 00

54.2 54.1 54.1 54.1 54.2 54.3

01 01 01 01 01 01

21.1 19.9 18.7 17.5 16.4 15.3

27 28 29 1 2 3

347 348 348 348 348 348

59 02 04 06 08 11

50.3 05.4 20.8 36.5 52.5 08.7

-1 1 1 1 1 1

00 00 00 00 00 00

54.4 54.5 54.7 54.9 55.2 55.4

-1 1 1 1 1 1

01 01 01 01 01 01

14.2 13.2 12.2 11.2 10.2 09.3

4 5 6 7 8 9

348 348 348 348 348 348

13 15 17 20 22 24

25.2 41.8 58.5 15.2 31.9 48.2

-1 1 1 1 1 1

00 00 00 00 00 00

55.8 56.1 56.5 57.0 57.7 58.2

53.2 40.1 28.4 17.8 08.5 00.4

-1 1 1 1 1 1

01 01 01 01 01 01

08.3 07.4 06.6 05.7 04.9 04.1

10 11 12 13 14 15

348 348 348 348 348 348

27 29 31 33 36 38

04.8 21.3 37.8 54.3 10.6 26.9

-1 1 1 1 1 1

00 00 00 01 01 01

58.5 59.0 59.5 00.1 00.8 01.5

00 02 04 06 08 10

53.5 47.7 43.1 39.6 37.3 36.0

-1 1 1 1 1 1

01 01 01 01 01 01

03.4 02.6 01.9 01.2 00.6 00.0

16 17 18 19 20 21

348 348 348 348 348 348

40 42 45 47 49 51

43.0 58.9 14.5 29.8 44.8 59.4

-1 1 1 1 1 1

01 01 01 01 01 01

02.2 02.9 03.7 04.6 05.4 06.3

347 347 347 347 347 347

12 14 16 18 20 22

35.8 36.7 38.5 41.2 44.8 49.2

-1 1 1 1 1 1

00 00 00 00 00 00

59.4 58.8 58.3 57.8 57.3 56.9

22 23 24 25 26 27

348 348 348 349 349 349

54 56 58 00 03 05

13.6 27.3 40.6 53.5 05.8 17.6

-1 1 1 1 1 1

01 01 01 01 01 01

07.2 08.2 09.2 10.2 11.3 12.3

347 347 347 347 347

24 27 29 31 33

54.4 00.3 07.1 14.7 23.0

-1 1 1 1 -1

00 00 00 00 00

56.5 56.1 55.7 55.4 55.2

28 29 30 31 1

349 349 349 349 349

07 09 11 13 16

28.9 39.6 49.7 59.3 08.1

-1 1 1 1 -1

01 01 01 01 01

13.5 14.6 15.8 17.0 18.3

Feb.

Mar.

Apr.

185

NEPTUNE, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Apr.

May

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 349 349 349 349 349 349

' 16 18 20 22 24 26

" 08.1 16.3 23.7 30.3 36.1 41.0

º -1 1 1 1 1 1

' 01 01 01 01 01 01

" 18.3 19.5 20.8 22.2 23.6 25.0

7 8 9 10 11 12

349 349 349 349 349 349

28 30 32 34 36 38

45.0 48.2 50.5 51.9 52.5 52.2

-1 1 1 1 1 1

01 01 01 01 01 01

13 14 15 16 17 18

349 349 349 349 349 349

40 42 44 46 48 50

50.8 48.5 45.2 40.7 35.1 28.3

-1 1 1 1 1 1

19 20 21 22 23 24

349 349 349 349 349 350

52 54 56 57 59 01

20.3 11.2 00.8 49.3 36.5 22.4

25 26 27 28 29 30

350 350 350 350 350 350

03 04 06 08 09 11

1 2 3 4 5 6

350 350 350 350 350 350

7 8 9 10 11 12 13 14 15 16 17

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

17 18 19 20 21 22

º 350 350 350 350 350 350

' 35 36 37 38 39 40

" 22.2 31.6 39.3 45.3 49.5 51.9

º -1 1 1 1 1 1

' 02 02 02 02 02 02

" 46.0 48.5 50.9 53.4 55.9 58.4

26.4 27.9 29.4 30.9 32.5 34.0

23 24 25 26 27 28

350 350 350 350 350 350

41 42 43 44 45 46

52.6 51.6 48.7 44.0 37.4 29.0

-1 1 1 1 1 1

03 03 03 03 03 03

00.9 03.4 06.0 08.5 11.1 13.7

01 01 01 01 01 01

35.7 37.3 39.0 40.7 42.4 44.2

29 30 31 1 2 3

350 350 350 350 350 350

47 48 48 49 50 50

18.6 06.4 52.2 36.0 18.0 58.2

-1 1 1 1 1 1

03 03 03 03 03 03

16.3 18.9 21.5 24.1 26.7 29.4

-1 1 1 1 1 1

01 01 01 01 01 01

46.0 47.8 49.7 51.5 53.4 55.3

4 5 6 7 8 9

350 350 350 350 350 350

51 52 52 53 53 54

36.4 12.9 47.4 20.1 50.9 19.7

-1 1 1 1 1 1

03 03 03 03 03 03

32.0 34.7 37.4 40.0 42.7 45.4

07.1 50.5 32.7 13.4 52.8 30.8

-1 1 1 1 1 1

01 01 02 02 02 02

57.3 59.3 01.3 03.3 05.3 07.4

10 11 12 13 14 15

350 350 350 350 350 350

54 55 55 55 56 56

46.5 11.3 34.2 55.0 13.9 30.8

-1 1 1 1 1 1

03 03 03 03 03 04

48.1 50.8 53.5 56.2 58.9 01.6

13 14 16 17 19 20

07.3 42.3 15.8 47.8 18.3 47.2

-1 1 1 1 1 1

02 02 02 02 02 02

09.5 11.6 13.8 15.9 18.1 20.3

16 17 18 19 20 21

350 350 350 350 350 350

56 56 57 57 57 57

45.7 58.8 09.8 19.0 26.2 31.5

-1 1 1 1 1 1

04 04 04 04 04 04

04.3 07.0 09.7 12.4 15.1 17.8

350 350 350 350 350 350

22 23 25 26 27 29

14.7 40.7 05.1 28.1 49.4 09.1

-1 1 1 1 1 1

02 02 02 02 02 02

22.6 24.8 27.1 29.4 31.7 34.0

22 23 24 25 26 27

350 350 350 350 350 350

57 57 57 57 57 57

34.8 36.2 35.6 33.0 28.3 21.7

-1 1 1 1 1 1

04 04 04 04 04 04

20.5 23.1 25.8 28.5 31.2 33.8

350 350 350 350 350

30 31 32 34 35

27.2 43.5 58.1 11.0 22.2

-1 1 1 1 -1

02 02 02 02 02

36.4 38.8 41.2 43.6 46.0

28 29 30 1 2

350 350 350 350 350

57 57 56 56 56

13.1 02.6 50.2 35.9 19.8

-1 1 1 1 -1

04 04 04 04 04

36.5 39.2 41.8 44.5 47.1

May

June

July

186

NEPTUNE, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

July

Aug.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 350 350 350 350 350 350

' 56 56 56 55 55 54

" 35.9 19.8 01.8 42.0 20.4 56.8

º -1 1 1 1 1 1

' 04 04 04 04 04 04

" 44.5 47.1 49.7 52.3 54.9 57.5

7 8 9 10 11 12

350 350 350 350 350 350

54 54 53 53 52 51

31.4 04.0 34.8 03.7 30.8 56.1

-1 1 1 1 1 1

05 05 05 05 05 05

13 14 15 16 17 18

350 350 350 350 350 350

51 50 50 49 48 47

19.5 41.2 01.2 19.5 36.0 50.9

-1 1 1 1 1 1

19 20 21 22 23 24

350 350 350 350 350 350

47 46 45 44 43 42

04.1 15.6 25.4 33.6 40.0 44.8

25 26 27 28 29 30

350 350 350 350 350 350

41 40 39 38 37 36

31 1 2 3 4 5

350 350 350 350 350 350

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 350 350 350 350 350 350

' 15 13 12 10 09 07

" 08.5 42.3 15.2 47.1 18.0 48.1

º -1 1 1 1 1 1

' 06 06 06 06 06 06

" 26.0 27.5 29.0 30.5 32.0 33.4

00.1 02.7 05.2 07.8 10.3 12.8

22 23 24 25 26 27

350 350 350 350 350 349

06 04 03 01 00 58

17.3 45.8 13.5 40.7 07.2 33.2

-1 1 1 1 1 1

06 06 06 06 06 06

34.7 36.1 37.4 38.6 39.9 41.0

05 05 05 05 05 05

15.3 17.7 20.2 22.6 25.0 Sept. 27.4

28 29 30 31 1 2

349 349 349 349 349 349

56 55 53 52 50 48

58.5 23.4 47.7 11.4 34.7 57.6

-1 1 1 1 1 1

06 06 06 06 06 06

42.2 43.3 44.4 45.4 46.4 47.3

-1 1 1 1 1 1

05 05 05 05 05 05

29.8 32.2 34.5 36.8 39.1 41.4

3 4 5 6 7 8

349 349 349 349 349 349

47 45 44 42 40 39

20.0 42.0 03.8 25.3 46.6 07.7

-1 1 1 1 1 1

06 06 06 06 06 06

48.2 49.1 49.9 50.7 51.5 52.2

47.9 49.5 49.6 48.2 45.4 41.1

-1 1 1 1 1 1

05 05 05 05 05 05

43.6 45.8 48.0 50.2 52.3 54.5

9 10 11 12 13 14

349 349 349 349 349 349

37 35 34 32 30 29

28.7 49.6 10.5 31.3 52.1 13.0

-1 1 1 1 1 1

06 06 06 06 06 06

52.8 53.4 54.0 54.5 55.0 55.5

35 34 33 32 30 29

35.5 28.4 20.0 10.2 59.0 46.4

-1 1 1 1 1 1

05 05 06 06 06 06

56.6 58.6 00.7 02.7 04.7 06.6

15 16 17 18 19 20

349 349 349 349 349 349

27 25 24 22 20 19

33.8 54.7 15.8 36.9 58.3 20.0

-1 1 1 1 1 1

06 06 06 06 06 06

55.9 56.3 56.6 56.9 57.1 57.3

350 350 350 350 350 350

28 27 26 24 23 22

32.5 17.3 00.8 43.1 24.3 04.3

-1 1 1 1 1 1

06 06 06 06 06 06

08.5 10.4 12.3 14.1 15.9 17.7

21 22 23 24 25 26

349 349 349 349 349 349

17 16 14 12 11 09

42.1 04.6 27.6 51.0 14.9 39.3

-1 1 1 1 1 1

06 06 06 06 06 06

57.5 57.6 57.7 57.7 57.7 57.7

350 350 350 350 350

20 19 17 16 15

43.2 21.1 57.9 33.7 08.5

-1 1 1 1 -1

06 06 06 06 06

19.4 21.1 22.7 24.4 26.0

27 28 29 30 1

349 349 349 349 349

08 06 04 03 01

04.2 29.6 55.6 22.2 49.5

-1 1 1 1 -1

06 06 06 06 06

57.6 57.5 57.3 57.1 56.9

Aug.

Oct.

187

NEPTUNE, 2020 GEOCENTRIC LONGITUDE AND LATITUDE FOR 0h TERRESTRIAL TIME Date

Oct.

Nov.

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 2 3 4 5 6

º 349 349 348 348 348 348

' 01 00 58 57 55 54

" 49.5 17.5 46.3 15.8 46.3 17.6

º -1 1 1 1 1 1

' 06 06 06 06 06 06

" 56.9 56.6 56.3 55.9 55.5 55.1

7 8 9 10 11 12

348 348 348 348 348 348

52 51 49 48 47 45

49.9 23.1 57.3 32.6 08.8 46.1

-1 1 1 1 1 1

06 06 06 06 06 06

13 14 15 16 17 18

348 348 348 348 348 348

44 43 41 40 39 37

24.5 03.9 44.5 26.2 09.2 53.6

-1 1 1 1 1 1

19 20 21 22 23 24

348 348 348 348 348 348

36 35 34 33 31 30

39.3 26.4 15.0 05.0 56.4 49.2

25 26 27 28 29 30

348 348 348 348 348 348

29 28 27 26 25 24

31 1 2 3 4 5

348 348 348 348 348 348

6 7 8 9 10 11 12 13 14 15 16

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

16 17 18 19 20 21

º 348 348 348 348 348 348

' 12 12 11 11 11 10

" 38.6 13.3 50.0 28.6 09.3 51.9

º -1 1 1 1 1 1

' 06 06 06 06 06 06

" 09.8 08.2 06.6 05.0 03.4 01.7

54.6 54.1 53.6 53.0 52.3 51.7

22 23 24 25 26 27

348 348 348 348 348 348

10 10 10 10 09 09

36.5 23.1 11.6 02.2 54.9 49.6

-1 1 1 1 1 1

06 05 05 05 05 05

00.0 58.4 56.7 55.0 53.3 51.6

06 06 06 06 06 06

51.0 50.3 49.5 48.7 47.9 47.0

28 29 30 1 2 3

348 348 348 348 348 348

09 09 09 09 09 10

46.4 45.3 46.3 49.4 54.6 01.9

-1 1 1 1 1 1

05 05 05 05 05 05

49.8 48.1 46.4 44.6 42.9 41.1

-1 1 1 1 1 1

06 06 06 06 06 06

46.1 45.2 44.2 43.2 42.2 41.2

4 5 6 7 8 9

348 348 348 348 348 348

10 10 10 10 11 11

11.2 22.6 36.1 51.6 09.1 28.6

-1 1 1 1 1 1

05 05 05 05 05 05

39.4 37.6 35.9 34.1 32.4 30.6

43.4 39.1 36.3 35.0 35.4 37.3

-1 1 1 1 1 1

06 06 06 06 06 06

40.1 39.0 37.8 36.6 35.4 34.2

10 11 12 13 14 15

348 348 348 348 348 348

11 12 12 13 13 14

50.3 14.0 39.9 07.9 38.1 10.4

-1 1 1 1 1 1

05 05 05 05 05 05

28.9 27.1 25.4 23.6 21.9 20.2

23 22 21 21 20 19

40.9 46.1 53.1 01.8 12.2 24.5

-1 1 1 1 1 1

06 06 06 06 06 06

33.0 31.7 30.4 29.0 27.7 26.3

16 17 18 19 20 21

348 348 348 348 348 348

14 15 15 16 17 18

44.7 21.1 59.5 39.9 22.2 06.5

-1 1 1 1 1 1

05 05 05 05 05 05

18.4 16.7 15.0 13.3 11.6 09.9

348 348 348 348 348 348

18 17 17 16 15 15

38.5 54.2 11.8 31.1 52.2 15.1

-1 1 1 1 1 1

06 06 06 06 06 06

24.9 23.5 22.0 20.6 19.1 17.6

22 23 24 25 26 27

348 348 348 348 348 348

18 19 20 21 22 23

52.8 41.1 31.4 23.7 18.0 14.2

-1 1 1 1 1 1

05 05 05 05 05 05

08.2 06.6 04.9 03.2 01.6 00.0

348 348 348 348 348

14 14 13 13 12

39.9 06.6 35.2 05.9 38.6

-1 1 1 1 -1

06 06 06 06 06

16.1 14.5 13.0 11.4 09.8

28 29 30 31 32

348 348 348 348 348

24 25 26 27 28

12.4 12.6 14.6 18.6 24.4

-1 1 1 1 -1

04 04 04 04 04

58.3 56.7 55.2 53.6 52.0

Nov.

Dec.

188

NEPTUNE, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Jan. 0 1 2 3 4 5

h 23 23 23 23 23 23

m 10 11 11 11 11 11

s 58.33 02.52 06.82 11.24 15.76 20.40

º -6 6 6 6 6 6

' 22 21 21 20 20 19

" 21.2 53.3 24.8 55.5 25.5 54.9

30.299 337 30.315 289 30.331 119 30.346 822 30.362 395 30.377 833

" 0.29 0.29 0.29 0.29 0.29 0.29

" 1.11 1.11 1.10 1.10 1.10 1.10

h 16 16 16 16 16 16

m 31 27 24 20 16 12

s 47 55 03 12 21 29

6 7 8 9 10 11

23 23 23 23 23 23

11 11 11 11 11 11

25.15 30.01 34.98 40.05 45.23 50.52

-6 6 6 6 6 6

19 18 18 17 17 16

23.5 51.5 18.9 45.5 11.5 36.9

30.393 131 30.408 286 30.423 292 30.438 146 30.452 844 30.467 382

0.29 0.29 0.29 0.29 0.29 0.29

1.10 1.10 1.10 1.10 1.10 1.10

16 16 16 15 15 15

08 04 00 57 53 49

38 47 56 06 15 24

12 13 14 15 16 17

23 23 23 23 23 23

11 12 12 12 12 12

55.90 01.38 06.96 12.63 18.40 24.26

-6 6 6 6 6 6

16 15 14 14 13 12

01.7 25.9 49.6 12.6 35.1 57.0

30.481 757 30.495 964 30.509 999 30.523 860 30.537 541 30.551 038

0.29 0.29 0.29 0.29 0.29 0.29

1.10 1.10 1.10 1.10 1.10 1.10

15 15 15 15 15 15

45 41 37 34 30 26

34 43 53 03 13 23

18 19 20 21 22 23

23 23 23 23 23 23

12 12 12 12 12 13

30.21 36.26 42.41 48.65 54.97 01.39

-6 6 6 6 6 6

12 11 10 10 09 08

18.3 39.0 59.1 18.7 37.8 56.3

30.564 348 30.577 467 30.590 390 30.603 114 30.615 633 30.627 946

0.29 0.29 0.29 0.29 0.29 0.29

1.10 1.10 1.10 1.09 1.09 1.09

15 15 15 15 15 15

22 18 14 11 07 03

33 43 53 04 14 25

24 25 26 27 28 29

23 23 23 23 23 23

13 13 13 13 13 13

07.89 14.47 21.13 27.86 34.68 41.56

-6 6 6 6 6 6

08 07 06 06 05 04

14.3 31.9 48.9 05.5 21.6 37.3

30.640 047 30.651 933 30.663 600 30.675 045 30.686 265 30.697 256

0.29 0.29 0.29 0.29 0.29 0.29

1.09 1.09 1.09 1.09 1.09 1.09

14 14 14 14 14 14

59 55 51 48 44 40

35 46 57 07 18 29

30 31 Feb. 1 2 3 4

23 23 23 23 23 23

13 13 14 14 14 14

48.52 55.56 02.66 09.84 17.08 24.39

-6 6 6 6 6 6

03 03 02 01 00 00

52.6 07.4 21.8 35.7 49.3 02.4

30.708 016 30.718 542 30.728 830 30.738 879 30.748 685 30.758 246

0.29 0.29 0.29 0.29 0.29 0.29

1.09 1.09 1.09 1.09 1.09 1.09

14 14 14 14 14 14

36 32 29 25 21 17

40 52 03 14 25 37

5 6 7 8 9 10

23 23 23 23 23 23

14 14 14 14 15 15

31.77 39.21 46.72 54.28 01.89 09.56

-5 5 5 5 5 5

59 58 57 56 56 55

15.1 27.5 39.5 51.2 02.6 13.6

30.767 560 30.776 625 30.785 439 30.794 000 30.802 306 30.810 354

0.29 0.29 0.29 0.29 0.29 0.29

1.09 1.09 1.09 1.09 1.09 1.09

14 14 14 14 13 13

13 09 06 02 58 54

48 60 11 23 35 46

11 12 13 14 15

23 23 23 23 23

15 15 15 15 15

17.27 25.03 32.85 40.71 48.62

-5 5 5 5 -5

54 53 52 51 51

24.4 34.9 45.2 55.1 04.7

30.818 144 30.825 673 30.832 939 30.839 940 30.846 675

0.29 0.29 0.29 0.29 0.29

1.09 1.09 1.09 1.09 1.09

13 13 13 13 13

50 47 43 39 35

58 10 22 34 46

189

NEPTUNE, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Feb. 15 16 17 18 19 20

h 23 23 23 23 23 23

m 15 15 16 16 16 16

s 48.62 56.57 04.58 12.62 20.71 28.83

º -5 5 5 5 5 5

' 51 50 49 48 47 46

" 04.7 14.1 23.2 32.1 40.8 49.2

30.846 675 30.853 140 30.859 334 30.865 255 30.870 902 30.876 272

" 0.29 0.29 0.28 0.28 0.28 0.28

" 1.09 1.09 1.09 1.09 1.09 1.08

h 13 13 13 13 13 13

m 35 31 28 24 20 16

s 46 58 10 22 34 46

21 22 23 24 25 26

23 23 23 23 23 23

16 16 16 17 17 17

36.98 45.17 53.38 01.62 09.89 18.18

-5 5 5 5 5 5

45 45 44 43 42 41

57.5 05.6 13.5 21.4 29.0 36.6

30.881 363 30.886 176 30.890 707 30.894 956 30.898 922 30.902 603

0.28 0.28 0.28 0.28 0.28 0.28

1.08 1.08 1.08 1.08 1.08 1.08

13 13 13 13 12 12

12 09 05 01 57 54

59 11 23 35 48 00

27 28 29 Mar. 1 2 3

23 23 23 23 23 23

17 17 17 17 17 18

26.49 34.82 43.17 51.55 59.93 08.34

-5 5 5 5 5 5

40 39 38 38 37 36

44.0 51.4 58.6 05.7 12.8 19.7

30.906 000 30.909 112 30.911 937 30.914 476 30.916 728 30.918 694

0.28 0.28 0.28 0.28 0.28 0.28

1.08 1.08 1.08 1.08 1.08 1.08

12 12 12 12 12 12

50 46 42 38 35 31

13 25 37 50 02 15

4 5 6 7 8 9

23 23 23 23 23 23

18 18 18 18 18 18

16.76 25.18 33.62 42.06 50.50 58.92

-5 5 5 5 5 5

35 34 33 32 31 31

26.7 33.6 40.5 47.4 54.6 01.7

30.920 373 30.921 765 30.922 871 30.923 691 30.924 225 30.924 474

0.28 0.28 0.28 0.28 0.28 0.28

1.08 1.08 1.08 1.08 1.08 1.08

12 12 12 12 12 12

27 23 19 16 12 08

27 40 52 05 17 30

10 11 12 13 14 15

23 23 23 23 23 23

19 19 19 19 19 19

07.34 15.77 24.19 32.61 41.03 49.44

-5 5 5 5 5 5

30 29 28 27 26 25

08.5 15.5 22.6 29.7 36.9 44.2

30.924 438 30.924 117 30.923 511 30.922 621 30.921 446 30.919 988

0.28 0.28 0.28 0.28 0.28 0.28

1.08 1.08 1.08 1.08 1.08 1.08

12 12 11 11 11 11

04 00 57 53 49 45

42 54 07 19 32 44

16 17 18 19 20 21

23 23 23 23 23 23

19 20 20 20 20 20

57.85 06.24 14.61 22.97 31.31 39.62

-5 5 5 5 5 5

24 23 23 22 21 20

51.5 59.0 06.6 14.3 22.2 30.3

30.918 245 30.916 219 30.913 909 30.911 317 30.908 443 30.905 287

0.28 0.28 0.28 0.28 0.28 0.28

1.08 1.08 1.08 1.08 1.08 1.08

11 11 11 11 11 11

41 38 34 30 26 22

57 09 22 34 46 59

22 23 24 25 26 27

23 23 23 23 23 23

20 20 21 21 21 21

47.91 56.17 04.41 12.61 20.79 28.93

-5 5 5 5 5 5

19 18 17 17 16 15

38.6 47.1 55.7 04.6 13.7 23.0

30.901 851 30.898 136 30.894 143 30.889 874 30.885 329 30.880 511

0.28 0.28 0.28 0.28 0.28 0.28

1.08 1.08 1.08 1.08 1.08 1.08

11 11 11 11 11 11

19 15 11 07 04 00

11 23 36 48 00 12

28 29 30 31 Apr. 1

23 23 23 23 23

21 21 21 22 22

37.05 45.13 53.17 01.18 09.14

-5 5 5 5 -5

14 13 12 12 11

32.5 42.3 52.4 02.7 13.2

30.875 420 30.870 060 30.864 431 30.858 537 30.852 378

0.28 0.28 0.28 0.28 0.29

1.09 1.09 1.09 1.09 1.09

10 10 10 10 10

56 52 48 45 41

24 37 49 01 13

190

NEPTUNE, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Apr. 1 2 3 4 5 6

h 23 23 23 23 23 23

m 22 22 22 22 22 22

s 09.14 17.07 24.94 32.77 40.55 48.28

º -5 5 5 5 5 5

' 11 10 09 08 07 07

" 13.2 24.1 35.3 46.9 58.8 11.1

30.852 378 30.845 958 30.839 278 30.832 341 30.825 149 30.817 705

" 0.29 0.29 0.29 0.29 0.29 0.29

" 1.09 1.09 1.09 1.09 1.09 1.09

h 10 10 10 10 10 10

m 41 37 33 29 26 22

s 13 25 36 48 00 12

7 8 9 10 11 12

23 23 23 23 23 23

22 23 23 23 23 23

55.95 03.57 11.13 18.65 26.11 33.51

-5 5 5 5 5 5

06 05 04 04 03 02

23.7 36.7 50.1 03.8 17.9 32.4

30.810 011 30.802 069 30.793 881 30.785 450 30.776 778 30.767 866

0.29 0.29 0.29 0.29 0.29 0.29

1.09 1.09 1.09 1.09 1.09 1.09

10 10 10 10 10 9

18 14 10 06 03 59

24 35 47 58 10 21

13 14 15 16 17 18

23 23 23 23 23 23

23 23 23 24 24 24

40.86 48.14 55.36 02.52 09.60 16.61

-5 5 5 4 4 4

01 01 00 59 58 58

47.2 02.5 18.3 34.5 51.1 08.3

30.758 717 30.749 333 30.739 716 30.729 869 30.719 794 30.709 495

0.29 0.29 0.29 0.29 0.29 0.29

1.09 1.09 1.09 1.09 1.09 1.09

9 9 9 9 9 9

55 51 47 44 40 36

33 44 55 06 18 29

19 20 21 22 23 24

23 23 23 23 23 23

24 24 24 24 24 24

23.55 30.42 37.22 43.94 50.58 57.15

-4 4 4 4 4 4

57 56 56 55 54 54

25.9 44.0 02.6 21.7 41.3 01.4

30.698 973 30.688 233 30.677 276 30.666 107 30.654 728 30.643 142

0.29 0.29 0.29 0.29 0.29 0.29

1.09 1.09 1.09 1.09 1.09 1.09

9 9 9 9 9 9

32 28 25 21 17 13

40 50 01 12 23 33

25 26 27 28 29 30

23 23 23 23 23 23

25 25 25 25 25 25

03.64 10.05 16.39 22.64 28.80 34.88

-4 4 4 4 4 4

53 52 52 51 50 50

22.0 43.2 04.9 27.1 49.9 13.3

30.631 354 30.619 367 30.607 184 30.594 810 30.582 247 30.569 501

0.29 0.29 0.29 0.29 0.29 0.29

1.09 1.09 1.09 1.09 1.10 1.10

9 9 9 8 8 8

09 05 02 58 54 50

44 54 05 15 25 35

May 1 2 3 4 5 6

23 23 23 23 23 23

25 25 25 25 26 26

40.88 46.77 52.58 58.29 03.91 09.44

-4 4 4 4 4 4

49 49 48 47 47 46

37.2 01.8 27.0 52.8 19.3 46.3

30.556 574 30.543 470 30.530 195 30.516 750 30.503 141 30.489 371

0.29 0.29 0.29 0.29 0.29 0.29

1.10 1.10 1.10 1.10 1.10 1.10

8 8 8 8 8 8

46 42 39 35 31 27

45 55 05 15 24 34

7 8 9 10 11 12

23 23 23 23 23 23

26 26 26 26 26 26

14.88 20.23 25.48 30.64 35.70 40.66

-4 4 4 4 4 4

46 45 45 44 44 43

13.9 42.2 11.0 40.5 10.6 41.4

30.475 443 30.461 361 30.447 128 30.432 749 30.418 226 30.403 562

0.29 0.29 0.29 0.29 0.29 0.29

1.10 1.10 1.10 1.10 1.10 1.10

8 8 8 8 8 8

23 19 16 12 08 04

43 53 02 11 20 29

13 14 15 16 17

23 23 23 23 23

26 26 26 26 27

45.53 50.28 54.93 59.48 03.92

-4 4 4 4 -4

43 42 42 41 41

12.9 45.0 17.8 51.4 25.6

30.388 763 30.373 831 30.358 771 30.343 586 30.328 281

0.29 0.29 0.29 0.29 0.29

1.10 1.10 1.10 1.10 1.10

8 7 7 7 7

00 56 52 49 45

38 47 56 04 13

191

NEPTUNE, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

May 17 18 19 20 21 22

h 23 23 23 23 23 23

m 27 27 27 27 27 27

s 03.92 08.25 12.48 16.60 20.61 24.51

º -4 4 4 4 4 4

' 41 41 40 40 39 39

" 25.6 00.5 36.1 12.4 49.4 27.1

30.328 281 30.312 860 30.297 327 30.281 686 30.265 942 30.250 100

" 0.29 0.29 0.29 0.29 0.29 0.29

" 1.10 1.11 1.11 1.11 1.11 1.11

h 7 7 7 7 7 7

m 45 41 37 33 29 25

s 13 21 29 37 46 53

23 24 25 26 27 28

23 23 23 23 23 23

27 27 27 27 27 27

28.31 32.00 35.58 39.04 42.40 45.63

-4 4 4 4 4 4

39 38 38 38 37 37

05.5 44.7 24.5 05.1 46.4 28.5

30.234 165 30.218 140 30.202 030 30.185 841 30.169 577 30.153 243

0.29 0.29 0.29 0.29 0.29 0.29

1.11 1.11 1.11 1.11 1.11 1.11

7 7 7 7 7 7

22 18 14 10 06 02

01 09 17 24 32 39

29 30 31 June 1 2 3

23 23 23 23 23 23

27 27 27 27 28 28

48.75 51.76 54.64 57.41 00.06 02.59

-4 4 4 4 4 4

37 36 36 36 36 35

11.3 54.9 39.3 24.4 10.3 56.9

30.136 844 30.120 385 30.103 869 30.087 303 30.070 690 30.054 035

0.29 0.29 0.29 0.29 0.29 0.29

1.11 1.11 1.11 1.11 1.11 1.11

6 6 6 6 6 6

58 54 50 47 43 39

46 53 60 07 13 20

4 5 6 7 8 9

23 23 23 23 23 23

28 28 28 28 28 28

05.02 07.32 09.52 11.60 13.56 15.40

-4 4 4 4 4 4

35 35 35 35 35 34

44.3 32.3 21.2 10.7 01.1 52.2

30.037 343 30.020 616 30.003 861 29.987 080 29.970 278 29.953 460

0.29 0.29 0.29 0.29 0.29 0.29

1.12 1.12 1.12 1.12 1.12 1.12

6 6 6 6 6 6

35 31 27 23 19 15

26 33 39 45 51 57

10 11 12 13 14 15

23 23 23 23 23 23

28 28 28 28 28 28

17.12 18.72 20.19 21.54 22.77 23.89

-4 4 4 4 4 4

34 34 34 34 34 34

44.1 36.8 30.3 24.6 19.6 15.5

29.936 630 29.919 792 29.902 950 29.886 110 29.869 276 29.852 453

0.29 0.29 0.29 0.29 0.29 0.29

1.12 1.12 1.12 1.12 1.12 1.12

6 6 6 6 5 5

12 08 04 00 56 52

03 08 14 19 25 30

16 17 18 19 20 21

23 23 23 23 23 23

28 28 28 28 28 28

24.88 25.75 26.50 27.13 27.65 28.04

-4 4 4 4 4 4

34 34 34 34 34 34

12.1 09.4 07.5 06.4 06.0 06.4

29.835 645 29.818 858 29.802 096 29.785 364 29.768 668 29.752 011

0.29 0.29 0.30 0.30 0.30 0.30

1.12 1.12 1.12 1.12 1.13 1.13

5 5 5 5 5 5

48 44 40 36 32 28

35 40 45 49 54 58

22 23 24 25 26 27

23 23 23 23 23 23

28 28 28 28 28 28

28.32 28.47 28.51 28.42 28.20 27.87

-4 4 4 4 4 4

34 34 34 34 34 34

07.6 09.5 12.2 15.7 20.0 25.1

29.735 401 29.718 840 29.702 335 29.685 890 29.669 511 29.653 202

0.30 0.30 0.30 0.30 0.30 0.30

1.13 1.13 1.13 1.13 1.13 1.13

5 5 5 5 5 5

25 21 17 13 09 05

03 07 11 15 19 23

28 29 30 July 1 2

23 23 23 23 23

28 28 28 28 28

27.41 26.83 26.14 25.33 24.41

-4 4 4 4 -4

34 34 34 34 35

30.9 37.5 44.8 52.9 01.6

29.636 968 29.620 813 29.604 742 29.588 760 29.572 870

0.30 0.30 0.30 0.30 0.30

1.13 1.13 1.13 1.13 1.13

5 4 4 4 4

01 57 53 49 45

26 30 33 36 39

192

NEPTUNE, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

July 1 2 3 4 5 6

h 23 23 23 23 23 23

m 28 28 28 28 28 28

s 25.33 24.41 23.37 22.22 20.96 19.58

º -4 4 4 4 4 4

' 34 35 35 35 35 35

" 52.9 01.6 11.1 21.3 32.2 43.9

29.588 760 29.572 870 29.557 077 29.541 385 29.525 798 29.510 320

" 0.30 0.30 0.30 0.30 0.30 0.30

" 1.13 1.13 1.13 1.13 1.13 1.14

h 4 4 4 4 4 4

m 49 45 41 37 33 29

s 36 39 42 45 48 51

7 8 9 10 11 12

23 23 23 23 23 23

28 28 28 28 28 28

18.09 16.48 14.75 12.90 10.95 08.88

-4 4 4 4 4 4

35 36 36 36 36 37

56.3 09.4 23.3 37.9 53.2 09.2

29.494 955 29.479 708 29.464 582 29.449 583 29.434 713 29.419 978

0.30 0.30 0.30 0.30 0.30 0.30

1.14 1.14 1.14 1.14 1.14 1.14

4 4 4 4 4 4

25 21 17 14 10 06

53 56 58 01 03 05

13 14 15 16 17 18

23 23 23 23 23 23

28 28 28 27 27 27

06.70 04.41 02.01 59.51 56.91 54.20

-4 4 4 4 4 4

37 37 38 38 38 38

25.8 43.2 01.2 19.9 39.2 59.2

29.405 383 29.390 930 29.376 626 29.362 474 29.348 479 29.334 645

0.30 0.30 0.30 0.30 0.30 0.30

1.14 1.14 1.14 1.14 1.14 1.14

4 3 3 3 3 3

02 58 54 50 46 42

07 08 10 12 13 15

19 20 21 22 23 24

23 23 23 23 23 23

27 27 27 27 27 27

51.38 48.46 45.44 42.31 39.08 35.75

-4 4 4 4 4 4

39 39 40 40 40 41

19.8 41.1 03.0 25.5 48.8 12.6

29.320 976 29.307 478 29.294 154 29.281 010 29.268 048 29.255 273

0.30 0.30 0.30 0.30 0.30 0.30

1.14 1.14 1.14 1.14 1.14 1.15

3 3 3 3 3 3

38 34 30 26 22 18

16 17 18 19 20 21

25 26 27 28 29 30

23 23 23 23 23 23

27 27 27 27 27 27

32.31 28.78 25.15 21.43 17.63 13.73

-4 4 4 4 4 4

41 42 42 42 43 43

37.0 02.1 27.7 53.9 20.6 47.8

29.242 690 29.230 301 29.218 112 29.206 124 29.194 342 29.182 768

0.30 0.30 0.30 0.30 0.30 0.30

1.15 1.15 1.15 1.15 1.15 1.15

3 3 3 3 2 2

14 10 06 02 58 54

21 22 22 23 23 23

31 Aug. 1 2 3 4 5

23 23 23 23 23 23

27 27 27 26 26 26

09.75 05.69 01.53 57.29 52.97 48.56

-4 4 4 4 4 4

44 44 45 45 46 46

15.6 43.9 12.7 42.0 11.9 42.3

29.171 406 29.160 260 29.149 331 29.138 623 29.128 139 29.117 883

0.30 0.30 0.30 0.30 0.30 0.30

1.15 1.15 1.15 1.15 1.15 1.15

2 2 2 2 2 2

50 46 42 38 34 30

23 23 23 23 23 23

6 7 8 9 10 11

23 23 23 23 23 23

26 26 26 26 26 26

44.06 39.49 34.84 30.11 25.31 20.44

-4 4 4 4 4 4

47 47 48 48 49 49

13.1 44.5 16.3 48.5 21.2 54.3

29.107 856 29.098 063 29.088 506 29.079 188 29.070 113 29.061 284

0.30 0.30 0.30 0.30 0.30 0.30

1.15 1.15 1.15 1.15 1.15 1.15

2 2 2 2 2 2

26 22 18 14 10 06

22 22 21 21 20 19

12 13 14 15 16

23 23 23 23 23

26 26 26 26 25

15.49 10.49 05.42 00.28 55.08

-4 4 4 4 -4

50 51 51 52 52

27.8 01.6 35.9 10.5 45.5

29.052 703 29.044 374 29.036 299 29.028 482 29.020 925

0.30 0.30 0.30 0.30 0.30

1.15 1.15 1.15 1.15 1.15

2 1 1 1 1

02 58 54 50 46

18 17 16 15 14

193

NEPTUNE, 2020 h RIGHT ASCENSION AND DECLINATION FOR 0 TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Aug. 16 17 18 19 20 21

h 23 23 23 23 23 23

m 25 25 25 25 25 25

s 55.08 49.82 44.50 39.12 33.69 28.19

º -4 4 4 4 4 4

' 52 53 53 54 55 55

" 45.5 20.8 56.5 32.5 08.9 45.6

29.020 925 29.013 631 29.006 603 28.999 844 28.993 356 28.987 142

" 0.30 0.30 0.30 0.30 0.30 0.30

" 1.15 1.15 1.15 1.16 1.16 1.16

h 1 1 1 1 1 1

m 46 42 38 34 30 26

s 14 13 12 11 09 08

22 23 24 25 26 27

23 23 23 23 23 23

25 25 25 25 25 24

22.64 17.05 11.41 05.73 00.01 54.26

-4 4 4 4 4 4

56 56 57 58 58 59

22.5 59.8 37.2 14.9 52.7 30.8

28.981 203 28.975 542 28.970 160 28.965 058 28.960 239 28.955 704

0.30 0.30 0.30 0.30 0.30 0.30

1.16 1.16 1.16 1.16 1.16 1.16

1 1 1 1 1 1

22 18 14 10 06 01

07 05 04 02 00 59

28 29 30 31 Sept. 1 2

23 23 23 23 23 23

24 24 24 24 24 24

48.47 42.64 36.78 30.89 24.96 19.01

-5 5 5 5 5 5

00 00 01 02 02 03

09.0 47.5 26.1 04.8 43.8 22.8

28.951 453 28.947 487 28.943 809 28.940 419 28.937 317 28.934 506

0.30 0.30 0.30 0.30 0.30 0.30

1.16 1.16 1.16 1.16 1.16 1.16

0 0 0 0 0 0

57 53 49 45 41 37

57 55 54 52 50 48

3 4 5 6 7 8

23 23 23 23 23 23

24 24 24 23 23 23

13.03 07.03 01.00 54.96 48.91 42.84

-5 5 5 5 5 5

04 04 05 06 06 07

02.0 41.3 20.7 00.1 39.5 19.0

28.931 985 28.929 757 28.927 821 28.926 179 28.924 833 28.923 781

0.30 0.30 0.30 0.30 0.30 0.30

1.16 1.16 1.16 1.16 1.16 1.16

0 0 0 0 0 0

33 29 25 21 17 13

46 45 43 41 39 37

9 10 11 12 13 14

23 23 23 23 23 23

23 23 23 23 23 23

36.76 30.68 24.59 18.50 12.41 06.32

-5 5 5 5 5 5

07 08 09 09 10 11

58.5 38.0 17.4 56.9 36.2 15.6

28.923 026 28.922 568 28.922 408 28.922 547 28.922 984 28.923 721

0.30 0.30 0.30 0.30 0.30 0.30

1.16 1.16 1.16 1.16 1.16 1.16

0 0 0 23 23 23

09 05 01 53 49 45

35 33 31 27 25 23

15 16 17 18 19 20

23 23 23 23 23 23

23 22 22 22 22 22

00.23 54.14 48.06 41.98 35.92 29.87

-5 5 5 5 5 5

11 12 13 13 14 15

54.9 34.2 13.3 52.4 31.3 10.1

28.924 758 28.926 094 28.927 731 28.929 667 28.931 902 28.934 437

0.30 0.30 0.30 0.30 0.30 0.30

1.16 1.16 1.16 1.16 1.16 1.16

23 23 23 23 23 23

41 37 33 29 25 21

21 19 17 15 13 12

21 22 23 24 25 26

23 23 23 23 23 23

22 22 22 22 22 21

23.85 17.85 11.88 05.93 00.01 54.13

-5 5 5 5 5 5

15 16 17 17 18 18

48.6 27.0 05.1 43.1 20.8 58.2

28.937 269 28.940 398 28.943 823 28.947 542 28.951 554 28.955 858

0.30 0.30 0.30 0.30 0.30 0.30

1.16 1.16 1.16 1.16 1.16 1.16

23 23 23 23 23 22

17 13 09 05 01 57

10 08 06 04 02 01

27 28 29 30 Oct. 1

23 23 23 23 23

21 21 21 21 21

48.27 42.44 36.65 30.89 25.18

-5 5 5 5 -5

19 20 20 21 22

35.5 12.5 49.2 25.6 01.8

28.960 452 28.965 334 28.970 504 28.975 960 28.981 699

0.30 0.30 0.30 0.30 0.30

1.16 1.16 1.16 1.16 1.16

22 22 22 22 22

52 48 44 40 36

59 57 56 54 53

194

NEPTUNE, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Oct. 1 2 3 4 5 6

h 23 23 23 23 23 23

m 21 21 21 21 21 20

s 25.18 19.50 13.88 08.30 02.77 57.30

º -5 5 5 5 5 5

' 22 22 23 23 24 24

" 01.8 37.6 13.1 48.2 22.9 57.3

28.981 699 28.987 722 28.994 025 29.000 608 29.007 469 29.014 605

" 0.30 0.30 0.30 0.30 0.30 0.30

" 1.16 1.16 1.16 1.16 1.15 1.15

h 22 22 22 22 22 22

m 36 32 28 24 20 16

s 53 51 50 48 47 46

7 8 9 10 11 12

23 23 23 23 23 23

20 20 20 20 20 20

51.88 46.52 41.23 35.99 30.81 25.70

-5 5 5 5 5 5

25 26 26 27 27 28

31.2 04.7 37.8 10.5 42.8 14.6

29.022 016 29.029 699 29.037 653 29.045 875 29.054 364 29.063 116

0.30 0.30 0.30 0.30 0.30 0.30

1.15 1.15 1.15 1.15 1.15 1.15

22 22 22 22 21 21

12 08 04 00 56 52

44 43 42 41 40 39

13 14 15 16 17 18

23 23 23 23 23 23

20 20 20 20 20 19

20.65 15.67 10.76 05.92 01.15 56.47

-5 5 5 5 5 5

28 29 29 30 30 31

45.9 16.8 47.3 17.2 46.6 15.4

29.072 131 29.081 405 29.090 936 29.100 721 29.110 757 29.121 041

0.30 0.30 0.30 0.30 0.30 0.30

1.15 1.15 1.15 1.15 1.15 1.15

21 21 21 21 21 21

48 44 40 36 32 28

38 37 37 36 35 35

19 20 21 22 23 24

23 23 23 23 23 23

19 19 19 19 19 19

51.87 47.35 42.93 38.58 34.33 30.16

-5 5 5 5 5 5

31 32 32 33 33 33

43.6 11.3 38.4 04.9 30.8 56.2

29.131 570 29.142 339 29.153 345 29.164 584 29.176 053 29.187 748

0.30 0.30 0.30 0.30 0.30 0.30

1.15 1.15 1.15 1.15 1.15 1.15

21 21 21 21 21 21

24 20 16 12 08 04

35 34 34 34 34 34

25 26 27 28 29 30

23 23 23 23 23 23

19 19 19 19 19 19

26.08 22.09 18.19 14.38 10.67 07.06

-5 5 5 5 5 5

34 34 35 35 35 36

21.0 45.1 08.6 31.5 53.8 15.4

29.199 664 29.211 799 29.224 147 29.236 706 29.249 472 29.262 441

0.30 0.30 0.30 0.30 0.30 0.30

1.15 1.15 1.15 1.15 1.15 1.14

21 20 20 20 20 20

00 56 52 48 44 40

34 34 34 35 35 36

31 Nov. 1 2 3 4 5

23 23 23 23 23 23

19 19 18 18 18 18

03.55 00.14 56.84 53.65 50.56 47.57

-5 5 5 5 5 5

36 36 37 37 37 38

36.3 56.6 16.1 35.0 53.1 10.5

29.275 608 29.288 971 29.302 525 29.316 266 29.330 190 29.344 294

0.30 0.30 0.30 0.30 0.30 0.30

1.14 1.14 1.14 1.14 1.14 1.14

20 20 20 20 20 20

36 32 28 24 20 16

37 37 38 39 40 42

6 7 8 9 10 11

23 23 23 23 23 23

18 18 18 18 18 18

44.70 41.94 39.28 36.74 34.30 31.98

-5 5 5 5 5 5

38 38 38 39 39 39

27.2 43.2 58.5 13.1 27.0 40.1

29.358 574 29.373 025 29.387 642 29.402 423 29.417 362 29.432 456

0.30 0.30 0.30 0.30 0.30 0.30

1.14 1.14 1.14 1.14 1.14 1.14

20 20 20 20 19 19

12 08 04 00 56 52

43 44 46 47 49 51

12 13 14 15 16

23 23 23 23 23

18 18 18 18 18

29.77 27.67 25.70 23.85 22.12

-5 5 5 5 -5

39 40 40 40 40

52.5 04.1 14.9 24.9 34.2

29.447 699 29.463 087 29.478 615 29.494 278 29.510 070

0.30 0.30 0.30 0.30 0.30

1.14 1.14 1.14 1.14 1.14

19 19 19 19 19

48 44 40 36 33

53 55 57 60 02

195

NEPTUNE, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Apparent Declination

True Distance Hor. Semi from the Earth Parallax Diameter

Ephemeris Transit

Nov. 16 17 18 19 20 21

h 23 23 23 23 23 23

m 18 18 18 18 18 18

s 22.12 20.52 19.04 17.69 16.45 15.34

º -5 5 5 5 5 5

' 40 40 40 40 41 41

" 34.2 42.6 50.2 57.0 03.1 08.4

29.510 070 29.525 986 29.542 021 29.558 170 29.574 426 29.590 786

" 0.30 0.30 0.30 0.30 0.30 0.30

" 1.14 1.13 1.13 1.13 1.13 1.13

h 19 19 19 19 19 19

m 33 29 25 21 17 13

s 02 05 08 10 13 16

22 23 24 25 26 27

23 23 23 23 23 23

18 18 18 18 18 18

14.34 13.47 12.72 12.10 11.60 11.23

-5 5 5 5 5 5

41 41 41 41 41 41

12.9 16.6 19.5 21.6 22.9 23.4

29.607 242 29.623 791 29.640 427 29.657 144 29.673 939 29.690 805

0.30 0.30 0.30 0.30 0.30 0.30

1.13 1.13 1.13 1.13 1.13 1.13

19 19 19 18 18 18

09 05 01 57 53 49

20 23 26 30 34 38

28 29 30 Dec. 1 2 3

23 23 23 23 23 23

18 18 18 18 18 18

10.99 10.87 10.89 11.03 11.31 11.71

-5 5 5 5 5 5

41 41 41 41 41 41

23.1 21.9 19.9 17.1 13.5 09.0

29.707 738 29.724 733 29.741 784 29.758 888 29.776 037 29.793 229

0.30 0.30 0.30 0.30 0.30 0.30

1.13 1.13 1.13 1.13 1.13 1.12

18 18 18 18 18 18

45 41 37 33 29 26

41 46 50 54 59 03

4 5 6 7 8 9

23 23 23 23 23 23

18 18 18 18 18 18

12.24 12.90 13.68 14.59 15.62 16.78

-5 5 5 5 5 5

41 40 40 40 40 40

03.7 57.7 50.8 43.1 34.7 25.4

29.810 458 29.827 718 29.845 005 29.862 314 29.879 640 29.896 977

0.30 0.29 0.29 0.29 0.29 0.29

1.12 1.12 1.12 1.12 1.12 1.12

18 18 18 18 18 18

22 18 14 10 06 02

08 13 18 23 28 33

10 11 12 13 14 15

23 23 23 23 23 23

18 18 18 18 18 18

18.07 19.49 21.04 22.72 24.53 26.48

-5 5 5 5 5 5

40 40 39 39 39 39

15.3 04.4 52.7 40.1 26.7 12.5

29.914 320 29.931 664 29.949 002 29.966 331 29.983 643 30.000 933

0.29 0.29 0.29 0.29 0.29 0.29

1.12 1.12 1.12 1.12 1.12 1.12

17 17 17 17 17 17

58 54 50 46 43 39

39 44 50 56 02 08

16 17 18 19 20 21

23 23 23 23 23 23

18 18 18 18 18 18

28.55 30.75 33.07 35.51 38.08 40.77

-5 5 5 5 5 5

38 38 38 38 37 37

57.5 41.7 25.1 07.7 49.6 30.7

30.018 196 30.035 425 30.052 615 30.069 761 30.086 856 30.103 897

0.29 0.29 0.29 0.29 0.29 0.29

1.12 1.12 1.11 1.11 1.11 1.11

17 17 17 17 17 17

35 31 27 23 19 15

14 21 27 34 40 47

22 23 24 25 26 27

23 23 23 23 23 23

18 18 18 18 18 18

43.58 46.51 49.57 52.74 56.05 59.47

-5 5 5 5 5 5

37 36 36 36 35 35

11.0 50.6 29.4 07.4 44.6 21.1

30.120 878 30.137 794 30.154 639 30.171 409 30.188 099 30.204 704

0.29 0.29 0.29 0.29 0.29 0.29

1.11 1.11 1.11 1.11 1.11 1.11

17 17 17 17 16 16

11 08 04 00 56 52

54 01 09 16 23 31

28 29 30 31 32

23 23 23 23 23

19 19 19 19 19

03.01 06.68 10.46 14.36 18.37

-5 5 5 5 -5

34 34 34 33 33

56.8 31.8 06.1 39.6 12.4

30.221 220 30.237 642 30.253 965 30.270 185 30.286 298

0.29 0.29 0.29 0.29 0.29

1.11 1.11 1.11 1.11 1.11

16 16 16 16 16

48 44 40 37 33

39 46 54 02 11

196

PLUTO, 2020 HELIOCENTRIC POSITIONS FOR 0 h TERRESTRIAL TIME MEAN EQUINOX AND ECLIPTIC OF DATE Date

Jan.

Feb.

Mar.

Apr.

May

June

July

Heliocentric Longitude

Heliocentric Latitude

Radius Vector

Date

Heliocentric Heliocentric Longitude Latitude

Radius Vector

1 6 11 16 21 26

º 292 292 292 292 292 292

' 45 46 48 49 51 52

" º ' " 09.5 -0 40 17.8 40.0 0 40 45.4 10.5 0 41 13.0 41.0 0 41 40.7 11.5 0 42 08.3 42.0 0 42 35.8

º ' " º ' " 33.950 45 July 4 293 40 48.6 -0 57 15.9 33.953 74 9 293 42 18.5 0 57 43.3 33.957 02 14 293 43 48.4 0 58 10.7 33.960 31 19 293 45 18.3 0 58 38.1 33.963 59 24 293 46 48.2 0 59 05.5 33.966 88 29 293 48 18.0 0 59 32.8

34.072 19 34.075 49 34.078 78 34.082 08 34.085 38 34.088 68

31 5 10 15 20 25

292 292 292 292 293 293

54 55 57 58 00 01

12.5 -0 43 03.5 42.9 0 43 31.0 13.4 0 43 58.6 43.8 0 44 26.2 14.2 0 44 53.7 44.5 0 45 21.3

33.970 16 Aug. 33.973 45 33.976 73 33.980 02 33.983 31 33.986 59

3 8 13 18 23 28

293 293 293 293 293 293

49 51 52 54 55 57

47.9 -1 00 00.2 17.7 1 00 27.6 47.5 1 00 55.0 17.3 1 01 22.3 47.1 1 01 49.7 16.9 1 02 17.0

34.091 97 34.095 27 34.098 57 34.101 87 34.105 17 34.108 46

1 6 11 16 21 26

293 293 293 293 293 293

03 04 06 07 09 10

14.9 -0 45 48.9 45.2 0 46 16.4 15.6 0 46 44.0 45.9 0 47 11.5 16.2 0 47 39.0 46.4 0 48 06.6

33.989 88 Sept. 33.993 17 33.996 46 33.999 75 34.003 04 34.006 33

2 7 12 17 22 27

293 294 294 294 294 294

58 00 01 03 04 06

46.6 -1 02 44.4 16.3 1 03 11.7 46.0 1 03 39.0 15.7 1 04 06.3 45.4 1 04 33.6 15.0 1 05 01.0

34.111 76 34.115 06 34.118 36 34.121 66 34.124 96 34.128 26

31 5 10 15 20 25

293 293 293 293 293 293

12 13 15 16 18 19

16.7 -0 48 34.1 47.0 0 49 01.6 17.2 0 49 29.1 47.4 0 49 56.6 17.6 0 50 24.1 47.8 0 50 51.6

34.009 62 Oct. 2 294 07 44.7 -1 05 28.2 34.012 91 7 294 09 14.3 1 05 55.5 34.016 20 12 294 10 43.9 1 06 22.8 34.019 49 17 294 12 13.5 1 06 50.1 34.022 78 22 294 13 43.1 1 07 17.4 34.026 07 27 294 15 12.6 1 07 44.7

34.131 56 34.134 86 34.138 17 34.141 47 34.144 77 34.148 07

30 5 10 15 20 25

293 293 293 293 293 293

21 22 24 25 27 28

17.9 -0 51 19.1 48.1 0 51 46.6 18.2 0 52 14.1 48.3 0 52 41.5 18.4 0 53 09.0 48.5 0 53 36.4

34.029 37 Nov. 34.032 66 34.035 95 34.039 25 34.042 54 34.045 83

42.2 -1 08 11.9 11.7 1 08 39.2 41.2 1 09 06.5 10.7 1 09 33.7 40.1 1 10 00.9 09.6 1 10 28.2

34.151 37 34.154 68 34.157 98 34.161 29 34.164 59 34.167 89

30 4 9 14 19 24

293 293 293 293 293 293

30 31 33 34 36 37

18.6 -0 54 03.9 48.6 0 54 31.3 18.6 0 54 58.8 48.6 0 55 26.2 18.7 0 55 53.6 48.6 0 56 21.1

34.049 13 Dec. 1 294 25 39.0 -1 10 55.4 34.052 42 6 294 27 08.5 1 11 22.6 34.055 72 11 294 28 37.9 1 11 49.9 34.059 01 16 294 30 07.2 1 12 17.1 34.062 31 21 294 31 36.6 1 12 44.3 34.065 60 26 294 33 06.0 1 13 11.5

34.171 20 34.174 50 34.177 81 34.181 11 34.184 42 34.187 73

34.068 90 34.072 19

34.191 03 34.194 34

29 293 39 18.6 -0 56 48.5 4 293 40 48.6 -0 57 15.9

1 6 11 16 21 26

294 294 294 294 294 294

16 18 19 21 22 24

31 294 34 35.3 -1 13 38.7 36 294 36 04.6 -1 14 05.8

N.B: Pluto is now classified as a dwarf planet as per resolution of IAU

197

PLUTO, 2020 h GEOCENTRIC LONGITUDE AND LATITUDE FOR 0 TERRESTRIAL TIME Date

Jan.

Feb.

Mar.

Apr.

May

June

July

Apparent Geocentric Longitude

Apparent Geocentric Latitude

1 6 11 16 21 26

º 292 292 292 292 293 293

' 23 33 43 53 03 13

" 08.4 04.9 07.6 11.2 13.7 11.3

º -0 0 0 0 0 0

' 39 39 40 40 40 41

" 10.3 36.2 02.5 29.3 56.5 24.4

31 5 10 15 20 25

293 293 293 293 293 294

22 32 41 50 59 07

59.2 34.7 54.7 54.8 33.4 46.3

-0 0 0 0 0 0

41 42 42 43 43 44

52.8 21.6 51.1 21.1 51.6 22.7

1 6 11 16 21 26

294 294 294 294 294 294

15 22 29 35 40 45

30.4 44.1 23.8 28.2 55.3 42.1

-0 0 0 0 0 0

31 5 10 15 20 25

294 294 294 294 294 294

49 53 55 57 59 59

48.1 12.2 52.5 50.1 03.1 31.5

30 5 10 15 20 25

294 294 294 294 294 294

59 58 56 54 51 47

30 4 9 14 19 24

294 294 294 294 294 294

29 4

294 294

Date

Apparent Geocentric Longitude

Apparent Geocentric Latitude

July

4 9 14 19 24 29

º 294 293 293 293 293 293

' 01 54 46 39 32 25

" 17.8 10.4 56.6 41.6 29.2 22.8

º -0 0 0 1 1 1

' 58 59 59 00 00 01

" 58.3 28.0 56.9 25.0 52.3 18.7

Aug.

3 8 13 18 23 28

293 293 293 292 292 292

18 11 05 59 53 48

27.9 46.5 22.8 21.2 43.9 35.5

-1 1 1 1 1 1

01 02 02 02 03 03

44.4 09.2 33.2 56.4 18.9 40.6

44 45 45 46 47 47

54.2 Sept. 26.3 58.8 31.8 05.3 39.1

2 7 12 17 22 27

292 292 292 292 292 292

43 39 36 33 31 30

58.3 54.2 26.7 37.6 28.5 02.1

-1 1 1 1 1 1

04 04 04 05 05 05

01.6 21.9 41.7 00.8 19.5 37.8

-0 0 0 0 0 0

48 48 49 49 50 51

13.2 47.7 22.4 57.4 32.5 07.7

Oct.

2 7 12 17 22 27

292 292 292 292 292 292

29 29 30 31 33 36

17.9 17.3 01.6 29.7 43.2 40.4

-1 1 1 1 1 1

05 06 06 06 07 07

55.7 13.3 30.7 48.0 05.2 22.4

16.7 18.2 38.0 17.2 16.1 37.8

-0 0 0 0 0 0

51 52 52 53 54 54

43.0 18.2 53.4 28.5 03.4 38.0

Nov.

1 6 11 16 21 26

292 292 292 292 293 293

40 44 49 55 01 08

20.1 42.3 44.9 26.4 45.9 39.2

-1 1 1 1 1 1

07 07 08 08 08 09

39.6 57.0 14.7 32.6 51.0 09.7

43 38 33 27 21 15

24.3 37.5 21.6 37.8 29.8 01.8

-0 0 0 0 0 0

55 55 56 56 57 57

12.3 46.2 19.6 52.6 25.0 56.7

Dec.

1 6 11 16 21 26

293 293 293 293 293 293

16 24 32 41 50 59

05.0 00.9 23.0 09.9 17.3 41.5

-1 1 1 1 1 1

09 09 10 10 10 11

29.0 48.8 09.2 30.3 52.1 14.7

08 01

16.1 17.8

-0 -0

58 58

27.9 58.3

31 36

294 294

09 19

20.1 08.9

-1 -1

11 12

38.1 02.3

N.B : Pluto is now classified as a dwarf planet as per resolution of I.A.U

198

PLUTO, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Apparent Right Ascension

Red. To Astrom. (J 2000.0)

Apparent Declination

Red. To True Distance Hor. Ephemeris Astrom. from the Earth Parallax Transit (J 2000.0)

1 6 11 16 21 26

h 19 19 19 19 19 19

m 37 37 38 39 40 40

s 09.77 52.45 35.55 18.72 01.80 44.53

s +68.83 68.82 68.89 68.90 68.94 69.02

° ' -22 13 22 12 22 10 22 9 22 8 22 7

" 16.9 04.5 50.8 37.1 22.9 09.7

" -159.47 160.58 161.87 162.77 164.13 165.32

34.910 171 34.928 382 34.939 315 34.942 941 34.939 237 34.928 221

" 0.25 0.25 0.25 0.25 0.25 0.25

h 12 12 12 11 11 11

m 55 36 17 58 39 20

31 5 10 15 20 25

19 19 19 19 19 19

41 42 42 43 44 44

26.57 07.72 47.76 26.40 03.51 38.80

+69.06 69.13 69.24 69.29 69.41 69.51

-22 22 22 22 22 22

5 4 3 2 1 0

58.1 48.2 41.1 37.3 37.2 41.8

-166.34 167.65 168.76 169.82 171.10 172.04

34.910 001 34.884 769 34.852 777 34.814 291 34.769 579 34.718 976

0.25 0.25 0.25 0.25 0.25 0.25

11 10 10 10 9 9

01 42 23 04 45 26

1 6 11 16 21 26

19 19 19 19 19 19

45 45 46 46 47 47

12.05 43.14 11.84 38.03 01.60 22.31

+69.58 69.72 69.84 69.96 70.11 70.22

-21 21 21 21 21 21

59 59 58 57 57 57

51.3 06.3 27.6 55.1 29.6 11.5

-173.12 174.31 175.13 176.27 177.18 177.94

34.662 900 34.601 824 34.536 244 34.466 641 34.393 505 34.317 397

0.25 0.25 0.25 0.26 0.26 0.26

9 8 8 8 7 7

07 48 28 09 50 31

31 5 10 15 20 25

19 19 19 19 19 19

47 47 48 48 48 48

40.15 55.02 06.80 15.57 21.18 23.65

+70.37 70.54 70.67 70.85 71.01 71.15

-21 21 21 21 21 21

57 56 57 57 57 58

00.7 58.0 03.1 16.1 37.6 06.9

-178.93 179.65 180.33 181.14 181.57 182.14

34.238 925 34.158 715 34.077 375 33.995 472 33.913 601 33.832 398

0.26 0.26 0.26 0.26 0.26 0.26

7 6 6 6 5 5

11 52 32 13 53 34

30 5 10 15 20 25

19 19 19 19 19 19

48 48 48 48 47 47

23.06 19.39 12.75 03.25 50.90 35.90

+71.35 71.51 71.68 71.87 72.02 72.19

-21 58 21 59 22 0 22 1 22 2 22 3

44.2 29.5 22.1 22.1 29.1 42.2

-182.69 182.86 183.33 183.47 183.47 183.65

33.752 511 33.674 558 33.599 099 33.526 663 33.457 801 33.393 066

0.26 0.26 0.26 0.26 0.26 0.26

5 4 4 4 3 3

14 54 34 15 55 35

30 4 9 14 19 24

19 19 19 19 19 19

47 46 46 46 45 45

18.41 58.55 36.61 12.69 47.04 19.95

+72.38 72.51 72.70 72.85 72.97 73.14

-22 5 22 6 22 7 22 9 22 11 22 12

01.6 26.3 55.6 29.5 06.5 46.4

-183.47 183.27 183.16 182.64 182.28 181.85

33.332 983 33.278 009 33.228 522 33.184 889 33.147 475 33.116 614

0.26 0.26 0.26 0.27 0.27 0.27

3 2 2 2 1 1

15 55 35 15 55 35

29 4 9 14 19 24

19 19 19 19 19 19

44 44 43 43 42 42

51.59 22.31 52.37 21.95 51.43 21.06

+73.25 73.37 73.50 73.56 73.65 73.74

-22 22 22 22 22 22

14 16 17 19 21 23

28.6 11.8 55.9 39.8 22.7 04.3

-181.07 180.61 179.81 178.95 178.30 177.30

33.092 575 33.075 529 33.065 591 33.062 868 33.067 443 33.079 340

0.27 0.27 0.27 0.27 0.27 0.27

1 0 0 0 23 23

15 54 34 14 50 30

29 3 8 13 18

19 19 19 19 19

41 41 40 40 40

51.11 21.94 53.72 26.74 01.31

+73.77 73.85 73.87 73.86 +73.90

-22 22 22 22 -22

24 26 27 29 30

43.5 19.6 52.5 21.1 45.0

-176.43 175.64 174.56 173.75 -172.92

33.098 493 33.124 745 33.157 921 33.197 831 33.244 247

0.27 0.27 0.27 0.26 0.26

23 22 22 22 21

10 49 29 09 49

N.B: Pluto is now classified as a dwarf planet as per resolution of I A U

199

PLUTO, 2020 RIGHT ASCENSION AND DECLINATION FOR 0h TERRESTRIAL TIME Date

Apparent Right Ascension

Red. To Astrom. (J 2000.0)

Apparent Declination

Red. To True Distance Hor. Ephemeris Astrom. from the Earth Parallax Transit (J 2000.0)

Aug. 18 23 28 Sept. 2 7 12

h 19 19 19 19 19 19

m 40 39 39 38 38 38

s 01.31 37.59 15.90 56.43 39.30 24.76

s +73.90 73.87 73.86 73.84 73.76 73.72

° -22 22 22 22 22 22

' 30 32 33 34 35 36

" 45.0 03.9 16.8 24.0 24.7 18.5

" -172.92 171.89 171.27 170.38 169.61 169.13

33.244 247 33.296 871 33.355 308 33.419 125 33.487 891 33.561 163

" 0.26 0.26 0.26 0.26 0.26 0.26

h 21 21 21 20 20 20

m 49 29 09 49 29 09

17 22 27 Oct. 2 7 12

19 19 19 19 19 19

38 38 37 37 37 37

12.95 03.98 58.05 55.11 55.28 58.64

+73.67 73.58 73.54 73.44 73.34 73.28

-22 22 22 22 22 22

37 37 38 38 38 39

05.6 45.3 17.6 42.7 60.0 09.8

-168.40 167.98 167.65 167.18 167.09 167.02

33.638 458 33.719 218 33.802 832 33.888 700 33.976 243 34.064 874

0.26 0.26 0.26 0.26 0.26 0.26

19 19 19 18 18 18

49 30 10 50 31 11

17 22 27 Nov. 1 6 11

19 19 19 19 19 19

38 38 38 38 39 39

05.12 14.83 27.66 43.51 02.39 24.15

+73.16 73.09 73.01 72.90 72.83 72.76

-22 22 22 22 22 22

39 39 38 38 38 37

12.4 07.1 54.8 35.3 08.7 35.7

-166.85 167.18 167.23 167.52 168.08 168.42

34.153 975 34.242 874 34.330 906 34.417 460 34.501 954 34.583 812

0.26 0.26 0.26 0.26 0.25 0.25

17 17 17 16 16 16

51 32 12 53 34 14

16 21 26 Dec. 1 6 11

19 19 19 19 19 19

39 40 40 41 41 42

48.68 15.91 45.55 17.50 51.59 27.54

+72.67 72.64 72.56 72.50 72.49 72.43

-22 22 22 22 22 22

36 36 35 34 33 32

56.0 10.3 19.0 22.1 20.5 14.6

-169.11 169.85 170.45 171.43 172.33 173.16

34.662 436 34.737 222 34.807 634 34.873 203 34.933 502 34.988 115

0.25 0.25 0.25 0.25 0.25 0.25

15 15 15 14 14 14

55 36 17 58 39 20

16 21 26 31 36

19 19 19 19 19

43 43 44 45 45

05.25 44.42 24.78 06.16 48.26

+72.43 72.43 72.39 72.42 +72.43

-22 22 22 22 -22

31 29 28 27 25

04.4 51.1 34.9 16.3 56.4

-174.40 175.31 176.42 177.72 -178.71

35.036 625 35.078 668 35.113 975 35.142 348 35.163 627

0.25 0.25 0.25 0.25 0.25

14 13 13 13 12

00 41 22 04 45

N.B: Pluto is now classified as a dwarf planet as per resolution of I A U

200

MAJOR PLANETS, 2020 HELIOCENTRIC OSCULATING ORBITAL ELEMENTS REFERRED TO THE MEAN ECLIPTIC AND EQUINOX OF J 2000.0 Date

Nov'19 Jan'20 Feb Mar May Jun Jul Aug Oct Nov Dec Feb' 21

23 2 11 23 2 11 21 30 9 18 28 6

Julian Date 245

Inclination i

8800.5 8840.5 8880.5 8920.5 8960.5 9000.5 9040.5 9080.5 9120.5 9160.5 9200.5 9240.5

° 7.0038 7.0038 7.0038 7.0038 7.0038 7.0038 7.0037 7.0037 7.0037 7.0070 7.0037 7.0037

Longitude Asc. Node Perihelion  Ω ° 48.307 48.307 48.306 48.306 48.306 48.306 48.306 48.305 48.305 48.305 48.305 48.305

Mean Distance a

Daily Motion n

Eccentricity

MERCURY ° 77.489 0.387 098 77.489 0.387 098 77.490 0.387 097 77.489 0.387 097 77.489 0.387 098 77.489 0.387 097 77.490 0.387 100 77.491 0.387 010 77.492 0.387 099 77.492 0.387 099 77.491 0.387 098 77.492 0.387 098

° 4.092 36 4.092 36 4.092 37 4.092 37 4.092 36 4.092 37 4.092 31 4.092 34 4.092 33 4.092 34 4.092 35 4.092 36

0.205 651 0.205 651 0.205 651 0.205 652 0.205 648 0.205 647 0.205 635 0.205 634 0.205 633 0.205 633 0.205 637 0.205 636

° 64.2144 227.9086 31.6028 195.2971 358.9913 162.6855 326.3785 130.0715 293.7648 97.4582 261.1516 64.8455

1.602 14 1.602 16 1.602 15 1.602 15 1.602 15 1.602 10 1.602 12 1.602 16 1.602 15 1.602 14 1.602 15 1.602 14

0.006 733 0.006 744 0.006 746 0.006 746 0.006 745 0.006 752 0.006 772 0.006 787 0.006 791 0.006 793 0.006 790 0.006 786

286.2376 350.3233 54.4099 118.4955 182.5813 246.6655 310.7476 14.8333 78.9199 143.0053 207.0913 271.1773

0.985 62 0.985 60 0.985 60 0.985 61 0.985 62 0.985 61 0.985 58 0.985 59 0.985 61 0.985 62 0.985 62 0.985 61

0.016 749 0.016 754 0.016 755 0.016 750 0.016 742 0.016 728 0.016 703 0.016 706 0.016 714 0.016 717 0.016 719 0.016 724

51.5530 90.9764 130.3994 169.8236 209.2491 248.6754 288.1000 327.5224 6.9465 46.3717 85.7961 125.2195

e

Mean Longitude L

VENUS Nov'19 Jan' 20 Feb Mar May Jun Jul Aug Oct Nov Dec Feb' 21

23 2 11 23 2 11 21 30 9 18 28 6

8800.5 8840.5 8880.5 8920.5 8960.5 9000.5 9040.5 9080.5 9120.5 9160.5 9200.5 9240.5

3.3946 3.3946 3.3946 3.3946 3.3946 3.3946 3.3946 3.3946 3.3946 3.3946 3.3946 3.3945

76.625 76.625 76.625 76.625 76.624 76.624 76.623 76.623 76.623 76.623 76.623 76.623

131.51 131.53 131.50 131.46 131.46 131.63 131.73 131.80 131.77 131.72 131.70 131.75

0.723 331 0.723 324 0.723 326 0.723 328 0.723 327 0.723 342 0.723 336 0.723 323 0.723 325 0.723 329 0.723 325 0.723 330 EARTH*

Nov'19 Jan' 20 Feb Mar May Jun Jul Aug Oct Nov Dec Feb' 21

23 2 11 23 2 11 21 30 9 18 28 6

8800.5 8840.5 8880.5 8920.5 8960.5 9000.5 9040.5 9080.5 9120.5 9160.5 9200.5 9240.5

0.0026 0.0026 0.0026 0.0026 0.0026 0.0027 0.0027 0.0027 0.0027 0.0027 0.0027 0.0027

176.8 176.8 176.6 176.6 176.7 177.4 176.7 176.4 176.3 176.4 176.5 176.4

103.073 103.029 103.001 102.981 102.961 102.943 102.943 102.980 103.033 103.052 103.036 103.001

0.999 996 1.000 007 1.000 008 1.000 000 0.999 994 0.999 999 1.000 021 1.000 014 0.999 997 0.999 992 0.999 997 1.000 001

* Values labelled for the Earth are actually for the Earth/ Moon barycente FORMULAS Mean anomaly, M = L -  Argument of perihelion, measured from nodeω = - Ω True anomaly, =M + (2e - e 3/4)sin M + (5e 2/4)sin 2M + (13 e 3/12)sin 3M +…. in radians True distance, r = a (1 - e2)/ (1 + e cos ) Heliocentric rectangular co- ordinates, referred to the ecliptic of date, may be computed from x = r{ cos (ω ) cos Ω - sin ( + ω ) cos i sin Ω } y = r{ cos ( ω ) sin Ω + sin (+ ω ) cos i cos Ω} z = r sin ( + ω ) sin i

201

MAJOR PLANETS, 2020 HELIOCENTRIC OSCULATING ORBITAL ELEMENTS REFERRED TO THE MEAN ECLIPTIC AND EQUINOX OF J 2000.0 Date

Julian Date 245

Inclination i

Longitude Asc. Node Perihelion  Ω MARS ° ° 49.501 336.189 49.501 336.184 49.501 336.169 49.501 336.142 49.500 336.114 49.499 336.098 49.497 336.098 49.496 336.104 49.494 336.108 49.494 336.116 49.494 336.126 49.494 336.140

Mean Distance a

Daily Motion n

Eccentricity

1.523 60 1.523 61 1.523 65 1.523 72 1.523 78 1.523 79 1.523 75 1.523 68 1.523 63 1.523 61 1.523 63 1.523 67

° 0.524 080 0.524 075 0.524 055 0.524 020 0.523 989 0.523 982 0.524 004 0.524 040 0.524 069 0.524 076 0.524 066 0.524 048

0.093 505 0.093 505 0.093 495 0.093 482 0.093 476 0.093 463 0.093 435 0.093 393 0.093 355 0.093 334 0.093 330 0.093 332

° 197.5675 218.5313 239.4939 260.4543 281.4122 302.3687 323.3270 344.2887 5.2530 26.2186 47.1825 68.1446

e

Mean Longitude L

Nov'19 Jan' 20 Feb Mar May Jun Jul Aug Oct Nov Dec Feb' 21

23 2 11 23 2 11 21 30 9 18 28 6

8800.5 8840.5 8880.5 8920.5 8960.5 9000.5 9040.5 9080.5 9120.5 9160.5 9200.5 9240.5

° 1.8481 1.8481 1.8480 1.8480 1.8480 1.8479 1.8479 1.8479 1.8479 1.8480 1.8479 1.8479

Nov'19 Jan' 20 Feb Mar May Jun Jul Aug Oct Nov Dec Feb' 21

23 2 11 23 2 11 21 30 9 18 28 6

8800.5 8840.5 8880.5 8920.5 8960.5 9000.5 9040.5 9080.5 9120.5 9160.5 9200.5 9240.5

1.3037 1.3036 1.3036 1.3036 1.3036 1.3036 1.3036 1.3036 1.3036 1.3036 1.3036 1.3036

100.516 100.516 100.516 100.516 100.516 100.516 100.516 100.516 100.516 100.516 100.516 100.516

JUPITER 14.024 14.020 14.019 14.999 14.961 14.925 14.906 14.916 14.929 14.937 14.926 14.915

5.203 39 5.203 41 5.203 41 5.203 50 5.203 66 5.203 81 5.203 90 5.203 85 5.203 76 5.203 68 5.203 69 5.203 70

0.083 078 0.083 077 0.083 077 0.083 075 0.083 071 0.083 067 0.083 065 0.083 067 0.083 069 0.083 070 0.083 070 0.083 070

0.048 733 0.048 723 0.048 708 0.048 686 0.048 671 0.048 664 0.048 665 0.048 658 0.048 642 0.048 618 0.048 599 0.048 587

277.2581 280.5801 283.9014 287.2220 290.5431 293.8648 297.1873 300.5094 303.8306 307.1511 310.4715 313.7926

Nov'19 Jan' 20 Feb Mar May Jun Jul Aug Oct Nov Dec Feb' 21

23 2 11 23 2 11 21 30 9 18 28 6

8800.5 8840.5 8880.5 8920.5 8960.5 9000.5 9040.5 9080.5 9120.5 9160.5 9200.5 9240.5

2.4862 2.4862 2.4862 2.4863 2.4862 2.4862 2.4862 2.4862 2.4862 2.4863 2.4863 2.4863

113.595 113.595 113.595 113.595 113.595 113.595 113.595 113.595 113.595 113.595 113.595 113.595

SATURN 92.041 91.920 91.806 91.692 91.556 91.407 91.250 91.112 90.988 90.872 90.744 90.608

9.572 3 9.572 2 9.572 0 9.572 1 9.572 3 9.572 6 9.572 8 9.572 7 9.572 5 9.572 4 9.572 5 9.572 7

0.033 301 0.033 301 0.033 302 0.033 302 0.033 300 0.033 299 0.033 298 0.033 299 0.033 299 0.033 300 0.033 299 0.033 298

0.051 794 0.051 846 0.051 906 0.051 951 0.051 980 0.052 014 0.052 072 0.052 160 0.052 252 0.052 337 0.052 400 0.052 467

292.7290 294.0755 295.4216 296.7670 298.1138 299.4621 300.8122 302.1623 303.5113 304.8592 306.2068 307.5554

Nov'19 Feb' 20 May Jul Oct Dec Mar' 21

23 11 2 21 9 28 18

8800.5 8880.5 8960.5 9040.5 9120.5 9200.5 9280.5

0.7706 0.7705 0.7704 0.7704 0.7704 0.7703 0.7703

74.083 74.085 74.090 74.093 74.093 74.097 74.096

URANUS 174.12 173.89 173.70 173.39 172.98 172.62 172.21

19.147 3 19.154 5 19.160 7 19.169 3 19.178 6 19.186 2 19.194 9

0.011 771 0.011 765 0.011 759 0.011 751 0.011 742 0.011 735 0.011 728

0.047 739 0.047 388 0.047 066 0.046 651 0.046 283 0.045 987 0.045 661

38.1445 39.0751 40.0033 40.9305 41.8666 42.8032 43.7392

Nov'19 Feb' 20 May Jul Oct Dec Mar' 21

23 11 2 21 9 28 18

8800.5 8880.5 8960.5 9040.5 9120.5 9200.5 9280.5

1.7704 1.7702 1.7700 1.7698 1.7696 1.7695 1.7693

131.780 131.775 131.771 131.765 131.760 131.758 131.752

NEPTUNE 23.51 30.142 0 22.28 30.157 0 21.06 30.171 5 19.92 30.189 7 19.69 30.203 7 19.59 30.215 1 19.52 30.227 8

0.005 960 0.005 955 0.005 951 0.005 946 0.005 942 0.005 938 0.005 935

0.008 522 0.008 990 0.009 434 0.010 014 0.010 523 0.010 940 0.011 410

348.0054 348.4950 348.9804 349.4722 349.9730 350.4698 350.9696

Distances are in astronomical units

202

CENTRE OF MASS OF THE SOLAR SYSTEM, 2020 HELIOCENTRIC RECTANGULAR CO-ORDINATES EQUATORIAL RECTANGULAR CO-ORDINATES OF THE BARYCENTRES (SUN TO MARS) AND S9 (SUN TO PLUTO) REFERRED TO THE MEAN EQUINOX AND EQUATOR OF J 2000.0 Barycentre S4 Date

4

Centre of Mass of the Solar System Barycentre S9

(In units of 10-10 a.u)

-9

(In units of 10 a.u) Jan.

Feb.

Mar. Apr.

May June

July Aug.

Sept. Oct.

Nov. Dec.

0 10 20 30 9 19

x +37911256 38740022 39565157 40386851 41205424 42021875

y -68162195 67963653 67756980 67542798 67321819 67094800

z -29801540 29740454 29675653 29607423 29536101 29462168

X +3790271 3873691 3956852 4039757 4122413 4204863

Y -6818756 6799200 6778730 6757378 6735180 6712174

Z -2981143 2975172 2968796 2962030 2954890 2947401

29 10 20 30 9 19

+42837811 43654276 44471756 45290529 46110699 46932095

-66861652 66621546 66373652 66117157 65851191 65574846

-29385691 29306355 29223772 29137584 29047404 28952834

+4287179 4369406 4451561 4533649 4615668 4697602

-6688356 6663686 6638123 6611627 6584156 6555665

-2939565 2931368 2922790 2913813 2904418 2894586

29 9 19 29 8 18

+47754206 48576339 49398236 50219807 51040109 51857779

-65287341 64988218 64677261 64353594 64016248 63664718

-28853495 28749186 28639887 28525236 28404719 28278012

+4779417 4861071 4942543 5023821 5104850 5185554

-6526117 6495490 6463775 6430929 6396906 6361682

-2884298 2873544 2862324 2850620 2838407 2825669

28 8 18 28 7 17

+52671381 53479532 54280879 55074148 55858391 56633701

-63298900 62919010 62525521 62119270 61701569 61273791

-28144992 28005672 27860209 27708902 27552350 27391253

+5265853 5345671 5424932 5503565 5581514 5658777

-6325254 6287635 6248850 6208944 6167984 6126042

-2812401 2798604 2784287 2769465 2754169 2738435

27 6 16 26 6 16

+57400433 58158547 58907983 59648897 60381588 61106466

-60836501 60390158 59935407 59472931 59003330 58527064

-27225910 27056475 26883234 26706477 26526504 26343515

+5735363 5811263 5886466 5960973 6034790 6107931

-6083148 6039328 5994617 5949052 5902666 5855485

-2722279 2705709 2688741 2671390 2653673 2635600

26 5 15 25 5 15

+61823896 62534572 63239844 63940803 64637713 65330490

-58044604 57556547 57063020 56563219 56056245 55541395

-26157757 25969583 25779183 25586234 25390279 25190970

+6180406 6252243 6323501 6394228 6464429 6534093

-5807536 5758852 5709443 5659272 5608298 5556490

-2617185 2598447 2579397 2560020 2540294 2520204

25 35

+66018879 +66702414

-55018068 -54485773

-24987976 -24781021

+6603200 +6671719

-5503821 -5450271

-2499734 -2478872

The heliocentric equatorial rectangular co-ordinates of the barycentre of the solar system referred to the mean equator and equinox of J 2020.5 are given by r = Pr0, where r and r0 are the column vectors of the co-ordinates X,Y, Z and X0,Y0, Z0 referred to J 2020.5 and J 2000.0 respectively.

PART - II STARS

204

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

35 9 82 902 22 783

280 74 674 9072 188 7957

 Sculptoris  Ceti φ Eridani  Piscium  Ceti  Cephei

4.31 3.56 3.56 4.01 2.04 3.43

º 0 1 1 2 2 4

' 46 12 17 52 52 58

Annual Annual Variation Proper Motion " " " 51.47 50.620 +0.025 10.08 50.350 -0.028 28.82 51.190 +0.110 12.75 50.340 +0.095 20.22 50.710 +0.242 08.98 51.240 +2.354

156 869 848 7 40 803

1336 8762 8585 39 334 8162

 Reticuli o Andromedae  Lacertae γ Pegasi  Ceti  Cephei

3.35 3.62 3.77 2.83 3.45 2.44

7 8 8 9 12 13

48 03 25 26 03 03

23.17 48.45 38.04 30.64 19.80 35.31

52.760 49.880 49.880 50.190 50.580 49.470

23.93 02.63 26.79 01.78 07.78 50.25

+0.080 +0.080 +0.040 +0.110 -0.080 +0.050

-0.015 -0.017 -0.070 -0.011 -0.213 -0.100

836 1 47 723 59 890

8465 15 402 7310 509 8961

 Cephei  Andromedae* θ Ceti  Draconis  Ceti λ Andromedae

3.35 2.06 3.6 3.07 3.5 3.82v

14 14 16 17 18 18

14 35 30 25 05 34

41.15 38.35 44.16 56.80 54.20 12.95

49.510 +0.028 +61 08 52.74 50.140 +0.056 +25 40 48.58 50.260 -0.163 -15 46 02.73 47.550 +0.757 +82 53 12.42 49.130 -1.371 -24 48 23.31 49.750 -0.133 +43 46 27.96

+0.140 -0.050 +0.000 +0.090 +1.650 -0.260

-0.008 -0.207 -0.171 -0.093 +1.463 -0.441

1075 71 1033 20 62 106

794 585 361 165 539 897

 Eridani  Ceti  Piscium* δ Andromedae  Ceti θ Eridani p

4.11 4 5.24 3.27 3.73 3.25

19 19 20 22 22 23

03 42 09 05 14 33

43.48 59.56 52.47 57.72 15.13 42.15

51.010 50.690 50.410 50.200 50.470 50.810

49.88 00.30 46.53 03.99 01.15 19.46

+0.090 +0.120 +0.090 +0.070 +0.160 +0.270

-0.095 -0.076 -0.106 -0.141 -0.051 +0.038

101 1154 50 33 42 863

841 2015 437 269 337 8694

 Fornacis  Doradus  Piscium  Andromedae  Andromedae  Cephei

4.46 4.35 3.62 3.87 2.06 3.52

26 26 27 29 30 33

31 48 06 27 41 31

28.56 50.920 +0.212 -45 51 14.68 11.39 63.160 -0.278 -88 15 08.04 08.14 50.280 +0.024 +5 22 44.24 41.03 50.250 +0.174 +29 39 36.13 28.66 50.240 +0.126 +25 56 37.99 16.60 49.280 -0.304 +62 37 03.36

+0.350 +0.280 +0.240 +0.230 +0.090 +0.270

+0.103 +0.030 -0.015 -0.038 -0.178 -0.017

66 1085 17 2 809 64

553 919 153 21 8238 544

 Arietis* 3  Eridani  Cassiopeiae  Cassiopeiae  Cephei  Trianguli

2.64 4.09 3.66 2.27 3.23 3.41

34 34 35 35 35 37

15 49 20 24 49 08

22.82 17.70 58.94 11.34 36.86 46.44

50.300 50.390 49.960 50.310 49.280 50.110

+0.051 -0.198 +0.016 +0.463 +0.028 -0.079

+8 -38 +44 +51 +71 +16

29 54 43 12 09 48

17.33 15.53 17.10 50.39 16.11 03.74

+0.160 +0.300 +0.280 -0.170 +0.300 +0.090

-0.138 +0.001 -0.018 -0.472 -0.008 -0.223

91 74 21 171 104

779 617 168 1465 874

 Ceti  Arietis  Cassiopeiae  Doradus  Eridani

4.07 2 2.23 3.27 3.89

37 37 38 38 39

51 56 04 07 02

29.91 57.31 05.66 25.41 14.20

50.390 50.370 49.960 51.700 50.460

+0.013 +0.130 +0.036 +0.155 +0.008

-14 +9 +46 -74 -24

27 57 37 34 32

35.82 56.75 25.25 48.59 46.36

+0.310 +0.110 +0.260 +0.290 +0.100

-0.008 -0.204 -0.056 -0.031 -0.233

*

Star

No. 1 : Alpheratz, Uttara Bhadrapada - 2 No. 1033 : Revati

+0.298 +0.022 +0.200 +0.001 +0.151 +0.340

+0.169 +0.134 +0.112 +0.092 +0.025 -0.051

No.

º -32 -10 -58 +6 -20 +71

' 30 01 59 21 47 46

" 46.83 17.64 09.12 44.39 00.88 56.41

-78 +43 +53 +12 -16 +68

02 45 17 36 07 54

-51 -31 -0 +24 -20 -53

42 02 12 21 20 44

Annual Annual Variation Proper Motion " " +0.040 -0.007 +0.030 -0.028 -0.030 -0.082 -0.110 -0.167 +0.000 -0.068 +0.450 +0.369

66 : Sheratan, Asvini

Annual rate of Precession in longitude for the middle of the year = 50".29

205

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

75 79 32 73 107 155

622 664 264 603 911 1326

 Trianguli γ Trianguli γ Cassiopeiae γ Andromed. p  Ceti  Horologii

3 4.01 var. 2.26 2.53 3.86

º 42 43 44 44 44 46

' 38 48 12 30 36 06

Annual Annual Variation Proper Motion " " " 20.54 50.310 +0.134 14.62 50.220 +0.028 56.32 49.980 +0.027 39.77 50.160 +0.024 24.23 50.330 -0.032 47.13 50.770 -0.073

48 127 100 135 121 123

403 1084 838 1136 1030 1038

δ Cassiopeiae  Eridani 41 Arietis*  Eridani o Tauri  Tauri

2.68 3.73 3.63 3.54 3.6 3.74

48 48 48 51 51 52

12 26 29 08 26 11

59.50 56.44 23.21 59.77 59.19 56.10

50.320 49.390 50.280 50.560 50.250 50.390

+0.323 -1.054 +0.029 +0.113 -0.084 +0.049

+46 -27 +10 -28 -9 -8

24 42 27 40 19 47

16.01 43.20 03.96 11.71 56.49 48.01

+0.170 +0.660 +0.250 +1.130 +0.340 +0.340

-0.202 +0.281 -0.132 +0.744 -0.059 -0.053

212 149 63 109 1129 111

1922 1231 542 921 1502 936

 Doradus γ Eridani  Cassiopeiae  Persei  Caeli  Persei

3.48v 2.95 3.38 var. 4.45 var.

52 54 55 55 56 56

25 09 02 11 26 27

32.71 18.02 55.23 50.19 05.78 12.48

53.300 50.490 50.060 50.310 50.390 50.200

+0.072 +0.039 +0.024 +0.099 -0.346 +0.003

-85 -33 +47 +20 -62 +22

02 12 33 34 59 25

30.97 01.95 01.24 34.19 09.69 51.26

+0.400 +0.280 +0.380 +0.270 +0.380 +0.410

+0.007 -0.123 -0.034 -0.139 -0.032 -0.002

103 99 136 170 151 139

854 834 1142 1464 1251 1165

 Persei  Persei 17 Tauri v 2 Eridani  Tauri  Tauri*

3.95 3.76 3.7 3.82 3.91 2.87

58 58 59 60 60 60

11 59 41 10 12 16

50.48 14.58 53.70 21.63 21.07 43.44

50.140 50.150 50.290 50.470 50.350 50.290

-0.003 +0.013 +0.009 -0.076 +0.005 +0.008

+34 +37 +4 -51 -14 +4

22 29 11 48 26 03

25.13 03.03 31.17 53.23 57.41 11.10

+0.410 +0.410 +0.380 +0.430 +0.420 +0.380

-0.005 -0.019 -0.049 -0.002 -0.004 -0.049

108 893 150 120 144 134

915 8974 1239 1017 1203 1135

γ Persei γ Cephei λ Tauri  Persei  Persei  Persei

2.93 3.21 3.47v 1.79 2.85 3.77

60 60 60 62 63 64

18 22 55 22 24 06

25.47 43.60 15.66 00.55 36.21 32.64

50.160 -0.002 +34 31 57.52 50.150 +0.268 +64 40 22.86 50.310 -0.009 -7 57 26.71 50.200 +0.018 +30 07 40.10 50.260 +0.004 +11 20 09.30 50.210 -0.015 +22 09 21.95

+0.430 +0.550 +0.420 +0.400 +0.430 +0.440

-0.004 +0.119 -0.011 -0.030 -0.011 +0.002

131 148 147 159 162 164

1122 1228 1220 1346 1373 1409

 Persei  Persei  Persei γ Tauri  Tauri  Tauri

3.01 4.04 2.89 3.65 3.76 3.54

65 65 65 66 67 68

05 15 57 05 09 45

17.15 30.96 50.17 34.32 27.83 07.28

50.240 50.260 50.260 50.420 50.410 50.400

+0.021 +27 18 14.67 +0.002 +14 56 46.80 +0.013 +19 07 00.92 +0.110 -5 43 47.99 +0.101 -3 58 02.05 +0.100 -2 33 53.68

+0.410 +0.440 +0.410 +0.410 +0.400 +0.400

-0.040 -0.000 -0.029 -0.044 -0.047 -0.054

168 1134 186 179 180

1457 1543 1654 1552 1567

 Tauri* 3  Orionis  Leporis 4  Orionis 5 Orionis

0.85 3.19 3.19 3.69 3.72

70 72 72 72 72

04 12 20 23 46

33.01 50.48 33.70 14.53 38.51

50.340 50.810 50.420 50.320 50.330

+0.036 +0.481 +0.021 -0.001 +0.000

+0.260 +0.420 +0.380 +0.460 +0.460

-0.197 -0.046 -0.076 +0.001 -0.000

*

Star

No. 100 : Bharani No. 139 : Alcyone , Krittika.

º +20 +18 +48 +27 -12 -61

' 34 56 49 48 35 43

" 55.71 59.72 00.51 28.38 02.32 47.95

-5 -15 -44 -16 -20

27 22 57 46 00

Annual Annual Variation Proper Motion " " +0.260 -0.091 +0.290 -0.064 +0.340 -0.019 +0.300 -0.065 +0.280 -0.072 +0.160 -0.211

57.16 54.62 44.79 09.45 08.90

No. : Aldebaran, Rohini

Annual rate of Precession in longitude for the middle of the year = 50".29

206

LONGITUDE AND LATITUDE OF STARS, 2020.5 MEAN PLACES FOR JULY 2d.125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

188 1144 695 181 194 195

1666 1702 6927 1577 1713 1735

 Eridani  Leporis  Draconis  Aurigae  Orionis  Orionis

2.79 3.31v 3.57 2.69 0.12 3.6

º 75 75 76 76 77 78

' 33 40 10 55 06 08

Annual Annual Variation Proper Motion " " " 42.50 50.220 -0.116 52.57 50.410 +0.051 55.35 44.150 +3.497 32.80 50.280 +0.001 58.27 50.330 +0.000 01.21 50.310 -0.018

1137 183 185 204 201 178

1612 1605 1641 1829 1790 1542

 Aurigae  Aurigae  Aurigae  Leporis γ Orionis  Camelopardi

3.75 var. 3.17 2.84 1.64 4.29

78 79 79 79 81 81

55 07 43 57 13 15

11.00 39.68 57.40 32.12 58.17 56.99

50.280 +0.007 +18 12 17.39 50.280 -0.001 +20 56 49.25 50.310 +0.024 +18 17 09.98 50.320 -0.015 -43 54 44.60 50.300 -0.010 -16 48 48.55 50.270 +0.001 +43 25 17.82

+0.440 +0.460 +0.400 +0.380 +0.460 +0.470

-0.023 -0.004 -0.070 -0.088 -0.013 +0.006

182 207 193 215 206 202

1603 1865 1708 1956 1852 1791

 Camelopardi  Leporis  Aurigae  Columbae  Orionis  Tauri

4.03 2.58 0.08 2.64 2.23 1.65

81 81 82 82 82 82

33 40 08 27 40 51

14.44 01.37 40.17 21.26 58.49 40.96

50.260 50.320 50.330 50.330 50.310 50.310

01.03 18.43 52.36 21.75 10.65 12.29

+0.460 +0.480 +0.050 +0.440 +0.460 +0.290

-0.015 +0.002 -0.429 -0.027 -0.002 -0.176

209 210 (GC) 211 217 219

1899 1903 1879 1910 1983 1998

 Orionis  Orionis  Orionis*  Tauri γ Leporis  Leporis

2.77 1.7 3.56 3 3.6 3.55

83 83 83 85 85 86

17 45 59 04 07 16

02.15 00.18 35.61 15.62 47.67 21.25

50.300 +0.000 -29 11 50.34 50.300 +0.001 -24 30 13.46 50.290 -0.001 -13 22 00.40 50.300 -0.000 -2 11 35.09 49.850 -0.440 -45 49 03.33 50.270 -0.020 -38 12 47.36

+0.470 +0.470 +0.470 +0.450 +0.120 +0.470

+0.001 -0.002 -0.002 -0.021 -0.359 -0.000

220 223 222 907 224 226

2004 2040 2035 424 2061 2085

 Orionis  Columbae  Leporis  Ursae Mins.  Orionis*  Leporis

2.06 3.12 3.81 2.02 var. 3.71

86 86 87 88 89 89

41 42 27 51 02 11

05.91 23.55 18.69 16.36 27.95 09.42

50.290 50.410 50.580 50.400 50.310 50.210

04.84 28.66 53.27 14.10 27.48 00.44

+0.470 +0.870 -0.190 +0.430 +0.480 +0.610

-0.002 +0.399 -0.653 -0.036 +0.009 +0.140

229 227 225 1168 241 244

2120 2088 2077 2219 2286 2298

Columbae Aurigae Aurigae  Aurigae  Geminorum 8 Monocerotis

3.96 1.9 3.72 4.35 2.88 4.44

89 90 90 93 95 96

53 11 12 39 35 32

51.41 47.38 24.13 02.57 18.92 27.58

50.260 +0.055 -66 15 05.89 50.250 -0.062 +21 30 39.11 50.410 +0.095 +30 50 50.69 50.240 -0.066 +6 06 17.27 50.360 +0.059 -0 49 05.28 50.250 -0.019 -18 42 53.39

+0.460 +0.470 +0.340 +0.200 +0.350 +0.470

-0.014 +0.000 -0.125 -0.264 -0.109 +0.010

1173 243 240 251 254

2343 2294 2282 2421 2473

 Geminorum  Canis Maj.  Canis Maj. γ Geminorum  Geminorum

4.15 97 1.98 97 3.02 97 1.93 99 2.98 100

05 28 39 23 13

19.48 50.280 -0.007 -3 03 13.78 25.33 50.200 -0.008 -41 15 03.99 47.84 50.170 +0.015 -53 22 12.27 28.50 50.330 +0.045 -6 44 24.50 30.62 50.290 -0.005 +2 04 20.81

+0.440 +0.460 +0.470 +0.410 +0.440

-0.014 -0.000 +0.003 -0.039 -0.014

*

Star

No. GC : Mrgasiras .

-0.010 +0.001 +0.046 +0.009 +0.002 +0.012

+0.002 +0.136 +0.301 +0.037 +0.027 -0.051

º -27 -39 +83 +10 -31 -29

+37 -41 +22 -57 -22 +5

-33 -59 -44 +66 -16 -37

' 51 02 34 27 07 50

26 03 51 22 57 23

04 10 17 06 01 36

" 34.30 51.36 17.28 25.36 12.48 06.16

Annual Annual Variation Proper Motion " " +0.390 -0.071 +0.440 -0.030 +0.620 -0.501 +0.450 -0.018 +0.470 -0.001 +0.460 -0.007

No. 224 : Betelgeuse , Mag. 0.4 to 1.3 Ardra.

Annual rate of Precession in longitude for the middle of the year = 50".29

207

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

261 256 257 245 269 252

2540 2484 2491 2326 2650 2451

º 3.6 101 θ Geminorum Geminorum 3.36 101  Canis Maj cg -1.5 104  Carinae -0.7 105  Geminorum 3.79v 105  Puppis 3.17 107

' 24 29 21 14 16 25

Annual Annual Variation Proper Motion " " " 35.85 50.330 +0.003 41.55 50.170 -0.101 50.11 49.610 -0.552 37.71 49.730 +0.075 35.43 50.280 -0.009 55.53 49.900 +0.008

279 1180 277 282 1187 287

2777 2538 2763 2821 2714 2891

 Geminorum 3.53  Canis Maj. 3.96  Geminorum 3.58  Geminorum 3.79 22  Monocerotis 4.15  Gemino. Cg* 1.95

108 108 109 109 109 110

48 51 03 14 40 31

19.84 03.51 53.48 35.33 49.84 34.76

50.270 50.010 50.230 50.200 50.210 50.170

-0.024 -0 10 33.76 -0.013 -55 08 42.28 -0.042 -5 37 58.86 -0.109 +5 45 36.53 -0.002 -21 44 33.13 -0.156 +10 05 51.85

+0.420 +0.430 +0.390 +0.330 +0.430 +0.300

-0.016 +0.003 -0.043 -0.103 +0.005 -0.126

268 270 1183 285 317 295

2618 2653 2646 2845 3323 2990

 Canis Maj. 2 o Canis Maj.  Canis Maj.  Canis Min. o Ursae Maj.  Geminorum

1.5 3.02 3.47 2.9 3.36 1.14

111 111 111 112 113 113

02 17 50 28 16 29

52.17 16.31 27.52 39.10 57.31 55.24

50.040 +0.006 -51 21 27.98 50.070 -0.007 -46 07 40.71 50.030 -0.009 -50 13 24.36 50.200 -0.047 -13 29 06.37 50.360 -0.121 +40 14 41.85 49.710 -0.614 +6 41 08.32

+0.430 +0.420 +0.430 +0.370 +0.270 +0.260

+0.003 +0.002 +0.004 -0.046 -0.145 -0.158

273 294 291 263 293 283

2693 2985 2943 2553 2970 2827

 Canis Maj.  Geminorum  C. Min. cg  Puppis 26  Monoceroti  Canis Maj.

1.86 3.57 0.38 2.93 3.93 2.45

113 113 116 118 119 119

40 57 04 00 33 49

51.28 50.030 -0.006 -48 27 07.45 50.280 -0.024 +3 04 06.27 49.680 -0.541 -16 01 33.60 49.650 +0.188 -72 51 57.65 50.060 -0.078 -30 27 15.43 49.960 -0.008 -50 36

02.99 49.97 25.42 04.88 05.52 23.53

+0.420 +0.350 -0.730 +0.330 +0.360 +0.390

+0.004 -0.057 -1.132 -0.056 -0.033 +0.004

278 335 341 312 321 1204

2773 3569 3594 3249 3366 3045

 Puppis  Ursae Maj.  Ursae Maj.  Cancri  Cancri  Puppis

2.7 3.14 3.6 3.52 5.33 3.34

120 123 124 124 125 126

35 05 13 32 41 19

03.97 49.830 05.58 50.060 26.25 50.440 35.70 50.200 38.20 50.270 34.64 49.980

368 328 358 1228 1194 326

3888 3475 3775 3449 2878 3461

v Ursae Maj.  Cancri θ Ursae Maj. γ Cancri  Puppis  Cancri*

3.8 4.02 3.17 4.66 3.25 3.94

126 126 127 127 128 129

33 37 32 49 58 00

1223 433 1224 308 352

3410 4434 3418 3185 3705

 Hydrae λ Draconis  Hydrae  Puppis  Lyncis

4.16 3.84 4.44 2.81 3.13

130 130 131 131 132

35 37 29 40 07

*

Star

º +11 -10 -39 -75 -2 -66

' 01 06 36 49 02 04

" 56.81 10.10 35.52 16.50 10.84 18.37

Annual Annual Variation Proper Motion " " +0.400 -0.048 +0.250 -0.200 -0.810 -1.256 +0.460 +0.024 +0.440 -0.002 +0.430 -0.006

-0.019 -0.399 -0.015 -0.032 -0.035 -0.003

-58 +29 +28 -10 +1 -44

31 34 58 17 34 56

21.99 30.79 52.49 09.08 23.08 14.90

+0.390 +0.010 +0.300 +0.310 +0.300 +0.350

+0.002 -0.358 -0.062 -0.058 -0.054 -0.003

15.46 57.89 49.34 27.85 18.67 31.04

50.320 -0.261 50.340 -0.013 49.700 -0.820 50.220 -0.092 49.380 -0.262 50.340 +0.043

+42 +10 +34 +3 -63 +0

39 25 53 11 46 04

10.19 41.69 35.10 31.46 18.18 40.09

+0.080 +0.310 -0.510 +0.280 +0.500 +0.120

-0.269 -0.047 -0.862 -0.066 +0.157 -0.225

23.94 22.75 44.23 21.68 41.60

50.160 50.800 50.190 49.840 50.180

-12 +57 -14 -43 +17

23 14 36 16 57

26.97 34.27 00.51 05.17 55.94

+0.310 +0.290 +0.310 +0.350 +0.270

-0.024 -0.040 -0.022 +0.023 -0.054

No. 287 : Castor, Punarvasu-2, Mag. 1.95 & 2.95.

-0.064 -0.026 -0.013 -0.128 -0.227

No. 326 : Pusya.

Annual rate of Precession in longitude for the middle of the year = 50".29

208

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

1239 550 337 334 417 (329)

3627 5563 3572 3547 4301 3482

 Cancri  Ursae Min.  Cancri  Hydrae  Ursae Maj.  Hydrae m*

5.14 2.08 4.25 3.11 1.79 3.38

º 133 133 133 134 135 136

' 29 36 55 51 29 22

Annual Annual Variation Proper Motion " " " 50.33 50.330 -0.000 44.13 51.410 -0.044 41.13 50.300 +0.041 40.00 50.120 -0.101 09.03 50.640 -0.087 21.93 49.900 -0.228

472 306 416 383 347 367

4787 3165 4295 4033 3665 3873

 Draconis  Puppis  Ursae Maj. λ Ursae Maj. θ Hydrae  Leonis

3.87v 2.25 2.37 3.45 3.88 2.98

136 138 139 139 140 140

32 50 43 50 34 59

46.72 00.27 25.30 11.82 32.31 29.08

386 371 569 262 365 327

4069 3905 5735 2550 3852 3468

 Ursae Maj.  Leonis γ Ursae Min.  Pictoris o Leonis  Pyxidis

3.05 3.88 3.05 3.27 3.52 3.68

141 141 141 144 144 146

31 42 53 22 31 47

19.14 50.410 57.07 50.190 33.38 51.710 18.27 45.040 57.44 50.150 02.60 49.790

354 309 384 1250 379 420

3748 3207 4031 3845 3975 4335

 Hydrae γ2 Velorum  Leonis  Hydrae  Leonis ψ Ursae Maj.

1.98 1.78 3.44 3.91 3.52 3.01

147 147 147 147 148 149

33 37 51 55 11 06

380 447 303 456 364 1243

3982 4554 3117 4660 3849 3718

 Leonis* γ Ursae Maj.  Carinae  Ursae Maj.  Hydrae θ Pyxidis

1.35 2.44 3.47 3.31 5.06 4.72

150 150 151 151 152 153

441 396 425 521 1261 483

4518 4133 4377 5291 3970 4905

 Ursae Maj.  Leonis  Ursae Maj.  Draconis 2 v Hydrae  Ursae Maj.

3.71 3.85 3.48 3.65 4.6 1.77

381 1270 345 422 423

3994 4116 3634 4357 4359

λ Hydrae  Sextantis λ Velorum  Leonis* θ Leonis

3.61 5.21 2.21 2.56 3.34

*

Star

No. 329 : Aslesa. No. 380 : Regulus , Magha.

Latitude º +5 +72 -5 -10 +49 -23

' 25 59 04 58 40 26

" 32.57 21.20 43.55 04.63 52.28 07.48

Annual Annual Variation Proper Motion " " +0.310 +0.005 +0.280 -0.031 +0.290 -0.020 +0.290 -0.014 +0.170 -0.125 +0.190 -0.105

50.900 -0.090 +61 45 49.17 49.630 -0.057 -58 20 46.42 50.760 +0.071 +45 08 05.83 50.360 -0.155 +29 53 10.66 50.420 +0.224 -13 03 07.63 50.320 -0.040 +9 43 00.17

+0.250 +0.280 +0.340 +0.170 +0.010 +0.240

-0.042 +0.000 +0.073 -0.103 -0.255 -0.026

58.39 58.54 32.95 15.45 22.68 17.71

+0.260 +0.140 +0.240 +0.390 +0.160 +0.230

-0.003 -0.127 -0.019 +0.148 -0.081 +0.006

52.24 51.79 08.87 40.90 30.13 03.05

50.100 -0.026 -22 22 51.75 49.410 -0.015 -64 27 46.57 50.400 +0.020 +11 51 58.61 50.250 +0.070 -14 16 34.66 50.330 -0.001 +4 52 00.87 50.550 -0.054 +35 32 18.96

+0.240 +0.220 +0.220 +0.170 +0.210 +0.150

+0.026 +0.004 +0.000 -0.044 -0.001 -0.055

06 45 00 21 57 20

51.23 59.63 28.80 17.98 42.68 36.85

50.070 -0.235 +0 27 55.81 50.860 +0.104 +47 08 34.76 48.980 -0.105 -70 19 32.00 50.960 +0.119 +51 39 29.55 50.050 -0.020 -26 35 55.20 49.930 -0.008 -39 02 00.64

+0.120 +0.260 +0.200 +0.260 +0.150 +0.160

-0.082 +0.065 +0.001 +0.074 -0.028 -0.012

153 156 156 157 158 159

56 40 56 44 36 13

51.80 31.07 27.84 52.10 35.80 27.41

50.510 -0.177 50.290 -0.005 50.480 -0.040 51.220 -0.111 50.060 -0.045 51.070 +0.150

+41 +0 +26 +66 -23 +54

32 09 09 21 10 19

40.56 01.94 48.11 45.64 37.56 11.81

+0.120 +0.140 +0.160 +0.100 +0.130 +0.200

-0.048 -0.005 +0.014 -0.037 +0.003 +0.070

159 160 161 161 163

39 23 28 36 42

05.04 32.24 12.16 16.93 34.98

49.950 -0.165 50.170 -0.040 49.580 -0.040 50.600 +0.188 50.350 -0.025

-22 -11 -55 +14 +9

00 20 52 20 40

50.98 42.83 12.63 01.79 27.34

-0.030 +0.090 +0.120 +0.050 -0.010

-0.159 -0.031 +0.001 -0.062 -0.096

-0.101 -0.188 -0.080 -1.937 -0.122 -0.022

+28 +12 +75 -83 -3 -48

59 20 14 02 45 55

No. 422 : Zosma , Purva Phalguni-1.

Annual rate of Precession in longitude for the middle of the year = 50".29

209

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

1227 389 497 1304 410 444

3447 4094 5054 4527 4232 4534

o Velorum  Hydrae  Ursae Maj. pr 93 Leonis*  Hydrae  Leonis

3.62 3.81 2.27 4.53v 3.11 2.14

º 165 165 165 169 170 171

' 00 19 59 15 39 54

Annual Annual Variation Proper Motion " " " 50.97 49.170 -0.073 16.13 49.990 -0.093 29.55 51.180 +0.188 38.64 50.300 -0.140 05.07 50.120 +0.004 07.72 49.980 -0.417

392 315 1283 485 426 509

4104 3307 4287 4915 4382 5191

 Antliae  Carinae  Crateris  CVn sq  Crateris  Ursae Maj.

4.25 1.86 4.08 2.9 3.56 1.86

172 173 173 174 176 177

43 24 58 51 58 13

28.73 24.05 18.52 13.12 16.87 20.51

39.25 47.83 00.15 14.39 18.46 14.80

-0.010 +0.000 -0.070 -0.070 +0.120 -0.110

-0.025 -0.011 -0.074 -0.069 +0.139 -0.083

445 353 531 639 361 460

4540 3734 5404 6396 3803 4689

 Virginis  Velorum θ Bootis  Draconis N Velorum Virginis

3.61 2.5 4.05 3.17 3.13 3.89

177 179 182 183 184 184

27 10 54 41 29 35

18.37 51.090 +0.789 +0 41 39.78 22.64 49.320 -0.027 -63 43 18.89 07.97 51.260 +0.148 +60 06 21.15 39.13 55.090 -0.288 +84 45 39.83 39.68 49.280 -0.056 -64 14 20.47 21.18 50.260 -0.051 +2 35 19.99

+0.030 -0.030 -0.520 -0.090 -0.100 -0.120

+0.047 +0.000 -0.456 -0.014 -0.020 -0.042

492 571 351 1326 375 434

4983 5744 3699 4828 3940 4450

 Com  Draconis  Carinae  Virginis φVelorum ξ Hydrae

4.26 3.29 2.25 4.88 3.54 3.54

184 185 185 185 186 188

38 14 36 48 13 16

45.87 36.43 22.53 03.60 42.23 18.45

49.270 -1.319 +32 30 51.590 -0.059 +71 05 49.150 -0.048 -67 07 50.520 +0.116 +13 32 49.470 -0.019 -59 57 49.820 -0.193 -31 35

50.70 35.07 00.97 31.84 03.72 59.67

+0.350 -0.080 -0.100 -0.140 -0.090 -0.240

+0.429 +0.004 -0.011 -0.049 -0.005 -0.131

488 457 484 453 475 465

4932 4662 4910 4630 4813 4757

 Virginis γ Corvi  Virginis  Corvi  Virginis  Corvi*

2.83 2.59 3.38 3 4.66 2.95

190 191 191 191 192 193

13 00 44 57 26 44

33.20 37.52 43.21 01.55 24.03 12.41

50.160 50.020 49.940 50.060 50.210 50.060

13.48 06.86 40.73 27.90 09.32 54.09

-0.210 -0.170 -0.370 -0.150 -0.190 -0.360

-0.091 -0.045 -0.232 -0.018 -0.052 -0.211

319 471 535 513 281 501

3347 4786 5435 5235 2803 5107

 Volantis  Corvi γ Bootis  Bootis  Volantis  Virginis

3.77 2.65 3.03 2.68 3.98 3.37

195 197 197 199 199 201

27 39 57 37 41 58

06.79 13.19 04.31 29.37 30.79 25.73

49.120 +0.547 -75 35 11.82 50.180 +0.026 -18 02 45.29 50.530 -0.268 +49 33 03.56 50.620 +0.095 +28 04 26.27 47.010 -0.039 -82 28 41.93 50.090 -0.284 +9 44 33.40

-0.250 -0.230 -0.100 -0.550 -0.200 -0.280

-0.082 -0.048 +0.079 -0.354 -0.006 -0.066

534 498 526 555 495

5429 5056 5340 5602 5020

 Bootis  Virginis*  Bootis*  Bootis γ Hydrae

3.58 0.98 -0 3.5 3

203 204 204 204 207

04 07 31 32 18

24.31 39.12 11.34 23.92 16.52

50.490 -0.191 50.250 -0.028 50.260 -0.285 50.830 -0.039 50.280 +0.079

-0.160 -0.270 -2.500 -0.270 -0.270

+0.066 -0.041 -2.265 -0.044 -0.017

*

Star

No. 1304 : Uttara Phalguni-2. No. 465 : Algorel , Hasta.

49.850 48.690 49.580 50.390 49.940 50.800

-0.089 -0.093 -0.512 -0.302 -0.206 -0.155

-0.269 -0.161 -0.415 -0.074 -0.060 -0.140

º -66 -24 +56 +17 -21 +12

' 16 40 22 18 47 15

" 33.36 18.32 47.09 33.26 47.74 54.97

-37 -72 -22 +40 -17 +54

25 40 43 07 34 23

+16 -14 +8 -19 -3 -12

+42 -2 +30 +54 -13

12 30 36 40 28 11

27 03 43 08 44

Annual Annual Variation Proper Motion " " +0.080 +0.001 -0.040 -0.125 +0.150 +0.067 -0.020 -0.065 +0.260 +0.221 -0.280 -0.306

03.17 21.62 19.32 57.97 39.11

No. 498 : Spica , Citra. No. 526 : Arcturus , Svati.

Annual rate of Precession in longitude for the middle of the year = 50".29

210

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

452 406 348 496 563 525

4621 4199 3685 5028 5681 5338

 Centauri θ Carinae  Carinae  Centauri  Bootis  Virginis

2.6 2.76 1.68 2.75 3.47 4.08

º 207 209 212 213 213 214

' 45 28 14 24 26 05

Annual Annual Variation Proper Motion " " " 59.05 49.880 -0.033 16.65 49.520 -0.046 45.22 48.660 -0.463 44.95 49.810 -0.305 50.67 50.910 +0.189 05.40 50.490 +0.140

523 436 455 468 1371 385

5315 4467 4656 4763 5359 4037

 Virginis λ Centauri  Crucis γ Crucis λ Virginis ω Carinae

4.19 3.13 2.8 1.63v 4.52 3.32

214 214 215 217 217 217

46 49 56 01 14 43

519 572 1189 545 442 508

5287 5747 2736 5487 4520 5193

 Hydrae  Cr. Borealis γ2 Volantis  Virginis λ Muscae  Centauri

3.27 3.68 3.78 3.88 3.64 3.04v

218 219 220 220 221 221

481 462 578 520 608 512

4853 4730 5793 5288 6092 5231

 Crucis  Crucis A  Cr.Borealis θ Centauri  Herculis  Centauri

1.25 1.33 2.23 2.06 3.89 2.55

548 504 297 391 564 583

5531 5132 3024 4102 5685 5867

2  Librae*  Centauri  Volantis  Carinae  Librae  Serpentis

537 474 556 559 582 591

5440 4798 5603 5652 5854 5933

541 518 469 588 553

5469 5267 4773 5892 5576 *

Star

Latitude

Annual Annual Variation Proper Motion " " -0.280 -0.026 -0.280 -0.012 -0.420 -0.133 -0.510 -0.219 -0.360 -0.069 -0.700 -0.409

º -44 -62 -72 -26 +48 +7

' 30 08 14 01 57 11

" 40.57 26.39 18.28 08.94 48.60 43.89

48.12 37.33 54.19 30.69 18.41 15.48

50.280 -0.039 +2 49.700 -0.045 -56 49.820 -0.042 -50 50.170 +0.257 -47 50.280 -0.024 +0 49.410 -0.054 -67

54 47 25 50 29 23

43.28 28.27 17.30 02.94 20.37 03.86

-0.170 -0.340 -0.340 -0.510 -0.290 -0.350

+0.135 -0.033 -0.033 -0.199 +0.023 -0.033

54 24 07 25 16 49

37.38 12.78 34.59 08.68 26.75 17.43

50.310 +0.092 -13 03 07.39 50.360 -0.286 +46 03 08.33 46.900 -0.682 -82 37 08.06 50.560 +0.203 +9 40 07.06 49.580 -0.181 -58 30 33.09 50.100 -0.015 -28 58 52.91

-0.440 -0.310 -0.350 -0.610 -0.390 -0.370

-0.115 +0.018 +0.065 -0.268 -0.054 -0.028

221 222 222 222 224 225

55 09 35 35 40 14

47.89 12.98 06.47 32.68 27.64 08.37

49.880 -0.046 -48 38 27.50 49.840 -0.031 -52 52 51.64 50.800 +0.201 +44 19 16.78 49.850 -0.317 -22 05 08.73 50.910 -0.065 +65 49 41.00 50.060 -0.040 -32 56 44.74

-0.380 -0.370 -0.390 -1.020 -0.330 -0.430

-0.039 -0.032 -0.044 -0.672 +0.032 -0.062

2.75 2.3 3.95 4 2.61 3.67

225 225 226 228 229 230

22 50 02 22 39 14

06.97 22.64 12.29 01.02 28.22 11.27

50.220 -0.082 +0 50.020 -0.023 -39 48.560 -0.031 -79 49.650 +0.052 -67 50.250 -0.089 +8 50.570 +0.093 +34

19 35 23 53 29 19

49.66 17.66 22.05 07.35 36.59 27.58

-0.450 -0.390 -0.350 -0.410 -0.430 -0.410

-0.095 -0.028 +0.034 -0.027 -0.044 -0.026

Centauri  Muscae  Librae  Librae  Serpentis γ Serpentis

2.31 2.69 3.29 4.54 2.65 3.85

230 230 230 231 232 233

32 39 58 17 21 04

04.01 28.26 23.20 27.28 46.99 22.94

50.140 -0.023 -25 49.850 -0.045 -56 50.200 -0.059 -7 50.260 -0.024 -1 50.550 +0.134 +25 51.240 +0.759 +35

30 33 38 51 30 11

55.81 34.11 49.38 07.39 22.41 12.61

-0.430 -0.430 -0.450 -0.440 -0.320 -1.560

-0.044 -0.043 -0.062 -0.047 +0.079 -1.164

 Lupi  Centauri γ Muscae  Serpentis  Centauri

2.3 0.61 3.87 3.71 3.13

233 234 234 234 235

47 04 18 37 04

21.51 37.66 06.80 07.32 49.75

50.140 -0.016 -30 50.030 -0.026 -44 49.830 -0.069 -58 50.520 +0.121 +24 50.180 -0.011 -24

01 08 52 00 02

41.82 24.39 23.53 17.74 02.15

-0.430 -0.440 -0.450 -0.320 -0.440

-0.024 -0.032 -0.045 +0.091 -0.029

No. 548 : Zuben el Genubi, Visakha.

Annual rate of Precession in longitude for the middle of the year = 50".29

211

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

552 577 585 487 566 1413

5571 5787 5881 4923 5705 5838

 Lupi γ Librae  Serpentis  Muscae φ' Lupi  Librae

2.68 3.91 3.54 3.62 3.56 4.74

º 235 235 236 236 237 238

' 18 25 13 28 46 02

Annual Annual Variation Proper Motion " " " 40.30 50.160 -0.023 29.56 50.370 +0.061 31.56 50.280 -0.082 35.19 50.310 +0.360 47.31 50.160 -0.067 37.22 50.280 -0.013

579 1402 626 609 538 401

5794 5695 6220 6095 5460 4174

Librae  Lupi  Herculis γ Herculis  Centauri cg γ Chamaeleontis

3.58 3.22 3.53 3.75 var. 4.11

238 238 239 239 239 240

53 56 04 30 44 42

44.13 33.95 36.61 05.10 09.73 16.75

50.250 -0.010 -8 30 35.49 50.210 -0.008 -21 25 42.71 50.770 +0.116 +60 17 13.38 50.390 -0.072 +40 00 19.86 45.220 -4.888 -42 36 12.71 49.760 -0.049 -68 05 12.71

-0.430 -0.450 -0.490 -0.390 -1.290 -0.470

+0.000 -0.029 -0.070 +0.032 -0.861 -0.040

558 618 613 603 539 594

5649 6148 6117 6056 5463 5953

 Lupi  Herculis  Herculis  Ophiuchi  Circini  Scorpii*

3.41 2.77 4.57 2.74 3.19 2.32

241 241 241 242 242 242

02 22 51 35 38 51

33.85 40.66 46.44 19.52 50.51 27.30

50.080 -0.099 -32 50 04.49 50.340 -0.126 +42 41 59.05 50.490 +0.067 +35 09 56.22 50.330 -0.018 +17 14 16.36 50.000 -0.104 -46 12 24.18 50.290 -0.001 -1 59 19.53

-0.540 -0.460 -0.480 -0.590 -0.730 -0.470

-0.104 -0.034 -0.050 -0.149 -0.292 -0.038

592 597 605 459 411 607

5944 5984 6075 4674 4234 6084

 Scorpii  Scorpii pr  Ophiuchi  Chamaeleontis 2 Chamaeleontis  Scorpii

2.89 2.62 3.24 4.26 4.45 2.89

243 243 243 245 245 248

13 28 47 43 56 05

34.19 35.11 49.88 18.98 24.71 09.26

50.280 -0.006 -5 28 40.82 50.300 -0.002 +1 00 18.69 50.430 +0.079 +16 26 15.04 49.900 -0.083 -63 35 49.15 49.890 -0.030 -67 47 36.61 50.280 -0.007 -4 02 24.33

-0.470 -0.460 -0.380 -0.480 -0.500 -0.470

-0.027 -0.020 +0.055 -0.034 -0.048 -0.022

634 622 560 616 620 633

6324 6175 5671 6134 6165 6299

 Herculis  Ophiuchi γ Tr. Austrini  Scorpii cg*  Scorpii  Ophiuchi

3.92 2.56 2.89 var. 2.82 3.2

248 249 249 250 251 252

36 30 40 02 44 06

50.27 56.88 42.69 54.65 35.64 22.79

50.390 -0.085 +53 14 45.19 50.330 +0.010 +11 23 20.01 50.070 -0.082 -48 06 20.90 50.280 -0.006 -4 34 21.57 50.280 -0.005 -6 07 23.39 50.020 -0.339 +31 49 59.84

-0.430 -0.430 -0.510 -0.470 -0.480 -0.510

+0.019 +0.028 -0.056 -0.022 -0.023 -0.047

589 653 643 542 641 628

5897 6536 6418 5470 6410 6241

 Tr.Australis  Draconis  Herculis  Apodis  Herculis  Scorpii

2.85 2.79 3.16 3.83 3.14 2.29

252 252 252 254 255 255

07 15 21 42 03 37

35.26 16.46 16.50 55.37 01.47 05.20

50.100 50.620 50.420 50.160 50.390 49.690

-0.100 -0.072 -0.051 -0.002 -0.004 -0.588

-41 +75 +59 -58 +47 -11

57 16 32 14 40 44

03.59 31.00 53.47 15.55 55.48 35.01

-0.890 -0.450 -0.460 -0.480 -0.620 -0.800

-0.435 +0.011 -0.000 -0.019 -0.158 -0.327

1439 1435 631 663 638

6247 6229 6285 6588 6380

1  Scorpii  Arae  Arae  Herculis  Scorpii

3.08v 3.76 3.13 3.8 3.33

256 259 260 260 261

26 11 06 10 01

30.73 50.270 -0.008 26.65 50.320 +0.051 36.24 50.250 -0.018 34.09 50.380 -0.015 46.28 50.340 +0.052

-15 -36 -33 +69 -20

25 16 05 15 11

33.53 45.21 40.33 46.39 16.07

-0.490 -0.490 -0.510 -0.460 -0.750

-0.026 -0.023 -0.038 +0.005 -0.284

*

Star

No. 594 : Dschubba, Anuradha

º -25 +4 +16 -56 -17 -0

' 02 23 14 46 10 01

" 55.57 01.36 08.18 37.22 52.59 20.40

Annual Annual Variation Proper Motion " " -0.450 -0.048 -0.380 +0.024 -0.460 -0.042 -0.250 +0.163 -0.530 -0.105 -0.530 -0.109

No. 616 : Antares , Jyestha, Mag. 0.9 to 1.8.

Annual rate of Precession in longitude for the middle of the year = 50".29

212

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

625 644 656 611 649 645

6217 6453 6556 6102 6508 6461

 Tr. Austr. θ Ophiuchi  Ophiuchi γ Apodis  Scorpii  Arae

1.92 3.27 2.08 3.89 2.69 2.85

º 261 261 262 262 264 264

' 10 40 44 59 17 29

Annual Annual Variation Proper Motion " " " 55.85 50.290 +0.028 52.49 50.290 -0.002 09.80 50.480 +0.163 19.15 50.080 -0.191 56.71 50.290 +0.000 31.90 50.280 -0.008

658 652 671 651 667 665

6561 6527 6688 6510 6623 6603

ξ Serpentis λ Scorpii* ξ Draconis  Arae  Herculis  Ophiuchi

3.54 1.63 3.75 2.95 3.42 2.77

264 264 265 265 265 265

49 52 02 13 30 37

56.02 19.74 40.92 13.90 30.29 22.25

50.260 -0.040 +7 55 54.09 50.300 -0.000 -13 47 28.66 50.820 +0.525 +80 16 49.04 50.270 -0.030 -26 33 49.36 49.840 -0.452 +51 05 48.52 50.240 -0.051 +27 56 16.58

-0.530 -0.500 -0.380 -0.540 -1.230 -0.310

-0.060 -0.029 +0.085 -0.072 -0.762 +0.158

648 654 660 668 666 669

6500 6553 6580 6629 6615 6630

 Arae θ Scorpii  Scorpii γ Ophiuchi 1  Scorpii G Scorpii

3.62 1.87 2.41 3.75 3.03 3.21

265 265 266 266 267 268

50 53 45 55 48 12

33.61 09.51 21.01 07.59 32.22 16.64

50.240 -0.067 -37 21 33.00 50.310 +0.016 -19 38 52.14 50.290 -0.005 -15 38 49.97 50.270 -0.023 +26 06 29.09 50.310 +0.000 -16 43 01.83 50.350 +0.049 -13 37 29.34

-0.570 -0.470 -0.500 -0.540 -0.480 -0.440

-0.099 -0.001 -0.027 -0.074 -0.008 +0.034

676 661 672 674 673 1471

6705 6582 6695 6703 6698 6743

γ Draconis  Pavonis θ Herculis ξ Herculis  Ophiuchi θ Arae

2.23 3.62 3.86 3.7 3.34 3.66

268 268 268 269 270 271

15 15 45 28 02 28

15.76 35.34 47.24 57.49 22.21 35.30

50.170 -0.028 +74 55 10.05 50.300 -0.017 -41 18 45.43 50.250 +0.009 +60 40 55.99 50.380 +0.139 +52 40 58.30 50.280 -0.007 +13 39 43.58 50.310 -0.012 -26 39 42.68

-0.490 -0.520 -0.470 -0.490 -0.580 -0.480

-0.020 -0.055 +0.006 -0.017 -0.116 -0.014

679 680 681 682 683 687

6746 6771 6779 6812 6832 6859

γ Sagittarii 72 Ophiuchi o Herculis  Sagittarii  Sagittarii  Sagittarii*

2.99 3.73 3.83 3.86 3.11 2.7

271 272 272 273 273 274

32 26 58 29 54 52

51.21 45.99 56.85 59.63 48.54 03.21

50.240 -0.056 -6 59 50.190 -0.070 +32 59 50.210 +0.002 +52 10 50.290 +0.002 +2 20 50.180 -0.137 -13 22 50.340 +0.034 -6 28

41.54 13.77 53.53 21.96 53.33 30.35

-0.660 -0.390 -0.450 -0.460 -0.630 -0.500

-0.185 +0.081 +0.009 +0.001 -0.162 -0.029

691 689 688 692 697 1482

6897 6879 6869 6913 6951 6973

 Telescopii  Sagittarii  Serpentis λ Sagittarii θ Coronae Aust.  Scuti

3.51 1.85 3.26 2.81 4.64 3.85

275 275 275 276 276 279

21 21 57 36 49 18

36.18 53.29 42.70 11.60 50.80 09.20

50.310 -0.021 -22 50.270 -0.045 -11 49.650 -0.614 +20 50.250 -0.053 -2 50.360 +0.031 -19 50.230 -0.037 +14

02.89 18.62 44.42 21.50 57.90 56.82

-0.520 -0.590 -1.140 -0.650 -0.480 -0.770

-0.053 -0.122 -0.677 -0.183 -0.024 -0.310

214 1487 1489 706 710

1953 7039 7063 7121 7150

γ Mensae φ Sagittarii  Scuti  Sagittarii* 2 ξ Sagittarii

5.19 3.17 4.22 2.02 3.51

279 280 282 282 283

51 28 39 40 44

15.42 05.15 58.26 18.51 15.61

50.810 50.360 50.250 50.320 50.320

+1.082 -79 59 19.24 +0.053 -3 57 23.85 -0.006 +18 11 00.04 +0.008 -3 27 08.65 +0.032 +1 39 30.97

-0.760 -0.460 -0.460 -0.500 -0.460

+0.239 -0.004 -0.016 -0.055 -0.015

*

Star

No. 652 : Schaula , Mula. No. 687 : Purvasadha-1.

º -46 -1 +35 -56 -14 -32

' 09 50 49 00 00 16

39 03 25 08 03 54

" 15.25 46.61 52.60 37.37 40.33 04.03

Annual Annual Variation Proper Motion " " -0.500 -0.031 -0.490 -0.020 -0.690 -0.220 -0.580 -0.106 -0.510 -0.031 -0.500 -0.026

No. 706 : Nunki , Uttarasadha.

Annual rate of Precession in longitude for the middle of the year = 50".29

213

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

1496 699 720 717 754 712

7234 7001 7264 7236 7665 7176

 Sagittarii  Lyrae  Sagittarii λ Aquilae  Pavonis  Aquilae

3.32 0.03 2.89 3.44 3.56 4.02

º 285 285 286 287 287 288

' 07 36 32 37 54 32

Annual Annual Variation Proper Motion " " " 13.06 50.230 -0.083 13.90 50.490 +0.505 17.38 50.290 -0.004 05.71 50.200 -0.029 25.71 51.620 +1.142 50.02 50.070 -0.075

705 810 716 713 775 730

7106 8254 7235 7178 7913 7377

 Lyrae  Octantis  Aquilae γ Lyrae  Pavonis  Aquilae

var. 3.76 2.99 3.24 3.42 3.36

289 289 290 292 292 293

10 58 04 12 46 55

06.73 32.53 53.22 25.12 53.45 30.74

50.010 +0.005 +55 58 54.07 50.400 -0.212 -57 46 58.95 50.120 -0.023 +36 10 57.78 49.990 -0.003 +55 00 38.12 50.470 -0.055 -45 57 24.57 50.490 +0.294 +24 48 53.75

-0.430 -0.650 -0.530 -0.420 -0.390 -0.370

-0.003 -0.217 -0.094 +0.003 +0.028 +0.040

764 751 785 769 1508 746

7790 7623 7986 7869 7405 7570

 Pavonis 1 θ Sagittarii  Indi  Indi  Vulpeculae  Aquilae

1.94 4.37 3.65 3.11 4.44 var.

294 295 298 299 299 300

06 09 04 23 47 43

16.77 24.35 23.63 30.66 28.41 10.48

50.440 50.350 50.510 50.510 49.810 50.190

-0.025 +0.001 +0.008 +0.078 -0.209 +0.010

-36 -14 -39 -27 +45 +21

16 23 09 45 51 31

13.75 17.49 34.15 20.18 20.46 15.72

-0.500 -0.440 -0.430 -0.340 -0.470 -0.400

-0.087 -0.027 -0.030 +0.048 -0.076 -0.009

741 11 1513 732 745 749

7525 98 7488 7417 7557 7602

γ Aquilae  Hydri  Sagittae  Cygni p  Aquilae*  Aquilae

2.72 2.8 4.37 3.08 0.77 3.71

301 301 301 301 302 302

13 16 29 32 03 42

28.25 34.17 28.16 10.75 57.20 31.95

50.140 53.530 50.070 49.970 50.830 50.080

+0.020 +2.664 +0.003 +0.002 +0.697 -0.064

+31 -64 +38 +48 +29 +26

14 47 12 57 18 39

28.96 52.75 56.80 55.84 10.19 15.37

-0.390 -2.310 -0.410 -0.380 -0.110 -0.850

-0.005 -1.952 -0.033 -0.002 +0.262 -0.481

743 761 762 756 752 1550

7536 7754 7776 7710 7635 8039

 Sagittae 2  Capricorni  Capricorni θ Aquilae γ Sagittae γ Microscopii

3.82 3.57 3.08 3.23 3.47 4.67

303 304 304 305 307 308

40 08 20 35 19 43

20.39 42.57 02.01 54.09 44.64 06.04

50.070 50.320 50.320 50.220 50.120 50.380

+0.011 +0.063 +0.042 +0.041 +0.090 -0.000

+38 +6 +4 +20 +39 -14

54 55 35 19 11 40

38.72 40.90 11.50 30.08 17.79 02.00

-0.360 -0.380 -0.370 -0.370 -0.350 -0.340

+0.006 -0.011 -0.008 -0.005 +0.006 +0.006

841 146 781 1547 768 726

8502 1208 7950 7990 7852 7328

 Tucanae γ Hydri  Aquarii  Aquarii  Delphini  Cygni

2.86 3.24 3.77 4.73 4.03 3.77

309 310 312 313 314 315

57 46 00 20 20 11

32.37 09.98 34.12 39.85 46.93 59.36

50.510 52.140 50.280 50.280 50.100 49.440

-0.120 +0.537 +0.024 +0.035 +0.007 +0.396

-45 -76 +8 +8 +29 +73

24 45 04 14 04 48

20.47 33.29 42.50 16.67 16.55 03.60

-0.340 -0.410 -0.360 -0.350 -0.340 -0.220

-0.000 -0.010 -0.042 -0.041 -0.024 +0.080

829 (771) 806 774 822

8425 7882 8204 7906 8353

 Gruis  Delphini m*  Capricorni  Delphini γ Gruis

1.74 3.64 3.74 3.77 3.01

316 316 317 317 317

11 37 13 39 42

42.45 50.590 +0.064 -32 36.56 50.130 +0.070 +31 25.03 50.350 +0.008 -6 57.65 50.120 +0.074 +33 25.75 50.550 +0.095 -23

54 54 59 01 03

57.83 57.19 32.91 13.86 08.15

-0.480 -0.370 -0.260 -0.310 -0.350

-0.191 -0.069 +0.022 -0.022 -0.058

*

Star

No. 745 : Altair , Sravana.

º -5 +61 +1 +17 -44 +37

' 05 43 26 33 42 33

" 34.01 54.39 03.68 45.99 36.34 52.14

Annual Annual Variation Proper Motion " " -0.690 -0.243 -0.190 +0.256 -0.480 -0.035 -0.530 -0.087 -1.880 -1.444 -0.500 -0.066

No. 771 : Rotanev , Dhanistha-1.

Annual rate of Precession in longitude for the middle of the year = 50".29

214

LONGITUDE AND LATITUDE OF STARS, 2020.5 d MEAN PLACES FOR JULY 2 .125 TERRESTRIAL TIME Cat. BS= No. HR FK5 No.

Mag.

Longitude

Latitude

733 778 1541 860 846 812

7420 7928 7948 8675 8556 8278

 Cygni  Delphini γ Delphini sq  Gruis 1 Gruis γ Capricorni

3.79 4.43 4.27 3.49 3.97 3.68

º 318 318 319 321 321 322

' 14 24 39 01 53 04

Annual Annual Variation Proper Motion " " " 59.92 49.420 +0.252 04.01 50.020 -0.037 10.44 49.940 -0.109 07.09 50.700 +0.077 25.46 50.570 +0.027 41.71 50.480 +0.172

º +71 +31 +32 -39 -31 -2

' 27 56 41 47 20 33

" 00.18 30.53 59.05 23.87 56.42 33.31

856 800 808 819 1569 765

8636 8131 8232 8322 8264 7796

 Gruis  Equulei  Aquarii  Capricorni  Aquarii γ Cygni

2.11v 3.92 2.91 2.87 4.69 2.2

322 323 323 323 324 325

36 24 40 49 24 07

58.12 50.720 +0.145 -35 10.70 50.170 +0.029 +20 52.44 50.250 +0.017 +8 47.69 50.470 +0.149 -2 18.94 50.350 +0.103 +5 27.73 49.670 +0.007 +57

26 07 36 36 57 07

02.30 11.46 48.66 18.63 21.42 23.08

-0.330 -0.350 -0.260 -0.610 -0.310 -0.230

-0.071 -0.102 -0.015 -0.368 -0.062 -0.001

780 815 849 797 827 867

7949 8308 8592 8115 8414 8728

 Cygni  Pegasi  Aquarii  Cygni  Aquarii  PsA

2.46 var. 5.2 3.2 2.96 1.16

328 332 332 333 333 334

01 10 49 19 52 08

59.64 13.77 48.58 30.96 13.26 56.69

50.510 50.150 50.530 49.840 50.220 50.720

+0.705 +0.031 +0.154 -0.031 +0.015 +0.253

25 05 54 41 15 08

18.89 55.47 11.55 36.38 29.98 17.65

-0.060 -0.200 -0.390 -0.230 -0.190 -0.450

+0.155 -0.011 -0.218 -0.051 -0.016 -0.287

777 842 834 861 866 3

7924 8518 8450 8679 8709 25

 Cygni γ Aquarii θ Pegasi  Aquarii  Aquarii  Phoenicis

1.25 3.84 3.53 4.01 3.27 3.88

335 337 337 338 339 339

36 00 07 52 09 56

40.75 02.82 13.14 56.12 35.91 12.72

49.540 50.350 50.440 50.320 50.310 50.720

+0.007 +59 54 18.98 +0.126 +8 14 02.68 +0.278 +16 20 21.63 -0.026 -5 39 55.60 -0.047 -8 11 31.67 +0.011 -41 57 28.89

-0.160 -0.190 -0.220 -0.160 -0.140 -0.350

+0.001 -0.042 -0.077 -0.030 -0.008 -0.220

850 792 864 72 831 54

8597 8079 8698 591 8430 472

 Aquarii  Cygni λ Aquarii*  Hydri  Pegasi  Eridani

4.02 3.72 3.74 2.86 3.76 0.46

340 341 341 342 344 345

46 04 51 24 41 36

42.65 55.37 45.49 44.21 42.84 09.69

50.300 49.620 50.320 51.660 50.320 51.160

+0.064 +0.014 +0.025 +0.420 +0.339 +0.084

+8 +56 -0 -64 +34 -59

21 34 23 14 15 22

48.87 52.89 13.46 37.86 15.78 44.76

-0.210 -0.120 -0.080 -0.300 -0.190 -0.170

-0.087 -0.003 +0.030 -0.194 -0.104 -0.092

12 855 141 878 871 1044

99 8634 1175 8852 8781 440

 Phoenicis  Pegasi  Reticuli γ Piscium  Pegasi δ Phoenicis

2.39 3.4 3.85 3.69 2.49 3.95

345 346 351 351 353 353

46 26 41 44 46 54

55.61 15.38 47.56 36.02 16.69 49.96

50.650 50.220 52.990 50.950 50.170 51.250

-0.042 +0.072 +0.795 +0.713 +0.043 +0.337

-40 +17 -76 +7 +19 -52

38 40 05 15 24 34

09.83 43.62 22.95 19.11 20.07 57.05

-0.520 -0.110 -0.290 -0.310 -0.070 +0.030

-0.444 -0.043 -0.260 -0.285 -0.065 +0.035

862 857 68 49 870

8684 8650 566 429 8775

 Pegasi  Pegasi  Eridani γ Phoenicis  Pegasi*

3.48 2.94 3.7 3.41 2.42v

354 355 356 358 359

40 59 32 25 39

17.63 52.00 43.08 54.41 37.89

50.160 49.960 52.320 50.630 50.280

+0.130 +0.002 +1.308 -0.186 +0.270

+29 +35 -57 -47 +31

23 06 01 35 08

10.57 28.98 06.79 09.06 27.40

-0.110 -0.020 -0.190 -0.140 +0.070

-0.102 -0.029 -0.210 -0.167 +0.037

*

Star

No. 864 : Satabhisaj.

BS = Bright Star Catalogue

+49 +22 -10 +43 +11 -21

Annual Annual Variation Proper Motion " " -0.180 +0.104 -0.310 -0.035 -0.450 -0.177 -0.370 -0.115 -0.270 -0.017 -0.340 -0.084

No. 870 : Scheat , Purva Bhadrapada-2.

HR = Havard Revised Catalogue

FK5 = Fifth Fundamental Catalogue

215

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

Declination

s (0.0001)

º

'

-42 +54 +30 +56 -17 +38

11 00 58 38 52 36

Annual Annual Variation Proper motion

"

"

" (0.001)

1 2 3 7 9 11

15 21 25 39 74 98

Andromedae Cassiopeiae Phoenicis γ Pegasi* Ceti  Hydri

2.06 B9 II 2.27 F2 IV 3.88 K0 III 2.83 B2 IV 3.56 K1.5 III 2.80 G0V

0 0 0 0 0 0

09 10 10 14 20 26

27.1 17.1 26.7 17.6 28.3 48.0

3.117 +104 +29 12 12.79 +19.86 3.245 +685 +59 15 45.97 19.84 3.025 +118 -45 38 04.02 19.84 3.098 +2 +15 17 50.68 19.99 3.056 -9 -8 42 37.57 19.93 3.056 +6633 -77 08 20.60 20.23

12 17 20 21 22 33

99 153 165 168 188 269

 Phoenicis  Cassiopeiae δ Andromedae Cassiopeiae  Ceti Andromedae

2.39 K0.5 III b 3.66 B2 IV 3.27 K3 III 2.23 K0- IIIa 2.04 K0III 3.87 A5 V

0 0 0 0 0 0

27 38 40 41 44 57

17.5 07.5 25.8 41.0 37.1 53.9

2.950 3.382 3.227 3.449 3.008 3.355

+183 +22 +106 +64 +164 +130

41.86 +19.50 34.10 19.76 22.21 19.64 58.08 19.68 27.87 19.70 38.16 19.44

-396 -9 -92 -32 +32 +33

32 35 40 42 1033 47

264 280 334 337 361 402

γ Cassiopeiae  Sculptoris  Ceti Andromedae* Piscium θ Ceti

2.47 B0 IVpe 4.31 B7IIIp 3.45 K1 III 2.06 M0III 5.24 A7IV 3.60 K0 III

0 0 1 1 1 1

57 59 09 10 14 25

57.8 35.5 37.3 53.2 48.3 02.9

3.678 2.885 3.019 3.382 3.143 3.001

+36 +60 49 36.35 +19.40 +17 -29 14 49.53 19.37 +147 -10 04 26.68 18.99 +146 +35 43 43.30 18.98 +97 +7 40 59.50 18.93 -53 -8 04 41.54 18.46

-5 +4 -138 -114 -56 -218

48 49 1044 50 54 52

403 429 440 437 472 464

δ Cassiopeiae γ Phoenicis δ Phoenicis  Piscium  Eridani 51 Andromedae

2.68 A5 III-IVv 3.41 Mo- IIIa 3.95 G9 III 3.62 G7 IIa 0.46 B6Vep 3.57 K3 III

1 1 1 1 1 1

27 29 32 32 38 39

10.5 15.2 06.2 35.0 28.5 15.7

3.987 2.597 2.489 3.222 2.226 3.721

+400 +60 20 27.86 +18.56 -13 -43 12 49.53 18.33 +144 -48 58 00.24 18.60 +19 +15 27 02.88 18.42 +117 -57 07 59.09 18.18 +65 +48 43 52.63 18.08

-52 -208 +151 -6 -35 -113

59 62 64 66 63 68

509 539 544 553 542 566

 Ceti  Ceti  Trianguli  Arietis  Cassiopeiae  Eridani

3.50 3.73 3.41 2.64 3.38 3.70

G8.5 V K0 III F5III A5 V B3III G8IV

1 1 1 1 1 1

45 52 54 55 55 56

01.3 28.4 15.4 46.6 53.6 45.2

2.789 2.964 3.440 3.329 4.394 2.329

-1190 -15 49 48.46 +18.83 +28 -10 14 04.20 17.64 +9 +29 40 40.36 17.37 +68 +20 54 11.95 17.43 +48 +63 46 26.58 17.51 +730 -51 30 26.97 17.79

+858 -39 -235 -111 -21 +291

72 71 73 70 74 75

591 585 603 580 617 622

 Hydri  Ceti γ Andromed. p 50 Cassiopeiae  Arietis  Trianguli

2.86 4.00 2.26 3.98 2.00 3.00

F0IV F7III K3- IIB A2V K2 III A5 III

1 2 2 2 2 2

59 00 05 05 08 10

24.9 58.3 10.0 13.7 20.0 46.2

1.889 2.827 3.714 5.270 3.399 3.594

+368 +97 +40 -99 +138 +122

14.26 +17.41 45.31 17.29 09.02 17.07 37.62 17.15 30.29 16.83 59.78 16.83

+26 -24 -52 +22 -149 -40

82 79 91

674 φ Eridani 664 γ Trianguli 779  Ceti

2 17 2 18 2 40

14.5 32.4 32.1

2.142 3.590 3.083

+102 -51 25 04.85 +16.53 +38 +33 56 27.63 16.44 +9 +0 24 59.95 +15.32

-27 -51 -4



3.56 B8IV- V 4.01 A1Vnn 4.07 B2 IV

No. 1 : Alpheratz, Uttara Bhadrapada - 2 No. 2 : Caph No. 7 : Algenib, Uttara Bhadrapada - 1 No. 21 : Schedar . Mag. 2.1 to 2.6 No. 22 : Deneb Kaitos or Diphda No. 32 : Cih . Mag. 1.6 to 3.2

-61 -20 +42 +72 +23 +35

28 58 25 31 33 04

No. 42 : Mirach No. 1033 : Revati No. 54 : Achernar No. 66 : Sheratan, Asvini No. 73 : Almach, Mag. f. 5.1 No. 74 : Hamal

-163 -181 -181 -12 -36 +324

216

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

s (0.0001)

Declination

º

'

"

Annual Annual Variation Proper motion "

1075 94 101 100 99 103

794 801 841 838 834 854

Eridani 35 Arietis  Fornacis 41 Arietis  Persei  Persei

4.11 K0III 4.66 B3 V 4.46 G8 5 IIIb 3.63 B8 Vn 3.76 K31b 3.95 G4 III+

2 2 2 2 2 2

41 44 49 51 52 55

28.6 39.6 56.9 11.8 12.5 43.5

-39 +27 -32 +27 +55 +52

46 47 19 20 58 50

57.23 +15.24 06.69 15.08 35.46 14.93 14.71 14.59 37.61 14.63 41.65 +14.43

104 907 106 1085 107 108

874 424 897 919 911 915

 Eridani Ursae Mins. θ Eridani p 3 Eridani  Ceti γ Persei

3.89 2.02 3.25 4.09 2.53 2.93

K1 III F7:Ib-Iiv A3 IV-V A3IV- V M1.5 IIIa G8 III+

2 2 2 3 3 3

57 57 59 03 03 06

25.8 2.936 +53 -8 48.5 85.762 +2140 +89 02.3 2.276 -39 -40 17.8 2.647 -105 -23 21.2 3.145 -6 +4 17.7 4.391 0 +53

49 20 13 32 10 35

03.51 44.67 24.34 08.26 42.19 06.61

109 111 120 121 123 127

921 936 1017 1030 1038 1084

 Persei  Persei  Persei Tauri Tauri  Eridani

3.39 2.12 1.79 3.60 3.74 3.73

M4 II B8V F5 Iab G6 III B9 Vn K2 Vk

3 3 3 3 3 3

06 09 25 25 28 33

29.9 30.6 47.8 55.2 17.0 53.9

135 131 141 136 134 146

1136 1122 1175 1142 1135 1208

 Eridani  Persei  Reticuli 17Tauri  Persei γ Hydri

3.54 B1III-IV 3.01 B5 III 3.85 K2 III 3.70 B6 IIIe 3.77 F5 Iab 3.24 M2 III

3 3 3 3 3 3

44 44 44 46 46 46

139 142 144 149 147 148

1165 1178 1203 1231 1220 1228

 Tauri 27 Tauri  Persei γ Eridani Persei Persei

2.87 B7 III 3.63 B8 III 2.85 B1 Ib 2.95 M 1 IIIb 2.89 B 0.5 V+ 4.04 O 7.5 IIIe

3 3 3 3 3 4

150 151 152 155 156 159

1239 1251 1273 1326 1336 1346

 Tauri  Tauri 48Persei  Horologii  Reticuli γ Tauri

3.47v B3 V+ 3.91 A0.5 Va 4.04 B3 Ve 3.86 K2 III 3.35 G8II-III 3.65 K0III

162 1121 164 171 170

1373 1393 1409 1465 1464

 Tauri 43 Eridani  Tauri  Doradus v 2 Eridani

3.76 K0III 3.96 K4 III 3.54 G9.5 III 3.27 A0IIIs 3.82 G8IIIa

*

No. 907 : (Nb) : Polaris, Dhruva No. 100 : Bharani No. 106 : Acamar. No. 107 : Menkar No. 109 : Mag. 3.3 to 4.0.

2.367 3.539 2.512 3.550 4.429 4.299

+120 +6 +71 +50 +20 -0

" (0.001)

-32 -12 +155 -118 -14 -5

14.11 14.29 14.25 13.91 13.88 13.77

-220 -19 +19 -53 -78 -5

3.871 3.931 4.320 3.238 3.261 2.832

+111 +38 55 05.88 +13.66 +3 +41 01 59.52 13.57 +25 +49 55 56.92 12.47 -45 +9 05 58.93 12.40 +40 +9 48 10.27 12.28 -658 -9 23 24.04 11.95

-106 -1 -25 -78 -39 +23

13.9 23.6 27.8 05.8 35.7 56.6

2.880 4.303 0.773 3.577 4.102 -0.855

-61 -9 41 04.86 +11.94 +28 +47 51 42.84 11.14 +490 -64 44 34.27 11.25 +14 +24 10 34.60 11.01 -13 +42 38 29.60 11.02 +116 -74 10 32.79 11.11

+745 -34 +75 -46 -2 +114

48 50 55 58 59 00

42.4 23.1 25.5 59.2 14.2 18.0

3.581 3.582 3.789 2.803 4.048 3.912

+14 +13 +4 +42 +16 +2

4 4 4 4 4 4

01 04 10 14 14 20

49.1 14.9 09.5 41.0 41.6 57.8

3.334 3.200 4.383 1.992 0.789 3.424

-4 +12 32 48.48 +3 +6 02 41.07 +20 +47 45 55.12 +41 -42 14 41.50 +65 -62 25 22.50 +80 +15 40 31.92

+9.87 9.69 9.21 8.68 8.93 8.37

-12 -3 -31 -209 +45 -25

4 4 4 4 4

24 24 29 34 36

07.2 48.5 49.0 26.5 20.9

3.470 2.257 3.513 1.304 2.336

+75 +17 35 20.26 +56 -33 58 13.30 +76 +19 13 27.21 +60 -55 00 12.07 -35 -30 31 17.35

+8.11 8.14 7.65 7.31 +7.14

-30 +50 -38 -4 -12

+24 +24 +31 -13 +40 +35

10 06 56 27 04 50

01.07 +10.82 52.38 10.69 34.29 10.35 03.88 9.99 05.25 10.05 53.59 10.00

No. 111 : Algol , Mag. 2.1 to 3.4. No. 120 : Mirphak. No. 139 : Alcyone , Krittika.

-46 -47 -10 -112 -26 0

217

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

168 172 1129 1134 179 180

1457 1481 1502 1543 1552 1567

 Tauri* 53 Eridani  Caeli 3 Orionis 4 Orionis 5 Orionis

178 181 183 1137 182 186

1542 1577 1605 1612 1603 1654

 Camelopardi  Aurigae  Aurigae Aurigae  Camelopardi  Leporis

185 188 1144 194 193 195

1641 1666 1702 1713 1708 1735

1147 201 202 204 214 206

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

Declination

s (0.0001)

º

'

+66 +33 +43 +41 +60 -22

22 11 51 06 28 20

"

"

37 39 41 50 52 55

06.0 07.2 13.4 57.3 18.0 19.3

3.451 2.751 1.937 3.263 3.201 3.131

4.29 O9.5 I ae 2.69 K3 II 2.99V A8 Iab 3.75 K4Ib-II+ 4.03 G1Ib-II 3.19 K4 III

4 4 5 5 5 5

56 58 03 03 05 06

06.1 19.9 26.7 54.9 15.0 19.8

6.012 3.918 4.320 4.207 5.366 2.543

-1 +3 -1 +8 -9 +18

21.67 47.94 05.40 13.30 10.53 41.22

+5.52 5.31 4.89 4.83 4.73 4.58

+6 -18 -4 -22 -16 -74

 Aurigae  Eridani  Leporis  Orionis  Aurigae Orionis

3.17 B3 V 2.79 A3III 3.31 B9IV 0.12 B8 Iab 0.08 G5IIIe+ 3.60 B5 III

5 5 5 5 5 5

07 08 13 15 18 18

57.4 51.5 51.2 31.4 12.4 36.2

4.220 2.954 2.698 2.887 4.444 2.917

+26 +41 15 36.52 -63 -5 03 41.08 +30 -16 10 57.52 0 -8 10 45.91 +72 +46 01 00.04 -10 -6 49 25.34

+4.44 4.35 3.98 3.86 3.21 3.59

-68 -81 -26 -1 -425 -8

1765 1790 1791 1829 1953 1852

22Orionis γ Orionis  Tauri  Leporis γ Mensae  Orionis

4.73 B2IV-V 1.64 B2 III 1.65 B7 III 2.84 G5 II 5.19 K2 III 2.23 O9.5 II+

5 5 5 5 5 5

22 26 27 29 31 33

49.0 13.9 35.4 07.5 04.9 03.6

3.085 3.222 3.799 2.574 -2.340 3.083

0 -0 23 49.78 -6 +6 21 59.75 +17 +28 37 22.14 -3 -20 44 39.94 +320 -76 19 30.87 +1 0 18 07.80

+3.24 2.93 2.65 2.60 2.80 2.35

-1 -14 -175 -89 +282 -2

207 212 (GC) 209 210 211

1865 1922 1879 1899 1903 1910

 Leporis  Doradus Orionis Orionis Orionis Tauri

5 5 5 5 5 5

33 33 36 36 37 38

38.1 48.3 16.1 26.2 15.3 52.3

2.649 0.528 3.308 2.938 3.048 3.590

215 1154 217 219 220 223

1956 2015 1983 1998 2004 2040

 Columbae Doradus γ Leporis Leporis  Orionis  Columbae

2.64 B7 IVe 4.35 A7V 3.60 F6 V 3.55 A2 IV-V(n) 2.06 B0Iab 3.12 K1 IIICN+1

5 5 5 5 5 5

40 44 45 47 48 51

23.5 48.7 19.1 53.1 43.8 41.0

2.176 0.114 2.503 2.721 2.848 2.119

+5 -49 -212 -11 +1 +49

-34 -65 -22 -14 -9 -35

3.81 K1IVFe 0.5 M2Iab

5 52 5 56

12.2 16.9

2.582 3.251

+161 +17

222 2035  Leporis 224 2061 Orionis 

2.58 3.76v 3.54 2.77 1.70 3.00

K5III K1III F2 V F6 V B2 III+ B3 III+

F0 Ib F6Ia O8 III O9 III B0 Iab B2IV

No. : Aldebaran, Rohini No. 183 : Mag. 2.9 to 3.8. No. 188 : C ursa . No. 194 : Rigel. No. 193 : Capella , Brahmahridaya. No. 201 : Bellatrix. No. 202 : El Nath , Agni. No. 206 : Mintaka .

+1 -17 +3 -62 -1 +9 0 -5 +1 -1 0 +21

+6.90 6.77 6.68 5.96 5.84 5.58

" (0.001)

4 4 4 4 4 4

0.85 3.87 4.45 3.19 3.69 3.72

+44 +16 32 55.89 -52 -14 15 54.52 -126 -41 49 32.29 +313 +6 59 43.64 -1 +5 38 18.87 0 +2 28 28.59

Annual Annual Variation Proper motion

-190 -155 -77 +11 +1 0

48 28 56 53 11 09

32.25 36.28 46.41 52.52 25.43 11.55

+2.30 2.29 2.07 2.06 1.98 1.82

+2 +9 -2 +1 -2 -21

03 43 26 48 39 45

51.78 34.82 40.54 56.59 49.73 42.41

+1.69 1.34 0.91 1.06 0.98 1.13

-26 +8 -369 -1 -2 +401

-20 52 43.43 +7 24 33.19

+0.03 +0.33

-649 +9

No. 207 : Arneb . No. GC : Mrgasiras . No. 210 : Alnilam. No. 215 : Phakt . No. 220 : Saiph . No. 224 : Betelgeuse , Mag. 0.4 to 1.3 Ardra.

218

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

226 229 227 225 1163 1168

2085 2120 2088 2077 2134 2219

Leporis Columbae Aurigae Aurigae 1 Geminorum  Aurigae

240 243 241 245 244 1173

2282 2294 2286 2326 2298 2343

252 251 254 257 256 262

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

3.71 F2 V 3.96 K01II 1.90 A2IV+ 3.72 K0 III 4.16 G5III 4.35 G8.5IIIb

5 5 6 6 6 6

57 59 01 01 05 16

20.4 46.5 02.0 13.0 22.0 41.1

2.735 1.839 4.404 4.943 3.649 3.823

Canis Maj. Canis Maj. Geminorum  Carinae 8Monocerotis Geminorum

3.02 B2.5V 1.98 B1 II/III 2.88 M3 III -0.72 F0II 4.44 A5 IV 4.15 B6 IIIe

6 6 6 6 6 6

21 23 24 24 24 30

06.1 36.2 12.0 24.5 51.3 10.8

2451 2421 2473 2491 2484 2550

 Puppis γ Geminorum Geminorum Canis Majcg Geminorum  Pictoris

3.17 B8 III 1.93 A0 IV 2.98 G8 Ib -1.46 A1V 3.36 F5 IV 3.27 A8VmkA6

6 6 6 6 6 6

38 38 45 46 46 48

263 1180 261 268 1183 270

2553 2538 2540 2618 2646 2653

 Puppis Canis Maj. θ Geminorum Canis Maj. Canis Maj. o 2 Canis Maj.

2.93 K1 III 3.96 B1.5IVe 3.60 A3III 1.50 B2 Iab 3.47 M1.5Iab 3.02 B3 Ia

6 6 6 6 7 7

269 1189 273 1187 281 278

2650 2736 2693 2714 2803 2773

 Geminorum γ2 Volantis Canis Maj. 22Monocerotis Volantis  Puppis

277 279 283 282 285 1194

2763 2777 2827 2821 2845 2878

 Geminorum  Geminorum  Canis Maj.  Geminorum  Canis Min  Puppis

287 2891  Gemino. cg 291 2943  C. Min. cg 297 3024  Volantis 

s (0.0001)

-28 +20 -54 +92 -6 -57

Declination

º

-14 -42 +44 +54 +23 +29

'

09 48 56 17 15 29

"

Annual Annual Variation Proper motion "

" (0.001)

55.41 54.16 50.28 01.71 37.61 18.86

+0.37 +0.01 -0.09 0.23 0.57 1.72

+139 -14 0 -126 -100 -262

2.306 2.644 3.630 1.333 3.181 3.562

+7 -30 04 25.28 -4 -17 58 02.80 +39 +22 30 04.31 +25 -52 42 50.96 -12 +4 34 27.34 -5 +20 11 50.41

-1.84 2.06 2.22 2.11 2.16 2.65

+3 0 -111 +21 +11 -14

23.3 53.8 11.6 03.0 26.4 24.0

1.838 3.465 3.689 2.643 3.366 0.612

+2 -43 12 48.23 +29 +16 22 53.57 -4 +25 06 32.25 -386 -16 44 43.90 -79 +12 52 18.42 -96 -61 57 49.38

-3.35 3.43 3.94 5.20 4.22 3.93

-6 -42 -13 -1204 -191 +269

50 50 54 59 02 03

26.7 36.4 08.3 25.9 32.2 52.8

1.490 2.243 3.949 2.360 2.392 2.507

+38 -50 38 59.84 -5 -32 31 23.42 -2 +33 56 04.47 +3 -29 00 04.10 -4 -27 57 55.37 -3 -23 51 52.20

-4.45 4.39 4.74 5.14 5.40 5.51

-70 +4 -48 +3 +5 +3

3.79v 3.78 1.86 4.15 3.98 2.70

G0Ibv K0III F8 Iab A2V F6II K3Ib

7 7 7 7 7 7

05 08 09 12 16 17

19.4 34.0 13.5 55.1 48.9 52.0

3.555 -0.532 2.441 3.085 -0.048 2.121

-6 +20 32 18.51 +47 -70 31 36.97 -2 -26 25 55.41 -1 -0 26 41.50 -12 -67 59 41.09 -8 -37 08 07.31

-5.64 5.80 5.96 6.26 6.59 6.67

0 +106 +4 +5 +5 +4

3.58 3.53 2.45 3.79 2.90 3.25

A3V F0 IV B5 Ia G9 IIIb B8Ve K5 III

7 7 7 7 7 7

19 21 24 26 28 29

16.2 20.7 54.4 59.9 15.7 52.9

3.444 3.578 2.375 3.719 3.251 1.905

-33 +16 30 06.26 -19 +21 56 34.28 -3 -29 20 39.20 -93 +27 45 20.03 -35 +8 14 47.29 -50 -43 20 37.96

-6.83 6.98 7.25 7.51 7.57 7.47

-37 -12 +5 -86 -38 +187

7 35 7 40 7 41

54.3 22.4 33.3

3.820 3.137 -0.783

-135 +31 50 30.62 -477 +5 10 15.73 +67 -72 39 01.04

-8.24 9.52 -8.57

-98 -1022 +18

1.95 A2Vm 0.38 F5 IV-V 3.95 K0III

No. 225 : Prajapati. No. 227 : Menkalinam . No. 243 : Mirzam. No. 245 : Canopus , Agastya. No. 251 : Alhena .

No. 257 : Sirius , Lubdhaka Mag. - 1.46. No. 268 : Adhara. No. 269 : Mekbuda Mag. 3.7 to 4.1. No. 285 : Gomeisa. No. 287 : Castor, Punarvasu-2, Mag. 1.95 & 2 No. 291 : Procyon , Mag. 0.38 & 11.3.

219

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

s

s

293 294 295 1204 301 303

2970 2985 2990 3045 3080 3117

26Monocerotis Geminorum Geminorum  Puppis 213 G. Puppis  Carinae

3.93 G9 III 3.57 G8 III 1.14 K0IIIb 3.34 G6 Ia 3.73 K1/2II+ 3.47 B3IVp

42 45 46 50 52 57

13.6 41.0 34.1 09.4 55.4 18.0

2.867 3.614 3.662 2.525 2.064 1.524

306 308 309 312 315 319

3165 3185 3207 3249 3307 3347

 Puppis Puppis γ2 Velorum Cancri Carinae Volantis

2.25 O4If(m)p 8 04 2.81 F6IIp 8 08 1.78 WC8+O7.5 8 10 3.52 K 3:IIIv 8 17 1.86 K2III 8 22 3.77 K2 III 8 25

18.3 25.1 09.9 37.6 56.0 57.2

2.111 2.557 1.850 3.249 1.225 0.633

316 317 321 1223 1224 1227

3314 3323 3366 3410 3418 3447

Br 1197 Hydrae o Ursae Maj. Cancri  Hydrae  Hydrae o Velorum

3.90 3.36 5.33 4.16 4.44 3.62

A0V G5 III K3 III A1Vnn K1 III B3 IV

8 8 8 8 8 8

26 31 33 38 39 40

41.1 57.1 53.5 44.4 49.7 52.8

1226 327 1228 326 (329) 328

3445 3468 3449 3461 3482 3475

53 G. Velorum  Pyxidis γ Cancri  Cancri  Hydrae m  Cancri

3.84 3.68 4.66 3.94 3.38 4.02

F3 Ia B1.5 III A1IV K0 III G5III G8Iab

8 8 8 8 8 8

41 44 44 45 47 47

336 334 337 335 342 341

3571 3547 3572 3569 3614 3594

108 G. Carinae  Hydrae  Cancri  Ursae Maj. 97 G. Velorum Ursae Maj.

3.84 3.11 4.25 3.14 3.75 3.60

B8.5II G9 II-III A5 m A7 V K2 III A1Vn

8 8 8 9 9 9

345 1239 348 347 351 352

3634 3627 3685 3665 3699 3705

 Velorum Cancri  Carinae θ Hydrae  Carinae  Lyncis

2.21 5.14 1.68 3.88 2.25 3.13

K4 Ib-II G9 III A2IV B9.5 V A8 Ib K7 III

1243 353 354 361 355 358

3718 3734 3748 3803 3757 3775

θ Pyxidis  Velorum  Hydrae N Velorum 23 Ursae Maj. θ Ursae Maj.

4.72 2.50 1.98 3.13 3.67 3.17

M0 III B2 IV-V K3 II-III K5 III F0 IV F7V



No. 295 : Pollux, Punarvasu-1. No. 326 : Pusya. No. 329 : Aslesa.

7 7 7 7 7 7

m

Declination

s (0.0001)

º

'

-24 -61 -4 -30 -35 -60

-40 -24 -47 +9 -59 -66

03 21 23 07 34 12

Annual Annual Variation Proper motion

"

-49 -9 36 17.84 -24 +24 20 49.82 -474 +27 58 30.10 -2 -24 54 44.63 -8 -40 37 46.82 -32 -53 02 16.82

"

-8.66 8.97 9.03 9.27 9.48 9.79

" (0.001)

-19 -52 -45 -2 +3 +21

42.92 52.14 52.31 15.56 33.86 28.26

-10.33 10.60 10.77 11.37 11.69 12.07

+12 +49 +6 -49 +14 -155

2.996 4.930 3.460 3.172 3.133 1.719

-44 -3 58 20.36 -182 +60 38 51.55 -34 +20 22 12.48 -44 +5 37 51.68 -12 +3 16 05.47 -24 -52 59 43.60

-11.99 12.44 12.51 12.80 12.89 12.92

-23 -107 -43 -7 -18 +20

18.5 25.0 28.1 50.8 51.5 56.0

1.994 2.414 3.462 3.401 3.170 3.617

0 -46 43 20.93 -9 -33 15 36.33 -76 +21 23 40.36 -13 +18 04 39.51 -155 +6 20 00.80 -19 +28 41 32.88

-12.97 13.17 13.22 13.50 13.44 13.45

+3 +11 -39 -228 -40 -42

55 56 59 00 04 05

30.6 28.6 36.4 36.1 51.8 01.0

1.355 3.167 3.275 4.076 2.073 4.065

-28 -60 43 24.43 -66 +5 51 58.85 +23 +11 46 37.84 -443 +47 57 35.05 -44 -47 10 26.50 -32 +47 04 48.45

-13.85 13.94 14.18 14.43 14.48 14.53

+38 +15 -31 -225 -13 -54

9 9 9 9 9 9

08 10 13 15 17 22

45.1 32.1 25.0 25.8 38.3 17.9

2.211 3.438 0.631 3.118 1.605 3.636

-17 -43 30 58.06 +1 +21 57 40.80 -311 -69 48 06.63 +86 +2 13 36.09 -26 -59 21 42.56 -179 +34 18 16.91

-14.69 14.80 14.87 15.40 15.21 15.46

+13 +5 +108 -310 +8 +19

9 9 9 9 9 9

22 22 28 31 33 34

24.1 45.0 35.7 50.8 07.4 13.0

2.660 1.861 2.948 1.826 4.657 3.974

-15.49 15.50 15.79 15.99 16.04 -16.65

-8 +9 +33 +4 +27 -530

-8 -26 03 -10 -55 05 -9 -8 44 -39 -57 07 +160 +62 58 -1024 +51 34

12.81 55.95 54.34 31.40 14.78 57.72

No. 337 : Acubens. (Aslesa.) No. 353 : Markeb . No. 354 : Alphard .

220

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

1250 364 365 367 368 371

3845 3849 3852 3873 3888 3905

 Hydrae  Hydrae o Leonis  Leonis v Ursae Maj. Leonis

3.91 5.06 3.52 2.98 3.80 3.88

9 9 9 9 9 9

40 41 42 47 52 53

54.1 17.4 14.6 00.7 25.8 55.5

3.062 2.878 3.196 3.393 4.210 3.399

375 1261 379 380 381 385

3940 3970 3975 3982 3994 4037

φVelorum v 2 Hydrae  Leonis  Leonis λ Hydrae ω Carinae

3.54 B5 Ib 9 4.60 B8 V 10 3.52 A0 Ib 10 1.35 B7 V 10 3.61 K0IIICN+1 10 3.32 B8 IIIe 10

57 06 08 09 11 14

35.1 07.4 26.9 27.7 35.3 13.3

382 1264 384 383 1268 386

4023 4050 4031 4033 4080 4069

191 G.Velorum 187 G. Carinae  Leonis λ Ursae Maj. 204 G.Velorum  Ursae Maj.

3.85 3.40 3.44 3.45 4.83 3.05

A2 Va K3 II a F0 III A2 IV K1 III M0 III

10 10 10 10 10 10

15 17 17 18 23 23

391 389 392 393 1270 397

4102 4094 4104 4114 4116 4140

I Carinae  Hydrae  Antliae 196 G. Carinae  Sextantis 203 G. Carinae

4.00 3.81 4.25 3.82 5.21 3.32

F3 V K4III K4 III F2II B9.5 V B4 Vne

10 10 10 10 10 10

396 401 406 411 410 412

4133 4174 4199 4234 4232 4247

 Leonis γ Chamaeleontis θ Carinae 2 Chamaeleontis  Hydrae 46 Leonis Min.

3.85 4.11 2.76 4.45 3.11 3.83

B1 Iab M0 III B0Vp B2.5 IV K0/K1III K0IIIV

1283 416 417 1289 420 422

4287 4295 4301 4337 4335 4357

 Crateris  Ursae Maj.  Ursae Maj. 260 G. Carinae ψ Ursae Maj.  Leonis

4.08 2.37 1.80 3.91 3.01 2.56

423 425 426 433 434 436

4359 4377 4382 4434 4450 4467

θ Leonis  Ursae Maj.  Crateris λ Draconis ξ Hydrae λ Centauri

3.34 3.48 3.56 3.84 3.54 3.13



s (0.0001)

Declination

º

'

"

Annual Annual Variation Proper motion "

" (0.001)

+32 -1 14 12.64 -19 -14 25 34.18 -96 +9 47 53.24 -34 +23 40 43.94 -379 +58 56 28.20 -160 +25 54 34.07

-16.53 16.50 16.57 16.77 17.17 17.14

2.115 2.924 3.262 3.189 2.927 1.420

-12 -54 39 57.40 -25 -13 09 53.24 -1 +16 39 42.85 -169 +11 51 58.48 -138 -12 27 21.87 -76 -70 08 24.11

-17.25 17.60 17.71 17.75 17.93 17.94

+3 +18 0 +7 -88 +7

36.0 46.2 49.6 19.5 12.6 32.6

2.529 2.013 3.325 3.592 2.585 3.549

-131 -42 13 27.04 -34 -61 26 51.85 +13 +23 18 06.68 -149 +42 48 40.42 -20 -41 45 13.51 -72 +41 23 44.40

-17.95 18.08 18.09 18.14 18.22 18.26

+45 +5 -7 -38 +56 +35

24 27 28 28 30 32

47.8 05.0 05.6 38.1 31.2 45.4

1.173 2.906 2.754 2.216 3.047 2.147

10 10 10 10 10 10

33 35 43 45 50 54

53.3 41.6 41.5 56.9 38.3 27.2

K1III A1V K0 Iab G0Iab K1 III A4V

11 11 11 11 11 11

00 03 04 09 10 15

A2V K3 III K0III M0 III G7 III B9III

11 11 11 11 11 11

15 19 20 32 34 36

K2.5 III B4IV/V F5I+ G1 II F2 IV K2 III

No. 380 : Regulus , Magha. No. 416 : Merak , Pulaha.

-52 -89 -58 -17 -32 -27

-64 -20 -37 -11 -151 -56

-74 -16 -31 -58 -2 -61

08 56 10 50 50 47

10.12 29.69 21.83 40.49 40.71 28.35

-18.36 18.50 18.44 18.47 18.55 18.60

-26 -80 +11 0 -14 +9

3.154 0.653 2.156 0.479 2.965 3.338

-4 +9 -143 -78 -35 -64 -201 -80 +66 -16 +70 +34

12 42 30 38 18 06

01.76 50.99 07.96 54.05 05.08 13.94

-18.65 18.69 18.93 19.00 18.93 19.51

-3 +14 +10 +8 +200 -279

46.5 03.9 58.6 28.3 48.5 11.8

2.929 3.577 3.647 2.586 3.348 3.182

-323 +99 -167 -9 -60 +101

24 16 38 05 23 24

29.97 19.37 23.04 10.99 12.81 39.79

-19.25 19.39 19.53 19.56 19.61 19.79

+130 +34 -66 0 -28 -130

18.8 34.9 22.1 36.0 00.9 44.2

3.142 3.225 3.006 3.488 2.965 2.802

-42 +15 19 01.86 -20 +32 58 55.70 -84 -14 53 23.15 -73 +69 13 03.72 -162 -31 58 16.44 -61 -63 08 00.08

-19.74 19.70 19.53 19.92 19.95 -19.94

-79 +28 +208 -17 -39 -5

-18 +56 +61 -59 +44 +20

No. 417 : Dubhe , Kratu. No. 422 : Zosma , Purva Phalguni-1. No. 423 : Purva Phalguni-2.

221

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

442 441 1304 444 445 447

4520 4518 4527 4534 4540 4554

λ Muscae  Ursae Maj. 93 Leonis  Leonis  Virginis γ Ursae Maj.

3.64 A7 V 3.71 K0.5 IIIb 4.53v A7V+ 2.14 A3 V 3.61 F9 V 2.44 A0 Ve

11 11 11 11 11 11

46 47 49 50 51 54

35.2 07.5 02.5 06.2 45.8 54.0

2.875 3.144 3.088 3.056 3.126 3.126

452 453 455 456 457 459

4621 4630 4656 4660 4662 4674

 Centauri  Corvi  Crucis  Ursae Maj. γ Corvi  Chamaeleontis

2.60 3.00 2.80 3.31 2.59 4.26

12 12 12 12 12 12

09 11 16 16 16 19

25.8 11.0 14.7 25.9 51.8 35.5

460 462 465 468 469 472

4689 4730 4757 4763 4773 4787

Virginis  CrucisA  Corvi γ Crucis γ Muscae  Draconis

3.89 A2 IV+ 12 20 1.33 B0.5 IV 12 27 2.95 A0IV(m)kB9 12 30 1.63v M3.5 III 12 32 3.87 B5V 12 33 3.87v B6IIIp 12 34

471 474 475 1326 481 483

4786 4798 4813 4828 4853 4905

 Corvi  Muscae  Virginis  Virginis  Crucis  Ursae Maj.*

2.65 2.69 4.66 4.88 1.25 1.77

G5 II B2 IV-V K2 III A0 V B0.5 IV A0p

12 12 12 12 12 12

484 485 488 487 492 495

4910 4915 4932 4923 4983 5020

 Virginis  CVn sq*  Virginis  Muscae  Com γ Hydrae

3.38 2.90 2.83 3.62 4.26 3.00

M3III A0spe G8 III K2 III G0 V G8 III

496 497 498 501 504 509

5028 5054 5056 5107 5132 5191

Centauri Ursae Maj.pr  Virginis  Virginis  Centauri Ursae Maj.

2.75 kA15hA3nA3va 2.27 A2V 0.98 B1 III-IV+ 3.37 A3V 2.30 B1 III 1.86 B3 V

508 5193  Centauri 513 5235  Bootis 512 5231  Centauri 

3.04 2.68 2.55

s (0.0001)

º

50 39 06 27 38 34

"

"

" (0.001)

-19.97 19.98 20.02 20.14 20.30 20.02

3.139 3.098 3.227 2.941 3.095 3.669

-36 -50 50 11.47 -51 -22 44 01.29 -53 -58 51 46.16 +127 +56 55 07.74 -112 -17 39 20.31 -174 -79 25 33.03

-20.03 20.00 20.00 19.98 19.96 19.95

-8 +13 -9 +9 +23 +17

57.3 45.2 55.7 18.9 43.0 20.8

3.070 3.390 3.114 3.370 3.674 2.526

-42 -0 -53 -63 -146 -16 +29 -57 -126 -72 -112 +69

50.12 44.81 45.66 39.81 45.28 31.49

-19.98 19.91 20.00 20.10 19.83 19.80

-18 -12 -138 -262 -2 +12

35 38 40 42 48 54

28.1 25.6 18.4 55.3 56.0 55.5

3.165 3.655 3.104 3.037 3.555 2.621

+2 -23 30 35.52 -90 -69 14 53.51 -51 -8 06 29.43 +57 +10 07 22.43 -63 -59 48 01.50 +132 +55 50 56.04

-19.86 19.77 19.76 19.78 19.60 19.47

-54 -13 -25 -90 -14 -6

12 12 13 13 13 13

56 56 03 03 12 20

38.2 59.0 11.8 42.7 49.7 02.4

3.025 2.797 2.987 4.236 2.795 3.277

-313 +3 17 11.03 -198 +38 12 28.93 -185 +10 50 57.70 +543 -71 39 31.75 -604 +27 46 28.91 +47 -23 16 44.98

-19.49 19.37 19.26 19.29 18.16 18.88

-54 +56 +20 -20 +881 -45

13 13 13 13 13 13

21 24 26 35 41 48

45.4 44.9 16.6 44.1 12.0 20.8

3.396 2.404 3.170 3.052 3.846 2.358

-284 -36 49 11.43 +141 +54 49 07.61 -28 -11 16 03.74 -190 -0 28 00.44 -32 -53 34 11.29 -125 +49 12 41.59

-18.87 18.71 18.67 18.28 18.14 17.85

-86 -20 -28 +42 -17 -11

B2Vmpe 13 50 G0 IV 13 55 B2.5 IV 13 56

51.6 39.6 49.7

3.644 2.857 3.778

-21 -42 34 30.18 -44 +18 17 44.31 -56 -47 23 18.18

-17.76 17.90 -17.54

-20 -358 -42

No. 1304 : Uttara Phalguni-2. No. 444 : Denebola, Uttara Phalguni-1. No. 447 : Phecda or Phad, Pulastya. No. 456 : Megrez, Atri. No. 457 : Minkar. No. 462 : Acrux . No. 465 : Algorel , Hasta.

-66 +47 +20 +14 +1 +53

'

Annual Annual Variation Proper motion

32.82 56.34 17.70 26.57 56.74 50.63

B2 IV ne K2III B2 IV A3 V B8III B5 Vn

-174 -136 -106 -342 +495 +107

Declination

32 12 37 13 14 40

+37 +30 -3 -114 -271 +12

No. 483 : Alioth, Angira. No. 484 : Minelauva. No. 485 : 12 Canum Venaticorum, Mag. p 2.9 No. 488 : Vindemiatrix. No. 497 : Mizar , Vasista. Mag. f . 4.0. No. 498 : Spica , Citra. No. 509 : Alkaid, Benetnasch, Marichi.

222

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

521 518 519 520 523 526

5291 5267 5287 5288 5315 5340

 Draconis Centauri  Hydrae θ Centauri  Virginis  Bootis

3.65 A0 III 14 04 0.61 B1 III 14 05 3.27 K1III-IV 14 07 2.06 K0 III 14 07 4.19 K2.5 III 14 13 -0.04 K1.5 III 14 16

525 1371 531 534 535 537

5338 5359 5404 5429 5435 5440

 Virginis λ Virginis θ Bootis Bootis γ Bootis Centauri

4.08 F7IV 4.52 A1V 4.05 F7 V 3.58 K3 III 3.03 A7 III 2.31 B1.5 IVne

14 14 14 14 14 14

538 541 545 539 544 547

5460 5469 5487 5463 5485 5511

Centauricg Lupi  Virginis Circini 371 G.Cen 109 Virginis

0.00 2.30 3.88 3.19 4.05 3.72

542 550 548 552 553 555

5470 5563 5531 5571 5576 5602

Apodis Ursae Min. Librae  Lupi  Centauri  Bootis

3.83 2.08 2.75 2.68 3.13 3.50

556 559 558 563 564 560

5603 5652 5649 5681 5685 5671

569 1402 566 571 572 578 577 579 1413 582 

s

s

56.7 17.3 32.7 53.8 59.5 35.8

1.629 4.297 3.435 3.555 3.211 2.739

17 20 25 32 32 36

05.6 13.4 53.7 42.8 54.2 49.1

3.155 3.258 2.042 2.585 2.415 3.839

14 14 14 14 14 14

41 43 44 44 44 47

00.3 18.2 08.6 11.3 55.1 17.2

4.128 4.026 3.171 4.932 3.693 3.040

14 14 A2HA5MA4IV- 14 B2 III 14 B2 IV 15 G8 IIIa 15

50 50 52 59 00 02

30.2 40.0 01.0 53.0 30.2 43.1

Librae  Librae  Lupi  Bootis  Librae γ Tr. Austrini

3.29 M3/M4III 15 05 4.54 B9IV pSc 15 13 3.41 G7 III 15 13 3.47 G8 III 15 16 2.61 B8 IV 15 18 2.89 A1 IV 15 20

5735 5695 5705 5744 5747 5793

γ Ursae Min.  Lupi φ' Lupi  Draconis  Cr. Borealis Cr.Borealis

3.05 3.22 3.56 3.29 3.68 2.23

A 3 Iab B1.5 IV K5 III K2 III F0p A0 V

15 15 15 15 15 15

5787 5794 5838 5854

γ Librae  Librae  Librae Serpentis

3.91 3.58 4.74 2.65

K0III K5 III K5III K2 III b

15 15 15 15

G+ B1.5 III F2 V A 7VpSrCrEu

K5 III A0 V K2.5 III K4 III

s (0.0001)

Declination

º

'

"

Annual Annual Variation Proper motion "

" (0.001)

-84 +64 16 14.85 -43 -60 28 41.86 +33 -26 46 48.79 -429 -36 28 11.78 +5 -10 22 05.73 -769 +19 04 35.24

-17.12 17.14 17.16 17.52 16.57 18.59

-2 -6 05 50.96 -11 -13 27 52.28 -253 +51 45 23.86 -77 +30 16 56.10 -97 +38 13 09.65 -31 -42 14 48.22

-16.99 16.38 16.51 15.64 15.59 15.56

-432 +30 -398 +119 +153 -35

07.57 29.59 46.59 46.12 38.81 26.81

-14.60 15.18 15.43 15.35 15.25 14.96

+692 -18 -316 -232 -180 -27

7.783 -0.105 3.331 3.959 3.932 2.261

-41 -79 07 45.38 -76 +74 04 17.94 -73 -16 07 32.95 -32 -43 12 54.73 -17 -42 11 06.61 -36 +40 18 37.97

-14.76 14.72 14.72 14.22 14.16 14.03

-16 +12 -67 -39 -24 -28

16.5 23.6 46.2 19.8 06.8 51.2

3.528 3.434 4.351 2.421 3.238 5.703

-54 -25 21 40.55 -25 -19 52 04.90 -122 -52 10 32.43 +69 +33 14 21.34 -65 -9 27 26.37 -132 -68 45 11.28

-13.88 13.36 13.37 13.24 13.03 12.86

-43 -39 -73 -112 -19 -31

20 22 23 25 28 35

42.7 43.5 06.8 23.3 40.5 33.4

-0.043 3.964 3.829 1.345 2.476 2.543

-40 -13 -74 -12 -137 +91

+71 -40 -36 +58 +29 +26

45 43 20 53 02 38

39.79 13.20 03.47 41.24 09.76 48.35

-12.81 12.73 12.76 12.50 12.21 11.90

+20 -26 -84 +17 +86 -88

36 38 43 45

40.6 16.4 07.9 16.8

3.367 3.658 3.469 2.961

+45 -7 -26 +92

-14 -28 -19 +6

51 12 44 21

23.57 05.20 37.91 44.67

-11.72 11.62 11.37 -11.07

+9 +3 -103 +47

No. 518 : Agena . No. 521 : Thuban . No. 526 : Arcturus , Svati. No. 538 : Rigil Kentaurus Mag. 0.33 & 1.70. No. 548 : Zuben el Genubi, Visakha.

-4998 -21 +73 -302 -52 -76

-60 -47 -5 -65 -35 +1

55 28 44 03 15 48

No. 550 : Kochab . No. 559 : Visakha. No. 564 : Zuben es Chamali. No. 578 : Margarita, Alphecca. No. 582 : Unukalhaly.

+18 -19 -139 -520 +140 -2000

223

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

s (0.0001)

Declination

º

'

"

Annual Annual Variation Proper motion "

" (0.001)

583 585 588 589 591 592

5867 5881 5892 5897 5933 5944

 Serpentis  Serpentis  Serpentis  Tr.Australis γ Serpentis Scorpii

3.67 3.54 3.71 2.85 3.85 2.89

A3V A0 V A2 m F1V F6 V B1 V+

15 15 15 15 15 16

47 50 51 56 57 00

08.1 41.5 50.4 58.0 24.1 05.8

2.773 3.138 2.996 5.349 2.776 3.643

594 597 603 605 608 607

5953 5984 6056 6075 6092 6084

 Scorpii  Scorpiipr  Ophiuchi  Ophiuchi  Herculis  Scorpii

2.32 2.62 2.74 3.24 3.89 2.89

B0.2 Ive B0.5 V M0.5 III G9.5 IIIb B5 IV B1 III

16 16 16 16 16 16

01 06 15 19 20 22

33.0 37.9 25.3 24.5 21.5 26.3

3.560 3.500 3.151 3.181 1.808 3.659

-8 -22 40 -4 -19 51 -29 -3 44 +57 -4 44 -11 +46 15 -8 -25 38

42.46 35.88 44.39 27.63 55.47 25.28

-9.93 9.53 8.97 8.48 8.40 8.30

-22 -19 -143 +41 +40 -21

609 613 616 618 611 620

6095 6117 6134 6148 6102 6165

γ Herculis  Herculis  Scorpiicg Herculis γ Apodis  Scorpii

3.75 B9 III 4.57 B9 p 0.96 M1.5 Iab-b 2.77 G7 III a 3.89 G8III 2.82 B0.2 V

16 16 16 16 16 16

22 26 30 31 36 37

49.5 21.8 40.1 06.1 39.5 09.7

2.650 2.773 3.690 2.582 9.418 3.746

-33 +19 06 22.31 +30 +13 59 14.52 -7 -26 28 32.74 -70 +21 26 46.12 -452 -78 56 20.05 -6 -28 15 24.54

-8.20 8.02 7.64 7.60 7.21 7.11

+43 -59 -20 -15 -77 -22

622 626 625 1438 628 1435

6175 6220 6217 6243 6241 6229

 Ophiuchi  Herculis  Tr. Austr. Ophiuchi  Scorpii  Arae

2.56 3.53 1.92 4.65 2.29 3.76

16 16 16 16 16 16

38 43 50 50 51 51

17.4 36.0 51.2 58.2 29.7 33.9

3.311 2.060 6.412 3.326 3.898 5.212

+9 -10 36 25.37 +32 +38 53 03.57 +26 -69 03 44.48 +65 -10 49 32.11 -493 -34 19 03.67 +49 -59 04 43.10

-6.97 6.64 5.99 6.04 6.16 5.92

+26 -82 -34 -93 -257 -28

1439 633 631 634 635 639

6247 6299 6285 6324 6355 6396

1 Scorpii  Ophiuchi  Arae  Herculis 60 Herculis  Draconis

3.08v B1.5Vp+ 16 53 3.20 K2 III 16 58 3.13 K3III 17 00 3.92 A0 V 17 01 4.91 A4 IV 17 06 3.17 B6 III 17 08

15.8 38.4 19.4 04.5 19.8 51.0

4.077 2.844 4.989 2.298 2.786 0.188

-9 -38 04 50.40 -197 +9 20 40.34 -23 -56 01 12.51 -36 +30 53 50.51 +35 +12 42 50.65 -33 +65 41 22.24

-5.78 5.31 5.20 5.07 4.66 4.41

-25 -11 -36 +27 -10 +22

638 643 641 644 645 1457

6380 6418 6410 6453 6461 6486

 Scorpii  Herculis Herculis θ Ophiuchi Arae 44 Ophiuchi

3.33 3.16 3.14 3.27 2.85 4.17

653 649 648 651 652 656

6536 6508 6500 6510 6527 6556

 Draconis v Scorpii  Arae  Arae λ Scorpii*  Ophiuchi

2.79 2.69 3.62 2.95 1.63 2.08



O9V G7 .5IIIb K2 II-III F7 V K1 III K5 III

+46 +15 21 31.86 -57 -3 29 29.82 +86 +4 25 02.38 -283 -63 29 30.06 +217 +15 35 45.43 -8 -26 10 17.52

-11.02 10.74 10.57 10.65 11.50 10.04

-45 -24 +63 -398 -1281 -26

17 17 17 17 17 kA5hA9mF1III 17

13 15 15 23 27 27

37.5 45.7 52.5 16.2 00.5 37.4

4.309 2.093 2.467 3.691 5.002 3.670

+23 -43 15 50.73 -22 +36 47 58.59 -15 +24 48 13.64 -3 -25 01 05.34 -10 -55 32 48.59 0 -24 11 32.48

-4.31 3.84 3.99 3.22 2.90 2.94

-287 +4 -157 -20 -25 -116

17 17 17 17 17 17

30 32 32 33 35 35

53.8 09.6 57.2 25.8 00.2 53.2

1.360 4.086 5.432 4.648 4.080 2.788

-17 +52 17 12.98 -1 -37 18 36.69 -80 -60 41 53.69 -32 -49 53 24.67 -1 -37 07 00.29 +83 +12 32 47.50

-2.52 2.46 2.46 2.39 2.21 -2.33

+15 -31 -96 -70 -29 -226

F5IV K3 Ib A3IV B2 IV K3 Ib-II G2Iab B2 IV B8 Vn B2 Vne B2 IV+ A5 III

No. 594 : Dschubba, Anuradha No. 597 : Graffias, Mag. 2.9, 5.1 No. 616 : Antares , Jyestha, Mag. 0.9 to 1.8.

No. 625 : Atria. No. 652 : Schaula , Mula. No. 656 : Ras Alhague.

224

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

17 17 17 17 17 17

38 38 40 43 44 47

45.7 47.6 02.7 54.5 29.2 15.7

3.439 4.318 1.697 4.156 2.966 2.351

3.62 K2II 3.75 A0 V 3.03 F2 I ae 3.21 K2 III 3.75 K2 III 3.86 K1 IIaCn+

17 17 17 17 17 17

47 48 49 51 53 56

44.9 55.3 01.2 15.3 53.0 57.4

5.900 3.011 4.200 4.087 1.040 2.060

γ Draconis ξ Herculis  Ophiuchi 67 Ophiuchi γ Sagittarii θ Arae

2.23 3.70 3.34 3.97 2.99 3.66

K5 III G8 III G 9 III B5 Ib K1III B2 Ib

17 17 18 18 18 18

57 58 00 01 07 08

05.0 33.7 09.3 40.4 07.5 13.6

1.396 2.334 3.305 3.007 3.855 4.671

6771 6779 6812 6832 6927 6859

72 Ophiuchi o Herculis  Sagittarii  Sagittarii Draconis Sagittarii

3.73 3.83 3.86 3.11 3.57 2.70

A4IVs B9.5V B2III M3.5 III F7 V K3IIIa

18 18 18 18 18 18

08 08 14 19 20 22

19.3 20.6 59.4 00.9 41.1 18.4

688 690 689 691 692 697

6869 6895 6879 6897 6913 6951

 Serpentis 109 Herculis  Sagittarii  Telescopii λ Sagittarii θ Coronae Aust.

3.26 K0 III-IV 3.84 K2 III 1.85 B9.5III 3.51 B3 IV 2.81 K0IV 4.64 G8 III

18 18 18 18 18 18

22 24 25 28 29 34

22.3 34.3 31.9 29.5 14.1 57.9

3.106 2.559 3.981 4.445 3.702 4.280

1482 699 1487 1489 705 706

6973 7001 7039 7063 7106 7121

 Scuti  Lyrae φ Sagittarii  Scuti  Lyrae Sagittarii

3.85 0.03 3.17 4.22 3.45 2.02

K3 III A0 V B8 III G4 IIa B7 Ve+ B2V

18 18 18 18 18 18

36 37 46 48 50 56

19.4 38.0 56.2 15.7 50.2 32.1

710 713 712 716 717 1496

7150 7178 7176 7235 7236 7234

ξ2 Sagittarii γ Lyrae  Aquilae  Aquilae λ Aquilae  Sagittarii

3.51 3.24 4.02 2.99 3.44 3.32

G9II/III B9 III K1 III A0 Vn B9Vn K1III

18 18 19 19 19 19

58 59 00 06 07 08

57.1 42.7 33.2 21.2 20.2 13.1

658 654 663 660 665 667

6561 6553 6588 6580 6603 6623

ξ Serpentis θ Scorpii  Herculis  Scorpii  Ophiuchi  Herculis

3.54 1.87 3.80 2.41 2.77 3.42

661 668 666 669 671 672

6582 6629 6615 6630 6688 6695

 Pavonis γ Ophiuchi 1 Scorpii G Scorpii ξ Draconis θ Herculis

676 674 673 677 679 1471

6705 6703 6698 6714 6746 6743

680 681 682 683 695 687

A9IIIpSr F1 II B3 IV B1.5 III K2 III G5IV

No. 676 : Eltanin. No. 687 : Purvasadha-1. No. 689 : Kaus Australis , Purvasadha-2.

s (0.0001)

Declination

º

'

"

Annual Annual Variation Proper motion "

" (0.001)

-29 -15 24 31.53 +14 -43 00 35.04 -5 +45 59 46.76 -5 -39 02 18.73 -27 +4 33 36.83 -233 +27 42 50.64

-1.91 1.85 1.74 1.43 1.20 1.87

-21 -64 43 -15 +2 42 -0 -40 07 +41 -37 02 +114 +56 52 +4 +37 14

35.40 58.49 03.90 52.10 11.92 55.95

-1.13 1.04 0.97 0.73 0.45 0.26

-54 -74 -8 +33 +80 +6

-8 +51 29 14.16 +64 +29 14 48.82 -4 -9 46 28.21 +1 +2 55 55.51 -41 -30 25 18.90 -10 -50 05 16.54

-0.27 0.14 -0.10 +0.14 0.44 0.71

-19 -17 -116 -8 -185 -14

2.846 -41 +9 34 05.55 2.342 +1 +28 45 59.44 3.589 +1 -21 03 06.01 4.059 -106 -36 45 12.77 -1.088 +1200 +72 44 03.15 3.840 +27 -29 49 28.56

+0.81 0.74 1.31 1.49 1.46 1.92

+80 +10 +1 -167 -346 -28

-364 -2 53 31.01 +141 +21 46 49.31 -31 -34 22 22.81 -15 -45 57 17.93 -32 -25 24 30.80 +28 -42 17 44.40

+1.25 1.90 2.10 2.43 2.36 3.02

-701 -242 -124 -54 -185 -22

3.265 2.033 3.745 3.183 2.217 3.716

-10 -8 13 41.17 +172 +38 48 13.59 +40 -26 58 04.38 -3 -4 43 27.77 +3 +33 23 15.32 +10 -26 16 10.12

+2.85 3.56 4.08 4.17 4.41 4.84

-312 +287 +1 -16 -3 -54

3.576 2.246 2.724 2.758 3.183 3.740

+24 -21 04 40.74 -2 +32 43 07.64 -35 +15 05 50.79 -3 +13 53 42.95 -11 -4 51 00.93 -40 -27 38 19.30

+5.09 5.16 5.16 5.63 5.71 +5.63

-12 +2 -74 -96 -90 -251

No. 699 : Vega , Abhijit. No. 705 : Sheliak Mag. 3.3 to 4.3. No. 706 : Nunki , Uttarasadha.

-58 -2 +5 -27 +159 -752

225

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

720 723 726 730 1508 733

7264 7310 7328 7377 7405 7420

 Sagittarii  Draconis  Cygni  Aquilae  Vulpeculae  Cygni

732 1513 741 743 745 746

7417 7488 7525 7536 7557 7570

Cygnip  Sagittae γ Aquilae  Sagittae  Aquilae  Aquilae

749 752 751 754 756 757

7602 7635 7623 7665 7710 7735

 Aquilae γ Sagittae θ1 Sagittarii  Pavonis θ Aquilae 31 o 2 Cygni

3.71 3.47 4.37 3.56 3.23 3.79

761 762 765 764 768 (771)

7754 7776 7796 7790 7852 7882

769 774 777 778 783 775

Right Ascension Annual Annual Spectral Type Variation Proper motion h

m

s

s

F2 II/III G9 III G9 III F0IV M0III A5V

19 19 19 19 19 19

10 12 17 26 29 30

58.9 33.3 34.5 31.9 33.5 13.3

3.564 -0.004 1.384 3.024 2.498 1.511

3.08 K3II+ 4.37 G8III a 2.72 K3 II 3.82 M2 II+ 0.77 A7 V 3.90V. F6Iab

19 19 19 19 19 19

31 41 47 48 51 53

32.9 58.2 14.1 18.1 47.0 31.0

2.421 2.695 2.852 2.676 2.926 3.054

19 19 20 20 20 20

56 59 01 10 12 14

2 Capricorni  Capricorni γ Cygni Pavonis  Delphini  Delphinim

3.57 G8.5III-IV 20 19 3.08 K0:II:+ 20 22 2.20 F8 I ab 20 22 1.94 B2IV 20 27 4.03 B6 III 20 34 3.64 F5 IV 20 38

7869 7906 7924 7928 7957 7913

 Indi  Delphini  Cygni  Delphini  Cephei  Pavonis

3.11 K0 III-IV 3.77 B9 IV 1.25 A2 Iae 4.43 A7IIIp 3.43 K0 IV 3.42 A7III

20 20 20 20 20 20

780 1541 781 1547 785 1550

7949 7948 7950 7990 7986 8039

 Cygni γ Delphinisq  Aquarii  Aquarii  Indi γ Microscopii

2.46 4.27 3.77 4.73 3.65 4.67

792 797 800 803 806

8079 8115 8131 8162 8204

 Cygni  Cygni  Equulei  Cephei  Capricorni

3.72 K4.5 Ib-II 3.20 G8III 3.92 G0III+ 2.44 A7IV 3.74 G4 Ibp



2.89 3.07 3.77 3.36 4.44 3.79

G9.5IV M0 III B3 IV G8 IV B9.5 III+ K2II+

K0 III K1 IV A1.5V A3m K1 II G6III

No. 732 : Albireo ., Mag. f . 5.4. No. 745 : Altair , Sravana. No. 749 : Alshain . No. 761 : Giedi or Algedi.

s (0.0001)

Declination

º

'

"

Annual Annual Variation Proper motion "

" (0.001)

0 +164 +66 +171 -92 +22

-20 +67 +53 +3 +24 +51

59 41 24 09 42 46

21.60 51.38 25.13 25.47 27.28 27.09

+6.07 6.33 6.78 7.47 7.53 7.82

+2 +7 +12 +5 +362 +7

+28 +17 +10 +18 +8 +1

00 31 39 35 55 03

13.90 29.18 52.26 09.79 25.71 34.69

+7.79 8.59 9.04 9.13 9.78 9.52

-2 -32 -2 +8 +387 -7

19.2 40.1 04.0 43.0 21.0 16.7

2.946 +33 +6 2.669 +46 +19 3.890 +5 -35 5.816 +1997 -66 3.061 +26 -0 1.890 +4 +46

27 32 13 07 52 48

33.32 56.49 09.22 38.25 33.69 15.63

+9.26 10.02 10.08 9.70 10.95 11.08

-482 +24 -26 -1126 +4 +3

11.4 09.7 57.9 15.4 11.5 30.6

3.323 3.364 2.155 4.703 2.866 2.814

+44 -12 28 47.72 +11.44 +29 -14 42 54.97 11.65 +4 +40 19 23.61 11.71 +9 -56 40 03.16 11.92 +9 +11 22 26.72 12.47 +81 +14 40 02.72 12.73

+4 +2 0 -89 -22 -48

39 40 42 44 45 46

00.0 35.4 07.9 25.0 42.2 46.8

4.191 2.787 2.047 2.801 1.210 5.322

+52 +46 +3 -13 +120 -76

06.33 +12.88 07.50 12.92 15.90 13.03 57.00 13.13 39.13 14.08 08.00 13.34

+66 -2 +2 -43 +819 +11

20 20 20 20 20 21

47 47 48 53 56 02

02.5 36.6 47.0 45.5 23.8 32.6

2.430 2.784 3.242 3.230 4.636 3.663

+286 +34 02 52.74 +13.68 -22 +16 11 57.16 13.19 +24 -9 25 10.21 13.43 +30 -8 54 18.76 13.75 +21 -58 22 30.64 13.92 -2 -32 10 34.87 14.33

+329 -197 -34 -30 -26 +5

21 21 21 21 21

05 13 16 19 27

40.7 48.6 50.9 04.0 50.0

2.186 2.557 2.998 1.427 3.413

+8 +44 00 37.47 +14.52 +1 +30 18 42.89 14.94 +39 +5 20 00.93 15.09 +219 +62 40 22.48 15.35 +1 -22 19 17.39 +15.81

+1 -56 -88 +50 +23

-47 +15 +45 +15 +61 -66

13 59 21 08 55 07

No. 771 : Rotanev , Dhanistha-1. No. 774 : Saulocin, Dhanistha-2. No. 777 : Deneb. No. 803 : Alderamin.

-35 +93 +125 +83 -106 +130

226

MEAN PLACES OF STARS, J 2020.5 FOR JULY 2d.125 TERRESTRIAL TIME (The Annual Variations are for the middle of the year) Cat. BS No. =HR FK5 No.

Star

Mag.

SpecRight Ascension Annual Annual tral Type Variation Proper motion

809 808 1569 812 810 815

8238 8232 8264 8278 8254 8308

 Cephei  Aquarii* Aquarii γ Capricorni  Octantis  Pegasi*

3.23 2.91 4.69 3.68 3.76 2.34

B2 IIIev G0 Ib A7 V A7 mp K1 III K2 Ib

819 822 827 831 829 834

8322 8353 8414 8430 8425 8450

 Capricorni γ Gruis  Aquarii*  Pegasi Gruis* θ Pegasi

2.87 3.01 2.96 3.76 1.74 3.53

kA5hF0mF2III

836 841 842 846 848 849

8465 8502 8518 8556 8585 8592

 Cephei Tucanae γ Aquarii 1 Gruis  Lacertae v Aquarii

3.35 2.86 3.84 3.97 3.77 5.20

850 855 856 857 860 863

8597 8634 8636 8650 8675 8694

 Aquarii  Pegasi  Gruis  Pegasi  Gruis  Cephei

861 862 864 866 867 869

8679 8684 8698 8709 8728 8762

870 871 873 878 890 893

8775 8781 8812 8852 8961 8974

m

s

s

s (0.0001)

º

'

"

Annual Annual Variation Proper motion "

28 32 38 41 43 45

55.0 38.2 50.5 13.4 40.7 11.6

0.747 3.154 3.188 3.315 6.411 2.947

B8III G2 Ib F5 V B6V A1Va

21 21 22 22 22 22

48 55 06 07 09 11

10.2 09.8 50.0 58.0 30.9 14.0

3.303 3.611 3.072 2.799 3.749 3.026

+183 -16 02 00.15 +16.52 +86 -37 16 03.20 17.12 +13 -0 24 10.33 17.64 +220 +25 26 45.17 17.72 +126 -46 51 39.18 17.61 +185 +6 17 57.85 17.85

-296 -21 -10 +25 -151 +27

K1.5 Iab K3 III A0V G7III A1 V F7 V

22 22 22 22 22 22

11 19 22 30 32 35

34.1 53.3 42.9 29.2 08.4 48.7

2.091 4.051 3.096 3.559 2.486 3.272

+19 +58 18 10.02 +17.84 -96 -60 09 23.72 18.12 +88 -1 17 00.29 18.27 +26 -43 23 24.73 18.53 +144 +50 23 18.19 18.61 +158 -20 36 09.42 18.56

+4 -43 +7 -5 +19 -144

4.02 B9 IV-V:n 3.40 B8V 2.10 M5 III 2.94 G2II-III+ 3.49 A2IVnSB2 3.52 K0III

22 22 22 22 22 22

36 42 43 43 49 50

24.5 29.1 53.0 58.0 47.0 24.9

3.080 2.995 3.552 2.822 3.588 2.154

+61 -0 12 40.65 +18.67 +55 +10 56 19.88 18.89 +133 -46 46 36.80 18.94 +11 +30 19 44.18 18.92 +115 -51 12 30.80 19.04 -108 +66 18 02.30 19.00

-56 -12 -8 -25 -71 -125

 Aquarii  Pegasi λ Aquarii* Aquarii  PsA* o Andromedae

4.01 K5III 3.48 G8 III 3.74 M2 III 3.27 A3 V 1.16 A4 V 3.62 B6III pe+

22 22 22 22 22 23

50 50 53 55 58 02

40.5 59.7 41.0 44.2 46.8 52.1

3.170 2.904 3.126 3.177 3.300 2.776

-8 -13 29 30.82 +19.09 +108 +24 42 36.97 19.10 +8 -7 28 12.33 19.25 -28 -15 42 40.92 19.23 +255 -29 30 47.45 19.17 +20 +42 26 11.33 19.42

-38 -42 +37 -25 -164 -6

 Pegasi*  Pegasi* 88 Aquarii γ Piscium λ Andromedae γ Cephei

2.42 M2.5 II-III 2.49 B9III 3.66 K1III 3.69 G9 III 3.82v G8 III 3.21 K1 IV

23 23 23 23 23 23

04 05 10 18 38 40

46.3 47.0 32.2 13.7 34.5 12.4

2.919 2.994 3.189 3.112 2.959 2.523

+143 +44 +40 +509 +157 -212

39.70 +19.60 57.24 19.44 38.87 19.61 40.42 19.73 09.78 19.53 49.16 20.12

+138 -42 +31 +17 -421 +151

0 00

22.0

3.086

+103

+6 58 36.33 +19.93

-115

4.01

BS = Bright Star Catalogue

F4V

HR = Havard Revised Catalogue

No. 808 : Sadalsuud. No. 815 : Enif . Mag. 0.7 to 3.5. No. 827 : Sadalmelik. No. 829 : Al Nair.

+21 +70 39 03.39 +15.85 +14 -5 28 48.18 16.03 +78 -7 45 40.92 16.33 +132 -16 34 07.64 16.45 +140 -77 17 49.91 16.36 +21 +9 58 11.22 16.67

" (0.001)

21 21 21 21 21 21

902 9072  Piscium



h

Declination

+28 +15 -21 +3 +46 +77

11 18 03 23 34 44

+7 -8 -25 -23 -240 -1

FK5 = Fifth Fundamental Catalogue No. 864 : Satabhisaj. No. 867 : Fomalhaut . No. 870 : Scheat , Purva Bhadrapada-2. No. 871 : Markab , Purva Bhadrapada-1.

227

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name  Pegasi  Phoenicis  Ceti  Andromedae 2.83 B2 IV 2.39 K0 III 2.04 K0 III 2.06 M0 III Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 0 14 15 +15 17 38 0 27 15 -42 12 11 0 44 35 -17 52 51 1 10 51 +35 43 38

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

0

14

15

15

17

37

0

27

15

42

12

11

0

44

34

17

52

52

1

10

51

35

43

38

21

0

14

15

15

17

36

0

27

15

42

12

11

0

44

34

17

52

52

1

10

50

35

43

37

31

0

14

15

15

17

35

0

27

15

42

12

10

0

44

34

17

52

52

1

10

50

35

43

36

10

0

14

15

15

17

34

0

27

14

42

12

08

0

44

34

17

52

52

1

10

50

35

43

35

20

0

14

15

15

17

33

0

27

14

42

12

07

0

44

34

17

52

51

1

10

50

35

43

33

1

0

14

14 +15

17

32

0

27

14 -42

12

05

0

44

34 -17

52

51

1

10

50 +35

43

31

11

0

14

14

15

17

32

0

27

14

42

12

02

0

44

34

17

52

49

1

10

50

35

43

30

21

0

14

14

15

17

31

0

27

14

42

12

01

0

44

34

17

52

48

1

10

50

35

43

28

31

0

14

15

15

17

30

0

27

14

42

11

57

0

44

34

17

52

47

1

10

50

35

43

27

10

0

14

15

15

17

30

0

27

14

42

11

54

0

44

34

17

52

45

1

10

50

35

43

25

20

0

14

15

15

17

31

0

27

14

42

11

51

0

44

34

17

52

43

1

10

50

35

43

24

30

0

14

15 +15

17

31

0

27

15 -42

11

48

0

44

34 -17

52

40

1

10

50 +35

43

23

10

0

14

15

15

17

32

0

27

15

42

11

45

0

44

35

17

52

38

1

10

50

35

43

23

20

0

14

15

15

17

33

0

27

15

42

11

42

0

44

35

17

52

36

1

10

50

35

43

23

30

0

14

16

15

17

34

0

27

16

42

11

39

0

44

35

17

52

33

1

10

51

35

43

23

9

0

14

16

15

17

36

0

27

16

42

11

36

0

44

35

17

52

31

1

10

51

35

43

24

19

0

14

16

15

17

38

0

27

16

42

11

34

0

44

36

17

52

29

1

10

51

35

43

25

29

0

14

17 +15

17

40

0

27

17 -42

11

32

0

44

36 -17

52

26

1

10

52 +35

43

26

9

0

14

17

15

17

42

0

27

17

42

11

31

0

44

36

17

52

24

1

10

52

35

43

28

19

0

14

17

15

17

44

0

27

17

42

11

30

0

44

37

17

52

23

1

10

53

35

43

30

29

0

14

18

15

17

46

0

27

18

42

11

30

0

44

37

17

52

22

1

10

53

35

43

32

8

0

14

18

15

17

48

0

27

18

42

11

29

0

44

37

17

52

20

1

10

53

35

43

34

18

0

14

18

15

17

51

0

27

18

42

11

30

0

44

37

17

52

20

1

10

54

35

43

37

28

0

14

18 +15

17

52

0

27

19 -42

11

31

0

44

38 -17

52

19

1

10

54 +35

43

39

7

0

14

18

15

17

54

0

27

19

42

11

32

0

44

38

17

52

20

1

10

54

35

43

41

17

0

14

19

15

17

56

0

27

19

42

11

34

0

44

38

17

52

20

1

10

54

35

43

44

27

0

14

19

15

17

57

0

27

19

42

11

36

0

44

38

17

52

20

1

10

54

35

43

46

7

0

14

19

15

17

58

0

27

19

42

11

38

0

44

38

17

52

22

1

10

54

35

43

48

17

0

14

19

15

17

59

0

27

19

42

11

40

0

44

38

17

52

23

1

10

54

35

43

50

27

0

14

19 +15

17

60

0

27

19 -42

11

42

0

44

38 -17

52

24

1

10

55 +35

43

52

6

0

14

19

15

17

60

0

27

19

42

11

45

0

44

38

17

52

25

1

10

55

35

43

54

16

0

14

19

15

17

60

0

27

19

42

11

47

0

44

38

17

52

27

1

10

54

35

43

55

26

0

14

18

15

18

00

0

27

19

42

11

48

0

44

38

17

52

28

1

10

54

35

43

56

6

0

14

18

15

17

60

0

27

19

42

11

50

0

44

38

17

52

29

1

10

54

35

43

57

16

0

14

18

15

17

59

0

27

18

42

11

51

0

44

38

17

52

30

1

10

54

35

43

58

26

0

14

18 +15

17

59

0

27

18 -42

11

51

0

44

38 -17

52

31

1

10

54 +35

43

58

36

0

14

18 +15

17

58

0

27

18 -42

11

51

0

44

38 -17

52

31

1

10

54 +35

43

58

228

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name  Ceti  Ceti  Arietis  Ceti 2.53 M1.5IIIa 3.73 K0 III 4.00 F7III 2.00 K2 III Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 1 52 26 -10 14 24 2 00 56 -20 59 08 2 08 18 +23 33 22 3 03 19 +4 09 55

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

1

52

26

10

14

25

2

00

56

20

59

09

2

08

18

23

33

21

3

03

19

4

09

55

21

1

52

26

10

14

25

2

00

56

20

59

10

2

08

18

23

33

21

3

03

19

4

09

54

31

1

52

26

10

14

25

2

00

56

20

59

10

2

08

17

23

33

21

3

03

19

4

09

54

10

1

52

26

10

14

25

2

00

56

20

59

10

2

08

17

23

33

20

3

03

19

4

09

53

20

1

52

26

10

14

25

2

00

56

20

59

09

2

08

17

23

33

19

3

03

19

4

09

53

1

1

52

26 -10

14

25

2

00

56 -20

59

09

2

08

17 +23

33

18

3

03

19

+4

09

53

11

1

52

26

10

14

25

2

00

55

20

59

07

2

08

17

23

33

17

3

03

19

4

09

53

21

1

52

25

10

14

24

2

00

55

20

59

06

2

08

17

23

33

16

3

03

18

4

09

53

31

1

52

25

10

14

23

2

00

55

20

59

05

2

08

17

23

33

15

3

03

18

4

09

53

10

1

52

25

10

14

21

2

00

55

20

59

03

2

08

17

23

33

15

3

03

18

4

09

53

20

1

52

25

10

14

20

2

00

55

20

59

00

2

08

17

23

33

15

3

03

18

4

09

54

30

1

52

26 -10

14

18

2

00

55 -20

58

58

2

08

17 +23

33

14

3

03

18

+4

09

55

10

1

52

26

10

14

16

2

00

56

20

58

56

2

08

17

23

33

14

3

03

18

4

09

56

20

1

52

26

10

14

14

2

00

56

20

58

53

2

08

17

23

33

14

3

03

18

4

09

57

30

1

52

26

10

14

12

2

00

56

20

58

50

2

08

17

23

33

15

3

03

19

4

09

59

9

1

52

26

10

14

09

2

00

56

20

58

48

2

08

18

23

33

16

3

03

19

4

09

60

19

1

52

27

10

14

07

2

00

56

20

58

45

2

08

18

23

33

17

3

03

19

4

10

02

29

1

52

27 -10

14

05

2

00

57 -20

58

43

2

08

18 +23

33

18

3

03

19

+4

10

03

9

1

52

27

10

14

03

2

00

57

20

58

40

2

08

19

23

33

20

3

03

20

4

10

05

19

1

52

28

10

14

01

2

00

57

20

58

39

2

08

19

23

33

21

3

03

20

4

10

07

29

1

52

28

10

14

01

2

00

58

20

58

37

2

08

19

23

33

23

3

03

20

4

10

09

8

1

52

28

10

13

58

2

00

58

20

58

36

2

08

20

23

33

25

3

03

21

4

10

10

18

1

52

28

10

13

56

2

00

58

20

58

35

2

08

20

23

33

27

3

03

21

4

10

12

28

1

52

29 -10

13

56

2

00

59 -20

58

34

2

08

20 +23

33

29

3

03

21

+4

10

13

7

1

52

29

10

13

55

2

00

59

20

58

34

2

08

20

23

33

30

3

03

21

4

10

14

17

1

52

29

10

13

55

2

00

59

20

58

34

2

08

21

23

33

32

3

03

22

4

10

15

27

1

52

29

10

13

55

2

00

59

20

58

35

2

08

21

23

33

34

3

03

22

4

10

15

7

1

52

29

10

13

56

2

00

59

20

58

36

2

08

21

23

33

35

3

03

22

4

10

15

17

1

52

30

10

13

56

2

00

60

20

58

38

2

08

21

23

33

36

3

03

22

4

10

16

27

1

52

30 -10

13

57

2

00

60 -20

58

39

2

08

21 +23

33

37

3

03

22

+4

10

15

6

1

52

30

10

13

58

2

00

60

20

58

41

2

08

21

23

33

38

3

03

23

4

10

15

16

1

52

30

10

14

00

2

00

60

20

58

43

2

08

21

23

33

39

3

03

23

4

10

14

26

1

52

30

10

14

01

2

00

60

20

58

44

2

08

21

23

33

40

3

03

23

4

10

14

6

1

52

30

10

14

02

2

00

60

20

58

46

2

08

21

23

33

40

3

03

23

4

10

13

16

1

52

30

10

14

03

2

00

60

20

58

47

2

08

21

23

33

40

3

03

23

4

10

13

26

1

52

29 -10

14

04

2

00

59 -20

58

49

2

08

21 +23

33

40

3

03

23

+4

10

12

36

1

52

29 -10

14

05

2

00

59 -20

58

49

2

08

21 +23

33

40

3

03

23

+4

10

11

229

APPARENT PLACES OF STARS, 2020 Name Mag. Spect. U.T. Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

FOR 0h TERRESTRIAL TIME Eridani Tauri Tauri γ Orionis K5 III 2.87 B7 III 0.85 2.79 K4 III 1.64 B2 III Right Declination Right Declination Right Declination Right Declination Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' "

1

3

48

41 +24

09

55

4

37

04 +16

32

50

5

08

50

-5

03

48

5

26

13

+6

21

55

11

3

48

41

24

09

55

4

37

04

16

32

50

5

08

50

5

03

49

5

26

13

6

21

54

21 31

3 3

48 48

40 40

24 24

09 09

55 55

4 4

37 37

04 04

16 16

32 32

50 50

5 5

08 08

50 50

5 5

03 03

50 51

5 5

26 26

13 13

6 6

21 21

54 53

10

3

48

40

24

09

55

4

37

04

16

32

50

5

08

50

5

03

52

5

26

12

6

21

53

20

3

48

40

24

09

55

4

37

04

16

32

49

5

08

50

5

03

52

5

26

12

6

21

52

1

3

48

40 +24

09

54

4

37

04 +16

32

49

5

08

50

-5

03

53

5

26

12

+6

21

52

11

3

48

40

24

09

54

4

37

04

16

32

49

5

08

50

5

03

53

5

26

12

6

21

52

21

3

48

40

24

09

54

4

37

03

16

32

49

5

08

49

5

03

53

5

26

12

6

21

52

31

3

48

39

24

09

53

4

37

03

16

32

49

5

08

49

5

03

52

5

26

12

6

21

52

10

3

48

39

24

09

52

4

37

03

16

32

49

5

08

49

5

03

52

5

26

11

6

21

53

20

3

48

39

24

09

52

4

37

03

16

32

49

5

08

49

5

03

51

5

26

11

6

21

53

30

3

48

39 +24

09

52

4

37

03 +16

32

49

5

08

49

-5

03

50

5

26

11

+6

21

53

10

3

48

39

24

09

51

4

37

03

16

32

49

5

08

49

5

03

49

5

26

11

6

21

54

20

3

48

39

24

09

51

4

37

03

16

32

49

5

08

49

5

03

47

5

26

11

6

21

55

30

3

48

39

24

09

52

4

37

03

16

32

50

5

08

49

5

03

46

5

26

11

6

21

56

9

3

48

40

24

09

52

4

37

03

16

32

50

5

08

49

5

03

44

5

26

11

6

21

57

19

3

48

40

24

09

52

4

37

03

16

32

51

5

08

49

5

03

42

5

26

11

6

21

58

29

3

48

40 +24

09

53

4

37

04 +16

32

52

5

08

49

-5

03

40

5

26

12

+6

21

59

9

3

48

40

24

09

54

4

37

04

16

32

53

5

08

50

5

03

38

5

26

12

6

22

01

19

3

48

41

24

09

55

4

37

04

16

32

54

5

08

50

5

03

37

5

26

12

6

22

02

29

3

48

41

24

09

56

4

37

04

16

32

55

5

08

50

5

03

35

5

26

12

6

22

03

8

3

48

41

24

09

57

4

37

05

16

32

56

5

08

50

5

03

33

5

26

12

6

22

04

18

3

48

42

24

09

58

4

37

05

16

32

57

5

08

51

5

03

32

5

26

13

6

22

05

28

3

48

42 +24

09

59

4

37

05 +16

32

58

5

08

51

-5

03

31

5

26

13

+6

22

06

7

3

48

42

24

10

01

4

37

06

16

32

58

5

08

51

5

03

30

5

26

13

6

22

07

17

3

48

43

24

10

02

4

37

06

16

32

59

5

08

51

5

03

29

5

26

14

6

22

07

27

3

48

43

24

10

03

4

37

06

16

32

60

5

08

52

5

03

29

5

26

14

6

22

07

7

3

48

43

24

10

04

4

37

06

16

32

60

5

08

52

5

03

30

5

26

14

6

22

07

17

3

48

43

24

10

05

4

37

07

16

33

00

5

08

52

5

03

30

5

26

14

6

22

07

27

3

48

44 +24

10

06

4

37

07 +16

33

01

5

08

52

-5

03

31

5

26

15

+6

22

07

6

3

48

44

24

10

06

4

37

07

16

33

01

5

08

53

5

03

32

5

26

15

6

22

06

16

3

48

44

24

10

07

4

37

07

16

33

00

5

08

53

5

03

34

5

26

15

6

22

05

26

3

48

44

24

10

07

4

37

08

16

33

01

5

08

53

5

03

35

5

26

15

6

22

04

6

3

48

44

24

10

08

4

37

08

16

33

00

5

08

53

5

03

37

5

26

16

6

22

03

16

3

48

44

24

10

08

4

37

08

16

33

00

5

08

53

5

03

38

5

26

16

6

22

02

26

3

48

44 +24

10

08

4

37

08 +16

32

60

5

08

53

-5

03

40

5

26

16

+6

22

01

36

3

48

44 +24

10

09

4

37

08 +16

32

60

5

08

53

-5

03

41

5

26

16

+6

22

01

230

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name  Orionis Leporis Orionis Columbae 2.64 B5 Ive 2.84 G5 II 2.77 O9 III 2.06 B0Iab Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 5 29 07 -20 44 46 5 36 25 -5 53 57 5 40 23 -34 03 58 5 48 43 -9 39 53

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

5

29

07

20

44

49

5

36

25

5

53

59

5

40

23

34

04

01

5

48

43

9

39

55

21

5

29

07

20

44

50

5

36

25

5

54

00

5

40

23

34

04

03

5

48

43

9

39

57

31 10

5 5

29 29

07 07

20 20

44 44

52 53

5 5

36 36

25 25

5 5

54 54

01 02

5 5

40 40

23 23

34 34

04 04

05 07

5 5

48 48

43 43

9 9

39 39

58 59

20

5

29

06

20

44

54

5

36

25

5

54

03

5

40

23

34

04

08

5

48

43

9

40

00

1

5

29

06 -20

44

55

5

36

25

-5

54

03

5

40

23 -34

04

09

5

48

42

-9

40

00

11 21

5 5

29 29

06 06

20 20

44 44

55 55

5 5

36 36

24 24

5 5

54 54

03 03

5 5

40 40

22 22

34 34

04 04

09 09

5 5

48 48

42 42

9 9

40 40

00 00

31

5

29

06

20

44

54

5

36

24

5

54

03

5

40

22

34

04

08

5

48

42

9

40

00

10

5

29

05

20

44

53

5

36

24

5

54

02

5

40

22

34

04

07

5

48

42

9

40

01

20

5

29

05

20

44

52

5

36

24

5

54

01

5

40

21

34

04

06

5

48

41

9

39

59

30

5

29

05 -20

44

51

5

36

24

-5

54

00

5

40

21 -34

04

04

5

48

41

-9

39

58

10

5

29

05

20

44

49

5

36

24

5

54

01

5

40

21

34

04

02

5

48

41

9

39

57

20

5

29

05

20

44

47

5

36

24

5

53

58

5

40

21

34

04

01

5

48

41

9

39

55

30

5

29

05

20

44

45

5

36

24

5

53

56

5

40

21

34

03

57

5

48

41

9

39

53

9

5

29

05

20

44

42

5

36

24

5

53

55

5

40

21

34

03

54

5

48

41

9

39

51

19

5

29

05

20

44

40

5

36

24

5

53

53

5

40

21

34

03

51

5

48

41

9

39

50

29

5

29

05 -20

44

37

5

36

24

-5

53

51

5

40

21 -34

03

48

5

48

41

-9

39

47

9

5

29

05

20

44

35

5

36

24

5

53

49

5

40

21

34

03

45

5

48

42

9

39

45

19

5

29

06

20

44

32

5

36

24

5

53

47

5

40

22

34

03

42

5

48

42

9

39

44

29

5

29

06

20

44

30

5

36

25

5

53

46

5

40

22

34

03

40

5

48

42

9

39

42

8

5

29

06

20

44

28

5

36

25

5

53

44

5

40

22

34

03

37

5

48

42

9

39

40

18

5

29

06

20

44

26

5

36

25

5

53

43

5

40

22

34

03

35

5

48

43

9

39

39

28

5

29

07 -20

44

25

5

36

25

-5

53

42

5

40

23 -34

03

34

5

48

43

-9

39

37

7

5

29

07

20

44

24

5

36

26

5

53

41

5

40

23

34

03

33

5

48

43

9

39

37

17

5

29

07

20

44

23

5

36

26

5

53

40

5

40

23

34

03

32

5

48

43

9

39

36

27

5

29

08

20

44

24

5

36

26

5

53

40

5

40

24

34

03

32

5

48

44

9

39

36

7

5

29

08

20

44

24

5

36

26

5

53

41

5

40

24

34

03

33

5

48

44

9

39

36

17

5

29

08

20

44

25

5

36

27

5

53

41

5

40

24

34

03

34

5

48

44

9

39

37

27

5

29

08 -20

44

26

5

36

27

-5

53

42

5

40

25 -34

03

35

5

48

45

-9

39

38

6

5

29

09

20

44

28

5

36

27

5

53

43

5

40

25

34

03

38

5

48

45

9

39

39

16

5

29

09

20

44

30

5

36

27

5

53

45

5

40

25

34

03

40

5

48

45

9

39

41

26

5

29

09

20

44

32

5

36

28

5

53

46

5

40

25

34

03

43

5

48

45

9

39

43

6

5

29

09

20

44

35

5

36

28

5

53

48

5

40

25

34

03

46

5

48

45

9

39

45

16

5

29

09

20

44

37

5

36

28

5

53

50

5

40

26

34

03

49

5

48

46

9

39

47

26

5

29

09 -20

44

40

5

36

28

-5

53

51

5

40

26 -34

03

52

5

48

46

-9

39

48

36

5

29

09 -20

44

42

5

36

28

-5

53

53

5

40

26 -34

03

54

5

48

46

-9

39

50

231

APPARENT PLACES OF STARS, 2020 Name Mag. Spect. U.T. Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

FOR 0h TERRESTRIAL TIME Orionis Canis Majoris Carinae γ Geminorum -0.72 F0II 0.4 - 1.3 M2Iab 3.02 B2.5V 1.93 A0 IV Right Declination Right Declination Right Declination Right Declination Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' "

1

5

56

16

+7

24

30

6

21

36 +30

03

10

6

24

26 -52

42

28

6

38

52 +16

22

47

11

5

56

16

7

24

29

6

21

36

30

03

10

6

24

26

52

42

32

6

38

52

16

22

47

21

5

56

16

7

24

29

6

21

36

30

03

11

6

24

26

52

42

35

6

38

52

16

22

47

31

5

56

16

7

24

28

6

21

36

30

03

12

6

24

25

52

42

37

6

38

52

16

22

47

10

5

56

16

7

24

28

6

21

36

30

03

12

6

24

25

52

42

40

6

38

52

16

22

47

20

5

56

15

7

24

28

6

21

36

30

03

13

6

24

25

52

42

42

6

38

52

16

22

47

1

5

56

15

+7

24

28

6

21

36 +30

03

14

6

24

25 -52

42

43

6

38

52 +16

22

47

11

5

56

15

7

24

28

6

21

36

30

03

14

6

24

24

52

42

44

6

38

52

16

22

47

21

5

56

15

7

24

28

6

21

35

30

03

14

6

24

24

52

42

45

6

38

52

16

22

47

31

5

56

15

7

24

28

6

21

35

30

03

14

6

24

24

52

42

45

6

38

52

16

22

47

10

5

56

15

7

24

28

6

21

35

30

03

14

6

24

23

52

42

44

6

38

51

16

22

48

20

5

56

14

7

24

28

6

21

35

30

03

14

6

24

23

52

42

43

6

38

51

16

22

48

30

5

56

14

+7

24

29

6

21

35 +30

03

14

6

24

23 -52

42

42

6

38

51 +16

22

48

10

5

56

14

7

24

29

6

21

35

30

03

14

6

24

22

52

42

40

6

38

51

16

22

48

20

5

56

14

7

24

30

6

21

35

30

03

13

6

24

22

52

42

37

6

38

51

16

22

49

30

5

56

14

7

24

31

6

21

35

30

03

13

6

24

22

52

42

34

6

38

51

16

22

49

9

5

56

14

7

24

32

6

21

35

30

03

12

6

24

22

52

42

31

6

38

51

16

22

49

19

5

56

14

7

24

33

6

21

35

30

03

12

6

24

22

52

42

28

6

38

51

16

22

49

29

5

56

15

+7

24

34

6

21

35 +30

03

12

6

24

22 -52

42

25

6

38

51 +16

22

50

9

5

56

15

7

24

35

6

21

35

30

03

11

6

24

22

52

42

21

6

38

51

16

22

50

19

5

56

15

7

24

36

6

21

35

30

03

11

6

24

22

52

42

18

6

38

51

16

22

51

29

5

56

15

7

24

37

6

21

35

30

03

11

6

24

22

52

42

15

6

38

52

16

22

51

8

5

56

15

7

24

38

6

21

36

30

03

11

6

24

23

52

42

12

6

38

52

16

22

52

18

5

56

16

7

24

39

6

21

36

30

03

11

6

24

23

52

42

10

6

38

52

16

22

52

28

5

56

16

+7

24

39

6

21

36 +30

03

10

6

24

23 -52

42

08

6

38

52 +16

22

52

7

5

56

16

7

24

40

6

21

37

30

03

10

6

24

24

52

42

06

6

38

53

16

22

52

17

5

56

17

7

24

41

6

21

37

30

03

10

6

24

24

52

42

05

6

38

53

16

22

52

27

5

56

17

7

24

41

6

21

37

30

03

10

6

24

24

52

42

05

6

38

53

16

22

52

7

5

56

17

7

24

40

6

21

38

30

03

10

6

24

25

52

42

05

6

38

54

16

22

52

17

5

56

17

7

24

40

6

21

38

30

03

10

6

24

25

52

42

06

6

38

54

16

22

51

27

5

56

18

+7

24

40

6

21

38 +30

03

10

6

24

26 -52

42

07

6

38

54 +16

22

51

6

5

56

18

7

24

39

6

21

39

30

03

10

6

24

26

52

42

10

6

38

55

16

22

50

16

5

56

18

7

24

38

6

21

39

30

03

10

6

24

26

52

42

12

6

38

55

16

22

49

26

5

56

18

7

24

37

6

21

39

30

03

10

6

24

26

52

42

15

6

38

55

16

22

49

6

5

56

19

7

24

36

6

21

40

30

03

10

6

24

27

52

42

18

6

38

55

16

22

48

16

5

56

19

7

24

35

6

21

40

30

03

10

6

24

27

52

42

22

6

38

56

16

22

47

26

5

56

19

+7

24

34

6

21

40 +30

03

11

6

24

27 -52

42

25

6

38

56 +16

22

47

36

5

56

19

+7

24

33

6

21

40 +30

03

11

6

24

27 -52

42

29

6

38

56 +16

22

47

232

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Canis Majoris A Canis Minoris Canis Minoris A 2Canis Majoris 0.38 F5 IV-V -1.46 A1V 3.02 B3 Ia 2.90 B8Ve Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 6 46 02 -16 44 43 7 03 52 -23 51 49 7 28 14 +8 14 50 7 40 21 +5 10 19

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

6

46

02

16

44

45

7

03

52

23

51

51

7

28

15

8

14

49

7

40

21

5

10

18

21

6

46

02

16

44

47

7

03

52

23

51

54

7

28

15

8

14

48

7

40

21

5

10

17

31

6

46

02

16

44

49

7

03

52

23

51

56

7

28

15

8

14

48

7

40

21

5

10

16

10 20

6 6

46 46

02 02

16 16

44 44

50 52

7 7

03 03

52 52

23 23

51 52

58 00

7 7

28 28

15 15

8 8

14 14

47 47

7 7

40 40

21 21

5 5

10 10

15 15

1

6

46

02 -16

44

53

7

03

52 -23

52

01

7

28

14

+8

14

46

7

40

21

+5

10

15

11 21

6 6

46 46

02 02

16 16

44 44

53 54

7 7

03 03

52 52

23 23

52 52

02 03

7 7

28 28

14 14

8 8

14 14

47 46

7 7

40 40

21 21

5 5

10 10

15 14

31

6

46

02

16

44

54

7

03

52

23

52

03

7

28

14

8

14

47

7

40

21

5

10

15

10

6

46

01

16

44

53

7

03

51

23

52

02

7

28

14

8

14

47

7

40

21

5

10

15

20

6

46

01

16

44

53

7

03

51

23

52

02

7

28

14

8

14

47

7

40

21

5

10

15

30

6

46

01 -16

44

52

7

03

51 -23

52

01

7

28

14

+8

14

48

7

40

20

+5

10

15

10

6

46

01

16

44

51

7

03

51

23

52

00

7

28

13

8

14

48

7

40

20

5

10

16

20

6

46

01

16

44

49

7

03

51

23

51

58

7

28

13

8

14

49

7

40

20

5

10

17

30

6

46

01

16

44

47

7

03

51

23

51

56

7

28

13

8

14

49

7

40

20

5

10

17

9

6

46

01

16

44

46

7

03

51

23

51

54

7

28

13

8

14

50

7

40

20

5

10

18

19

6

46

01

16

44

43

7

03

51

23

51

52

7

28

13

8

14

51

7

40

20

5

10

19

29

6

46

01 -16

44

41

7

03

51 -23

51

50

7

28

13

+8

14

52

7

40

20

+5

10

20

9

6

46

01

16

44

39

7

03

51

23

51

47

7

28

13

8

14

52

7

40

20

5

10

21

19

6

46

01

16

44

37

7

03

51

23

51

45

7

28

14

8

14

53

7

40

20

5

10

21

29

6

46

01

16

44

35

7

03

51

23

51

42

7

28

14

8

14

54

7

40

20

5

10

22

8

6

46

01

16

44

33

7

03

51

23

51

40

7

28

14

8

14

54

7

40

21

5

10

23

18

6

46

02

16

44

32

7

03

51

23

51

38

7

28

14

8

14

55

7

40

21

5

10

24

28

6

46

02 -16

44

30

7

03

52 -23

51

37

7

28

14

+8

14

55

7

40

21

+5

10

24

7

6

46

02

16

44

29

7

03

52

23

51

35

7

28

14

8

14

55

7

40

21

5

10

24

17

6

46

02

16

44

29

7

03

52

23

51

34

7

28

15

8

14

55

7

40

21

5

10

24

27

6

46

03

16

44

29

7

03

52

23

51

34

7

28

15

8

14

55

7

40

22

5

10

24

7

6

46

03

16

44

29

7

03

53

23

51

34

7

28

15

8

14

55

7

40

22

5

10

24

17

6

46

03

16

44

29

7

03

53

23

51

35

7

28

16

8

14

54

7

40

22

5

10

23

27

6

46

04 -16

44

31

7

03

53 -23

51

36

7

28

16

+8

14

53

7

40

23

+5

10

22

6

6

46

04

16

44

32

7

03

54

23

51

38

7

28

16

8

14

52

7

40

23

5

10

21

16

6

46

04

16

44

34

7

03

54

23

51

40

7

28

17

8

14

51

7

40

23

5

10

19

26

6

46

04

16

44

36

7

03

54

23

51

42

7

28

17

8

14

50

7

40

24

5

10

18

6

6

46

05

16

44

39

7

03

54

23

51

44

7

28

17

8

14

48

7

40

24

5

10

16

16

6

46

05

16

44

41

7

03

55

23

51

47

7

28

17

8

14

47

7

40

24

5

10

15

26

6

46

05 -16

44

44

7

03

55 -23

51

50

7

28

18

+8

14

46

7

40

24

+5

10

13

36

6

46

05 -16

44

46

7

03

55 -23

51

52

7

28

18

+8

14

45

7

40

24

+5

10

12

233

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Geminorum Puppis Puppis Hydrae G9 II-III 1.14 K0IIIb 3.34 G6 Ia 2.81 F6IIp 3.11 Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " 1 7 46 33 +27 58 32 7 50 09 -24 54 36 8 08 24 -24 21 42 8 56 27 +5 52 07 Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

7

46

33

27

58

32

7

50

09

24

54

39

8

08

25

24

21

45

8

56

27

5

52

05

21

7

46

33

27

58

32

7

50

09

24

54

42

8

08

25

24

21

48

8

56

27

5

52

04

31

7

46

33

27

58

33

7

50

09

24

54

44

8

08

25

24

21

50

8

56

28

5

52

03

10

7

46

33

27

58

34

7

50

09

24

54

46

8

08

25

24

21

53

8

56

28

5

52

02

20

7

46

33

27

58

34

7

50

09

24

54

48

8

08

25

24

21

55

8

56

28

5

52

01

1

7

46

33 +27

58

35

7

50

09 -24

54

50

8

08

25 -24

21

56

8

56

28

+5

52

01

11

7

46

33

27

58

36

7

50

09

24

54

51

8

08

24

24

21

58

8

56

28

5

52

01

21

7

46

32

27

58

37

7

50

09

24

54

52

8

08

24

24

21

59

8

56

28

5

52

01

31

7

46

32

27

58

37

7

50

08

24

54

53

8

08

24

24

22

01

8

56

27

5

52

01

10

7

46

32

27

58

38

7

50

08

24

54

53

8

08

24

24

22

00

8

56

27

5

52

02

20

7

46

32

27

58

38

7

50

08

24

54

53

8

08

24

24

22

00

8

56

27

5

52

02

30

7

46

32 +27

58

38

7

50

08 -24

54

52

8

08

23 -24

22

01

8

56

27

+5

52

02

10

7

46

32

27

58

38

7

50

08

24

54

51

8

08

23

24

21

59

8

56

27

5

52

03

20

7

46

31

27

58

38

7

50

07

24

54

50

8

08

23

24

21

57

8

56

27

5

52

03

30

7

46

31

27

58

38

7

50

07

24

54

49

8

08

23

24

21

56

8

56

27

5

52

04

9

7

46

31

27

58

38

7

50

07

24

54

47

8

08

23

24

21

54

8

56

27

5

52

05

19

7

46

31

27

58

38

7

50

07

24

54

45

8

08

23

24

21

52

8

56

26

5

52

05

29

7

46

31 +27

58

37

7

50

07 -24

54

42

8

08

23 -24

21

50

8

56

26

+5

52

06

9

7

46

31

27

58

37

7

50

07

24

54

40

8

08

23

24

21

48

8

56

26

5

52

07

19

7

46

32

27

58

36

7

50

07

24

54

38

8

08

23

24

21

46

8

56

26

5

52

07

29

7

46

32

27

58

36

7

50

07

24

54

36

8

08

23

24

21

44

8

56

27

5

52

08

8

7

46

32

27

58

35

7

50

08

24

54

33

8

08

23

24

21

41

8

56

27

5

52

08

18

7

46

32

27

58

34

7

50

08

24

54

31

8

08

23

24

21

40

8

56

27

5

52

09

28

7

46

32 +27

58

34

7

50

08 -24

54

30

8

08

23 -24

21

38

8

56

27

+5

52

09

7

7

46

33

27

58

33

7

50

08

24

54

28

8

08

24

24

21

36

8

56

27

5

52

09

17

7

46

33

27

58

32

7

50

08

24

54

27

8

08

24

24

21

35

8

56

27

5

52

09

27

7

46

33

27

58

31

7

50

09

24

54

27

8

08

24

24

21

35

8

56

28

5

52

08

7

7

46

34

27

58

31

7

50

09

24

54

26

8

08

24

24

21

34

8

56

28

5

52

08

17

7

46

34

27

58

30

7

50

09

24

54

27

8

08

25

24

21

35

8

56

28

5

52

07

27

7

46

34 +27

58

29

7

50

10 -24

54

28

8

08

25 -24

21

35

8

56

28

+5

52

05

6

7

46

35

27

58

28

7

50

10

24

54

29

8

08

25

24

21

37

8

56

29

5

52

04

16

7

46

35

27

58

27

7

50

10

24

54

31

8

08

26

24

21

39

8

56

29

5

52

03

26

7

46

35

27

58

27

7

50

10

24

54

33

8

08

26

24

21

41

8

56

29

5

52

01

6

7

46

36

27

58

26

7

50

11

24

54

36

8

08

26

24

21

43

8

56

30

5

51

59

16

7

46

36

27

58

26

7

50

11

24

54

38

8

08

27

24

21

46

8

56

30

5

51

57

26

7

46

36 +27

58

26

7

50

11 -24

54

41

8

08

27 -24

21

49

8

56

30

+5

51

56

36

7

46

36 +27

58

26

7

50

11 -24

54

44

8

08

27 -24

21

51

8

56

30

+5

51

54

234

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Velorum Hydrae Leonis Antliae K4 Ib-II 1.98 1.35 B7 V 4.25 K4 III K3 II-III 2.21 Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 9 08 45 -43 30 38 9 28 34 -8 44 40 10 09 26 +11 52 08 10 28 04 -31 09 58

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

9

08

45

43

30

42

9

28

35

8

44

43

10

09

26

11

52

06

10

28

05

31

10

01

21 31

9 9

08 08

45 45

43 43

30 30

45 49

9 9

28 28

35 35

8 8

44 44

45 47

10 10

09 09

26 27

11 11

52 52

05 04

10 10

28 28

05 05

31 31

10 10

04 07

10

9

08

45

43

30

52

9

28

35

8

44

49

10

09

27

11

52

03

10

28

05

31

10

10

20

9

08

45

43

30

55

9

28

35

8

44

50

10

09

27

11

52

03

10

28

05

31

10

13

1

9

08

45 -43

30

58

9

28

35

-8

44

51

10

09

27 +11

52

03

10

28

05 -31

10

16

11

9

08

45

43

31

00

9

28

35

8

44

52

10

09

27

11

52

03

10

28

05

31

10

18

21

9

08

45

43

31

03

9

28

35

8

44

53

10

09

27

11

52

03

10

28

05

31

10

20

31

9

08

45

43

31

04

9

28

35

8

44

54

10

09

27

11

52

04

10

28

05

31

10

22

10

9

08

45

43

31

06

9

28

35

8

44

54

10

09

27

11

52

05

10

28

05

31

10

23

20

9

08

44

43

31

07

9

28

35

8

44

54

10

09

27

11

52

05

10

28

05

31

10

25

30

9

08

44 -43

31

07

9

28

34

-8

44

54

10

09

26 +11

52

06

10

28

05 -31

10

25

10

9

08

44

43

31

07

9

28

34

8

44

53

10

09

26

11

52

06

10

28

05

31

10

26

20

9

08

44

43

31

06

9

28

34

8

44

53

10

09

26

11

52

07

10

28

04

31

10

26

30

9

08

43

43

31

05

9

28

34

8

44

52

10

09

26

11

52

08

10

28

04

31

10

26

9

9

08

43

43

31

04

9

28

34

8

44

51

10

09

26

11

52

08

10

28

04

31

10

25

19

9

08

43

43

31

02

9

28

34

8

44

50

10

09

26

11

52

09

10

28

04

31

10

24

29

9

08

43 -43

31

00

9

28

34

-8

44

49

10

09

26 +11

52

09

10

28

04 -31

10

23

9

9

08

43

43

30

58

9

28

34

8

44

48

10

09

26

11

52

09

10

28

04

31

10

21

19

9

08

43

43

30

55

9

28

34

8

44

47

10

09

26

11

52

10

10

28

04

31

10

19

29

9

08

43

43

30

53

9

28

34

8

44

45

10

09

26

11

52

10

10

28

04

31

10

17

8

9

08

43

43

30

50

9

28

34

8

44

44

10

09

26

11

52

10

10

28

04

31

10

15

18

9

08

43

43

30

47

9

28

34

8

44

43

10

09

26

11

52

09

10

28

04

31

10

13

28

9

08

43 -43

30

45

9

28

34

-8

44

42

10

09

26 +11

52

09

10

28

04 -31

10

11

7

9

08

43

43

30

42

9

28

34

8

44

41

10

09

26

11

52

09

10

28

04

31

10

09

17

9

08

43

43

30

40

9

28

34

8

44

41

10

09

26

11

52

08

10

28

04

31

10

08

27

9

08

44

43

30

39

9

28

34

8

44

41

10

09

26

11

52

07

10

28

04

31

10

07

7

9

08

44

43

30

38

9

28

35

8

44

41

10

09

27

11

52

06

10

28

04

31

10

05

17

9

08

44

43

30

37

9

28

35

8

44

41

10

09

27

11

52

05

10

28

04

31

10

05

27

9

08

45 -43

30

37

9

28

35

-8

44

42

10

09

27 +11

52

03

10

28

05 -31

10

05

6

9

08

45

43

30

38

9

28

36

8

44

43

10

09

27

11

52

01

10

28

05

31

10

05

16

9

08

45

43

30

39

9

28

36

8

44

45

10

09

28

11

51

59

10

28

05

31

10

06

26

9

08

46

43

30

41

9

28

36

8

44

47

10

09

28

11

51

58

10

28

06

31

10

07

6

9

08

46

43

30

43

9

28

37

8

44

49

10

09

28

11

51

56

10

28

06

31

10

09

16

9

08

47

43

30

46

9

28

37

8

44

51

10

09

29

11

51

54

10

28

06

31

10

12

26

9

08

47 -43

30

49

9

28

37

-8

44

53

10

09

29 +11

51

52

10

28

07 -31

10

14

36

9

08

47 -43

30

53

9

28

37

-8

44

55

10

09

29 +11

51

51

10

28

07 -31

10

17

235

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Hydrae ξ Hydrae γ Corvi Leonis 3.11 K0/K1III 3.54 G7 III 2.59 B8III 2.14 A3 V Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 10 50 37 -16 17 45 11 33 59 -31 57 50 11 50 04 +14 27 37 12 16 49 -17 38 58

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11 21

10 10

50 50

37 37

16 16

17 17

47 50

11 11

33 33

59 60

31 31

57 57

52 55

11 11

50 50

04 05

14 14

27 27

35 34

12 12

16 16

50 50

17 17

39 39

00 02

31

10

50

37

16

17

52

11

33

60

31

57

58

11

50

05

14

27

32

12

16

50

17

39

05

10 20

10 10

50 50

37 38

16 16

17 17

55 57

11 11

34 34

00 00

31 31

58 58

01 04

11 11

50 50

05 05

14 14

27 27

31 31

12 12

16 16

51 51

17 17

39 39

07 09

1

10

50

38 -16

17

58

11

34

00 -31

58

06

11

50

05 +14

27

31

12

16

51 -17

39

11

11

10

50

38

16

18

00

11

34

00

31

58

09

11

50

06

14

27

31

12

16

51

17

39

13

21

10

50

38

16

18

02

11

34

01

31

58

11

11

50

06

14

27

31

12

16

51

17

39

14

31

10

50

38

16

18

03

11

34

01

31

58

13

11

50

06

14

27

32

12

16

51

17

39

16

10

10

50

38

16

18

03

11

34

00

31

58

15

11

50

06

14

27

33

12

16

51

17

39

17

20

10

50

38

16

18

04

11

34

00

31

58

17

11

50

06

14

27

34

12

16

51

17

39

18

30

10

50

37 -16

18

04

11

34

00 -31

58

18

11

50

06 +14

27

35

12

16

51 -17

39

18

10

10

50

37

16

18

05

11

34

00

31

58

19

11

50

05

14

27

36

12

16

51

17

39

19

20

10

50

37

16

18

04

11

34

00

31

58

19

11

50

05

14

27

37

12

16

51

17

39

19

30

10

50

37

16

18

04

11

33

60

31

58

19

11

50

05

14

27

38

12

16

51

17

39

19

9

10

50

37

16

18

03

11

33

60

31

58

19

11

50

05

14

27

38

12

16

51

17

39

19

19

10

50

37

16

18

02

11

33

60

31

58

19

11

50

05

14

27

39

12

16

51

17

39

18

29

10

50

37 -16

18

02

11

33

59 -31

58

18

11

50

05 +14

27

40

12

16

51 -17

39

17

9

10

50

37

16

18

01

11

33

59

31

58

17

11

50

05

14

27

40

12

16

51

17

39

17

19

10

50

37

16

18

01

11

33

59

31

58

16

11

50

05

14

27

40

12

16

50

17

39

16

29

10

50

36

16

17

58

11

33

59

31

58

14

11

50

05

14

27

40

12

16

50

17

39

15

8

10

50

36

16

17

57

11

33

59

31

58

13

11

50

05

14

27

40

12

16

50

17

39

14

18

10

50

36

16

17

55

11

33

59

31

58

11

11

50

05

14

27

40

12

16

50

17

39

13

28

10

50

36 -16

17

54

11

33

59 -31

58

09

11

50

05 +14

27

39

12

16

50 -17

39

12

7

10

50

37

16

17

53

11

33

59

31

58

07

11

50

05

14

27

38

12

16

50

17

39

11

17

10

50

37

16

17

52

11

33

59

31

58

06

11

50

05

14

27

37

12

16

50

17

39

10

27

10

50

37

16

17

52

11

33

59

31

58

04

11

50

05

14

27

36

12

16

50

17

39

10

7

10

50

37

16

17

51

11

33

59

31

58

03

11

50

05

14

27

35

12

16

50

17

39

09

17

10

50

37

16

17

51

11

33

59

31

58

02

11

50

05

14

27

33

12

16

50

17

39

09

27

10

50

37 -16

17

52

11

33

60 -31

58

02

11

50

05 +14

27

31

12

16

51 -17

39

09

6

10

50

38

16

17

53

11

33

60

31

58

01

11

50

05

14

27

29

12

16

51

17

39

09

16

10

50

38

16

17

54

11

34

00

31

58

02

11

50

06

14

27

27

12

16

51

17

39

10

26

10

50

38

16

17

55

11

34

01

31

58

03

11

50

06

14

27

24

12

16

51

17

39

11

6

10

50

39

16

17

57

11

34

01

31

58

04

11

50

06

14

27

22

12

16

52

17

39

13

16

10

50

39

16

18

01

11

34

01

31

58

06

11

50

07

14

27

20

12

16

52

17

39

15

26

10

50

39 -16

18

02

11

34

02 -31

58

08

11

50

07 +14

27

18

12

16

52 -17

39

17

36

10

50

40 -16

18

04

11

34

02 -31

58

11

11

50

07 +14

27

16

12

16

53 -17

39

19

236

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Corvi Virginis  Centauri Virginis kA15hA3nA3va 2.83 G8 III 2.75 2.65 G5 II 3.38 M3III Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 12 35 26 -23 30 11 12 56 36 +3 17 25 13 03 09 +10 51 09 13 21 42 -36 48 43

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

12

35

26

23

30

13

12

56

36

3

17

23

13

03

10

10

51

07

13

21

43

36

48

45

21

12

35

26

23

30

15

12

56

36

3

17

21

13

03

10

10

51

05

13

21

43

36

48

47

31

12

35

27

23

30

18

12

56

37

3

17

19

13

03

10

10

51

03

13

21

43

36

48

49

10

12

35

27

23

30

20

12

56

37

3

17

18

13

03

10

10

51

02

13

21

44

36

48

52

20

12

35

27

23

30

23

12

56

37

3

17

17

13

03

11

10

51

01

13

21

44

36

48

54

1

12

35

27 -23

30

25

12

56

37

+3

17

16

13

03

11 +10

51

01

13

21

44 -36

48

56

11

12

35

27

23

30

27

12

56

37

3

17

15

13

03

11

10

51

01

13

21

45

36

48

59

21

12

35

28

23

30

29

12

56

38

3

17

15

13

03

11

10

51

01

13

21

45

36

49

01

31

12

35

28

23

30

30

12

56

38

3

17

15

13

03

11

10

51

01

13

21

45

36

49

04

10

12

35

28

23

30

32

12

56

38

3

17

15

13

03

11

10

51

02

13

21

45

36

49

06

20

12

35

28

23

30

33

12

56

38

3

17

15

13

03

11

10

51

03

13

21

45

36

49

08

30

12

35

28 -23

30

34

12

56

38

+3

17

16

13

03

11 +10

51

04

13

21

45 -36

49

10

10

12

35

28

23

30

35

12

56

38

3

17

17

13

03

11

10

51

05

13

21

45

36

49

11

20

12

35

27

23

30

35

12

56

38

3

17

17

13

03

11

10

51

06

13

21

45

36

49

12

30

12

35

27

23

30

35

12

56

38

3

17

18

13

03

11

10

51

07

13

21

45

36

49

13

9

12

35

27

23

30

35

12

56

38

3

17

19

13

03

11

10

51

08

13

21

45

36

49

14

19

12

35

27

23

30

35

12

56

37

3

17

20

13

03

11

10

51

09

13

21

45

36

49

14

29

12

35

27 -23

30

35

12

56

37

+3

17

20

13

03

11 +10

51

09

13

21

45 -36

49

15

9

12

35

27

23

30

34

12

56

37

3

17

21

13

03

11

10

51

10

13

21

44

36

49

15

19

12

35

27

23

30

33

12

56

37

3

17

21

13

03

11

10

51

10

13

21

44

36

49

14

29

12

35

27

23

30

32

12

56

37

3

17

22

13

03

11

10

51

11

13

21

44

36

49

13

8

12

35

27

23

30

31

12

56

37

3

17

22

13

03

11

10

51

11

13

21

44

36

49

13

18

12

35

27

23

30

30

12

56

37

3

17

22

13

03

11

10

51

11

13

21

44

36

49

11

28

12

35

26 -23

30

29

12

56

37

+3

17

22

13

03

10 +10

51

10

13

21

44 -36

49

10

7

12

35

26

23

30

28

12

56

37

3

17

22

13

03

10

10

51

10

13

21

44

36

49

08

17

12

35

26

23

30

27

12

56

37

3

17

22

13

03

10

10

51

09

13

21

43

36

49

07

27

12

35

26

23

30

26

12

56

37

3

17

21

13

03

10

10

51

08

13

21

43

36

49

05

7

12

35

26

23

30

25

12

56

37

3

17

20

13

03

10

10

51

07

13

21

43

36

49

04

17

12

35

27

23

30

24

12

56

37

3

17

19

13

03

10

10

51

05

13

21

43

36

49

02

27

12

35

27 -23

30

24

12

56

37

+3

17

18

13

03

11 +10

51

03

13

21

44 -36

49

01

6

12

35

27

23

30

24

12

56

37

3

17

16

13

03

11

10

51

02

13

21

44

36

49

00

16

12

35

27

23

30

25

12

56

37

3

17

15

13

03

11

10

50

59

13

21

44

36

49

00

26

12

35

27

23

30

26

12

56

38

3

17

13

13

03

11

10

50

57

13

21

44

36

49

00

6

12

35

28

23

30

27

12

56

38

3

17

10

13

03

11

10

50

55

13

21

45

36

49

00

16

12

35

28

23

30

28

12

56

38

3

17

08

13

03

12

10

50

52

13

21

45

36

49

01

26

12

35

28 -23

30

30

12

56

38

+3

17

06

13

03

12 +10

50

50

13

21

45 -36

49

02

36

12

35

29 -23

30

32

12

56

39

+3

17

04

13

03

12 +10

50

48

13

21

46 -36

49

04

237

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Lupi Virginis θ Centauri Librae KA2HA5MA4IV-V 0.98 B1 III-V+ 2.06 K0 III 2.68 B2 III 2.75 Mag. Spect. Declination Right Declination Right Declination Right Declination Right U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " 1 13 26 14 -11 15 44 14 07 50 -36 27 45 14 51 57 -16 07 15 14 59 49 -43 12 30 Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

13

26

14

11

15

46

14

07

51

36

27

46

14

51

58

16

07

17

14

59

49

43

12

31

21 31

13 13

26 26

14 15

11 11

15 15

48 50

14 14

07 07

51 51

36 36

27 27

48 50

14 14

51 51

58 58

16 16

07 07

18 20

14 14

59 59

50 50

43 43

12 12

31 33

10 20

13 13

26 26

15 15

11 11

15 15

52 54

14 14

07 07

52 52

36 36

27 27

52 54

14 14

51 51

59 59

16 16

07 07

22 23

14 14

59 59

50 51

43 43

12 12

34 36

1

13

26

15 -11

15

55

14

07

52 -36

27

56

14

51

59 -16

07

25

14

59

51 -43

12

38

11

13

26

16

11

15

57

14

07

53

36

27

58

14

51

60

16

07

26

14

59

51

43

12

40

21

13

26

16

11

15

58

14

07

53

36

28

01

14

51

60

16

07

27

14

59

52

43

12

42

31

13

26

16

11

15

59

14

07

53

36

28

03

14

52

00

16

07

28

14

59

52

43

12

44

10

13

26

16

11

16

01

14

07

53

36

28

05

14

52

00

16

07

29

14

59

52

43

12

46

20

13

26

16

11

16

00

14

07

53

36

28

07

14

52

00

16

07

30

14

59

53

43

12

48

30

13

26

16 -11

16

00

14

07

53 -36

28

08

14

52

01 -16

07

30

14

59

53 -43

12

50

10

13

26

16

11

16

00

14

07

54

36

28

10

14

52

01

16

07

30

14

59

53

43

12

52

20

13

26

16

11

16

00

14

07

54

36

28

11

14

52

01

16

07

30

14

59

53

43

12

53

30

13

26

16

11

16

00

14

07

54

36

28

13

14

52

01

16

07

31

14

59

53

43

12

55

9

13

26

16

11

16

00

14

07

53

36

28

13

14

52

01

16

07

31

14

59

53

43

12

56

19

13

26

16

11

16

01

14

07

53

36

28

14

14

52

01

16

07

30

14

59

53

43

12

58

29

13

26

16 -11

16

01

14

07

53 -36

28

15

14

52

01 -16

07

30

14

59

53 -43

12

59

9

13

26

16

11

15

59

14

07

53

36

28

15

14

52

01

16

07

30

14

59

53

43

13

01

19

13

26

16

11

15

58

14

07

53

36

28

15

14

52

01

16

07

30

14

59

53

43

13

00

29

13

26

15

11

15

57

14

07

53

36

28

14

14

52

00

16

07

29

14

59

52

43

13

00

8

13

26

15

11

15

57

14

07

53

36

28

14

14

52

00

16

07

29

14

59

52

43

13

00

18

13

26

15

11

15

56

14

07

52

36

28

13

14

52

00

16

07

29

14

59

52

43

13

01

28

13

26

15 -11

15

56

14

07

52 -36

28

12

14

51

60 -16

07

28

14

59

52 -43

12

59

7

13

26

15

11

15

55

14

07

52

36

28

11

14

51

60

16

07

28

14

59

52

43

12

58

17

13

26

15

11

15

55

14

07

52

36

28

10

14

51

60

16

07

27

14

59

51

43

12

57

27

13

26

15

11

15

55

14

07

52

36

28

08

14

51

60

16

07

27

14

59

51

43

12

55

7

13

26

15

11

15

54

14

07

52

36

28

07

14

51

60

16

07

26

14

59

51

43

12

54

17

13

26

15

11

15

55

14

07

52

36

28

05

14

51

59

16

07

26

14

59

51

43

12

52

27

13

26

15 -11

15

55

14

07

52 -36

28

04

14

51

60 -16

07

27

14

59

51 -43

12

51

6

13

26

15

11

15

56

14

07

52

36

28

03

14

51

60

16

07

27

14

59

51

43

12

49

16

13

26

15

11

15

57

14

07

52

36

28

03

14

51

60

16

07

27

14

59

51

43

12

48

26

13

26

16

11

15

58

14

07

53

36

28

02

14

51

60

16

07

28

14

59

51

43

12

47

6

13

26

16

11

16

01

14

07

53

36

28

03

14

52

00

16

07

29

14

59

52

43

12

47

16

13

26

16

11

16

01

14

07

53

36

28

03

14

52

00

16

07

30

14

59

52

43

12

46

26

13

26

17 -11

16

03

14

07

53 -36

28

04

14

52

01 -16

07

31

14

59

52 -43

12

46

36

13

26

17 -11

16

05

14

07

54 -36

28

05

14

52

01 -16

07

33

14

59

53 -43

12

47

238

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Librae  Serpentis Ophiuchi Scorpii 2.61 B8 IV 2.65 K2 III b 2.74 M0.5 III 2.32 B0.2 Ive Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 15 18 03 -9 27 12 15 45 13 +6 21 52 16 01 29 -22 40 29 16 15 22 -3 44 35

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

15

18

04

9

27

14

15

45

14

6

21

50

16

01

29

22

40

29

16

15

22

3

44

37

21

15

18

04

9

27

15

15

45

14

6

21

48

16

01

30

22

40

30

16

15

22

3

44

38

31

15

18

04

9

27

17

15

45

14

6

21

46

16

01

30

22

40

32

16

15

22

3

44

40

10

15

18

05

9

27

19

15

45

15

6

21

45

16

01

30

22

40

33

16

15

23

3

44

42

20

15

18

05

9

27

20

15

45

15

6

21

43

16

01

31

22

40

34

16

15

23

3

44

43

1

15

18

05

-9

27

21

15

45

15

+6

21

42

16

01

31 -22

40

35

16

15

23

-3

44

44

11

15

18

05

9

27

22

15

45

15

6

21

42

16

01

31

22

40

36

16

15

24

3

44

45

21

15

18

06

9

27

23

15

45

16

6

21

42

16

01

31

22

40

37

16

15

24

3

44

45

31

15

18

06

9

27

23

15

45

16

6

21

42

16

01

32

22

40

38

16

15

24

3

44

45

10

15

18

06

9

27

24

15

45

16

6

21

42

16

01

32

22

40

39

16

15

24

3

44

45

20

15

18

06

9

27

24

15

45

16

6

21

43

16

01

32

22

40

39

16

15

25

3

44

45

30

15

18

06

-9

27

24

15

45

16

+6

21

44

16

01

32 -22

40

40

16

15

25

-3

44

44

10

15

18

06

9

27

24

15

45

17

6

21

45

16

01

33

22

40

40

16

15

25

3

44

44

20

15

18

07

9

27

24

15

45

17

6

21

46

16

01

33

22

40

41

16

15

25

3

44

43

30

15

18

07

9

27

23

15

45

17

6

21

48

16

01

33

22

40

41

16

15

25

3

44

42

9

15

18

07

9

27

23

15

45

17

6

21

49

16

01

33

22

40

41

16

15

25

3

44

41

19

15

18

07

9

27

22

15

45

17

6

21

50

16

01

33

22

40

42

16

15

25

3

44

41

29

15

18

07

-9

27

22

15

45

17

+6

21

51

16

01

33 -22

40

42

16

15

25

-3

44

40

9

15

18

07

9

27

22

15

45

17

6

21

52

16

01

33

22

40

42

16

15

25

3

44

39

19

15

18

06

9

27

21

15

45

17

6

21

53

16

01

33

22

40

42

16

15

25

3

44

38

29

15

18

06

9

27

21

15

45

17

6

21

54

16

01

33

22

40

42

16

15

25

3

44

38

8

15

18

06

9

27

21

15

45

16

6

21

54

16

01

33

22

40

42

16

15

25

3

44

38

18

15

18

06

9

27

20

15

45

16

6

21

55

16

01

32

22

40

42

16

15

25

3

44

37

28

15

18

06

-9

27

20

15

45

16

+6

21

55

16

01

32 -22

40

42

16

15

25

-3

44

37

7

15

18

06

9

27

20

15

45

16

6

21

55

16

01

32

22

40

41

16

15

25

3

44

37

17

15

18

06

9

27

19

15

45

16

6

21

55

16

01

32

22

40

41

16

15

25

3

44

37

27

15

18

06

9

27

19

15

45

16

6

21

54

16

01

32

22

40

41

16

15

24

3

44

37

7

15

18

05

9

27

19

15

45

16

6

21

54

16

01

32

22

40

40

16

15

24

3

44

37

17

15

18

05

9

27

20

15

45

15

6

21

52

16

01

32

22

40

40

16

15

24

3

44

38

27

15

18

05

-9

27

20

15

45

15

+6

21

51

16

01

32 -22

40

40

16

15

24

-3

44

38

6

15

18

05

9

27

21

15

45

15

6

21

50

16

01

32

22

40

39

16

15

24

3

44

39

16

15

18

05

9

27

21

15

45

15

6

21

48

16

01

32

22

40

39

16

15

24

3

44

40

26

15

18

06

9

27

22

15

45

16

6

21

46

16

01

32

22

40

39

16

15

24

3

44

42

6

15

18

06

9

27

24

15

45

16

6

21

44

16

01

32

22

40

40

16

15

24

3

44

43

16

15

18

06

9

27

25

15

45

16

6

21

42

16

01

32

22

40

40

16

15

24

3

44

44

26

15

18

06

-9

27

27

15

45

16

+6

21

40

16

01

32 -22

40

41

16

15

25

-3

44

46

36

15

18

07

-9

27

28

15

45

16

+6

21

37

16

01

33 -22

40

42

16

15

25

-3

44

48

239

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name ScorpiiA Ophiuchi θ Ophiuchi Scorpii M1.5 Iab-b 2.56 O9V 3.27 B2 IV 2.29 K1 III Mag. Spect. 0.9 - 1.8 Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " 1 16 30 36 -26 28 20 16 38 13 -10 36 17 16 51 25 -34 19 31 17 23 12 -25 00 59 Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11 21

16 16

30 30

36 36

26 26

28 28

21 21

16 16

38 38

14 14

10 10

36 36

18 19

16 16

51 51

25 26

34 34

19 19

31 31

17 17

23 23

12 12

25 25

00 01

59 01

31 10

16 16

30 30

37 37

26 26

28 28

22 23

16 16

38 38

14 15

10 10

36 36

20 22

16 16

51 51

26 26

34 34

19 19

32 32

17 17

23 23

13 13

25 25

01 01

00 00

20

16

30

37

26

28

24

16

38

15

10

36

23

16

51

27

34

19

33

17

23

13

25

01

01

1

16

30

38 -26

28

25

16

38

15 -10

36

24

16

51

27 -34

19

33

17

23

14 -25

01

01

11

16

30

38

26

28

26

16

38

16

10

36

24

16

51

27

34

19

34

17

23

14

25

01

02

21

16

30

38

26

28

27

16

38

16

10

36

25

16

51

28

34

19

35

17

23

14

25

01

02

31

16

30

39

26

28

27

16

38

16

10

36

25

16

51

28

34

19

36

17

23

14

25

01

02

10

16

30

39

26

28

28

16

38

16

10

36

25

16

51

28

34

19

37

17

23

15

25

01

03

20

16

30

39

26

28

29

16

38

17

10

36

25

16

51

29

34

19

37

17

23

15

25

01

03

30

16

30

39 -26

28

29

16

38

17 -10

36

25

16

51

29 -34

19

38

17

23

15 -25

01

03

10

16

30

40

26

28

30

16

38

17

10

36

25

16

51

29

34

19

39

17

23

16

25

01

03

20

16

30

40

26

28

31

16

38

17

10

36

24

16

51

29

34

19

40

17

23

16

25

01

04

30

16

30

40

26

28

31

16

38

17

10

36

24

16

51

30

34

19

41

17

23

16

25

01

04

9

16

30

40

26

28

31

16

38

17

10

36

23

16

51

30

34

19

42

17

23

16

25

01

04

19

16

30

40

26

28

32

16

38

17

10

36

23

16

51

30

34

19

43

17

23

16

25

01

04

29

16

30

40 -26

28

32

16

38

18 -10

36

22

16

51

30 -34

19

44

17

23

16 -25

01

05

9

16

30

40

26

28

33

16

38

18

10

36

22

16

51

30

34

19

44

17

23

16

25

01

05

19

16

30

40

26

28

33

16

38

17

10

36

21

16

51

30

34

19

45

17

23

16

25

01

05

29

16

30

40

26

28

33

16

38

17

10

36

21

16

51

30

34

19

46

17

23

16

25

01

06

8

16

30

40

26

28

33

16

38

17

10

36

21

16

51

30

34

19

46

17

23

16

25

01

06

18

16

30

40

26

28

33

16

38

17

10

36

21

16

51

29

34

19

46

17

23

16

25

01

06

28

16

30

40 -26

28

33

16

38

17 -10

36

20

16

51

29 -34

19

47

17

23

16 -25

01

06

7

16

30

39

26

28

33

16

38

17

10

36

20

16

51

29

34

19

47

17

23

16

25

01

06

17

16

30

39

26

28

33

16

38

17

10

36

20

16

51

29

34

19

47

17

23

16

25

01

06

27

16

30

39

26

28

33

16

38

17

10

36

20

16

51

29

34

19

46

17

23

16

25

01

06

7

16

30

39

26

28

32

16

38

16

10

36

20

16

51

28

34

19

45

17

23

15

25

01

06

17

16

30

39

26

28

32

16

38

16

10

36

21

16

51

28

34

19

45

17

23

15

25

01

06

27

16

30

39 -26

28

31

16

38

16 -10

36

21

16

51

28 -34

19

44

17

23

15 -25

01

06

6

16

30

39

26

28

31

16

38

16

10

36

21

16

51

28

34

19

43

17

23

15

25

01

05

16

16

30

39

26

28

30

16

38

16

10

36

22

16

51

28

34

19

43

17

23

15

25

01

05

26

16

30

39

26

28

30

16

38

16

10

36

23

16

51

28

34

19

42

17

23

15

25

01

05

6

16

30

39

26

28

30

16

38

16

10

36

23

16

51

28

34

19

41

17

23

15

25

01

05

16

16

30

39

26

28

30

16

38

16

10

36

24

16

51

29

34

19

41

17

23

15

25

01

05

26

16

30

39 -26

28

31

16

38

17 -10

36

26

16

51

29 -34

19

40

17

23

15 -25

01

05

36

16

30

40 -26

28

31

16

38

17 -10

36

27

16

51

29 -34

19

40

17

23

16 -25

01

05

240

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name λ Scorpii Ophiuchi Ophiuchi  Sagittarii 1.63 B2 IV+ 2.08 A5 III 2.70 K3IIIa 2.77 K2 III Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 17 34 55 -37 06 54 17 35 50 +12 32 48 17 44 25 +4 33 38 18 22 14 -29 49 02

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

17

34

55

37

06

53

17

35

50

12

32

46

17

44

26

4

33

36

18

22

14

29

49

02

21 31

17 17

34 34

56 56

37 37

06 06

53 53

17 17

35 35

50 50

12 12

32 32

44 42

17 17

44 44

26 26

4 4

33 33

34 32

18 18

22 22

14 14

29 29

49 49

02 02

10

17

34

56

37

06

53

17

35

51

12

32

40

17

44

26

4

33

31

18

22

15

29

49

02

20

17

34

57

37

06

52

17

35

51

12

32

39

17

44

27

4

33

30

18

22

15

29

49

01

1

17

34

57 -37

06

53

17

35

51 +12

32

38

17

44

27

+4

33

29

18

22

15 -29

49

01

11

17

34

57

37

06

53

17

35

51

12

32

37

17

44

27

4

33

28

18

22

16

29

49

01

21

17

34

58

37

06

53

17

35

52

12

32

37

17

44

27

4

33

28

18

22

16

29

49

01

31

17

34

58

37

06

54

17

35

52

12

32

37

17

44

28

4

33

28

18

22

16

29

49

01

10

17

34

59

37

06

54

17

35

52

12

32

38

17

44

28

4

33

29

18

22

17

29

49

01

20

17

34

59

37

06

55

17

35

52

12

32

39

17

44

28

4

33

29

18

22

17

29

49

01

30

17

34

59 -37

06

55

17

35

53 +12

32

40

17

44

29

+4

33

31

18

22

17 -29

49

01

10

17

34

59

37

06

56

17

35

53

12

32

42

17

44

29

4

33

32

18

22

18

29

49

00

20

17

34

60

37

06

57

17

35

53

12

32

43

17

44

29

4

33

33

18

22

18

29

49

01

30

17

34

60

37

06

58

17

35

53

12

32

45

17

44

29

4

33

35

18

22

18

29

49

01

9

17

35

00

37

06

58

17

35

53

12

32

47

17

44

29

4

33

36

18

22

18

29

49

01

19

17

35

00

37

07

01

17

35

54

12

32

49

17

44

29

4

33

38

18

22

18

29

49

01

29

17

35

00 -37

07

00

17

35

54 +12

32

51

17

44

29

+4

33

39

18

22

19 -29

49

02

9

17

35

00

37

07

01

17

35

54

12

32

52

17

44

30

4

33

40

18

22

19

29

49

02

19

17

35

00

37

07

02

17

35

54

12

32

54

17

44

30

4

33

42

18

22

19

29

49

03

29

17

35

00

37

07

03

17

35

54

12

32

55

17

44

29

4

33

43

18

22

19

29

49

03

8

17

35

00

37

07

04

17

35

53

12

32

56

17

44

29

4

33

43

18

22

19

29

49

04

18

17

35

00

37

07

05

17

35

53

12

32

57

17

44

29

4

33

44

18

22

19

29

49

05

28

17

34

60 -37

07

05

17

35

53 +12

32

58

17

44

29

+4

33

45

18

22

19 -29

49

05

7

17

34

60

37

07

05

17

35

53

12

32

58

17

44

29

4

33

45

18

22

18

29

49

06

17

17

34

60

37

07

06

17

35

53

12

32

58

17

44

29

4

33

45

18

22

18

29

49

06

27

17

34

59

37

07

05

17

35

53

12

32

58

17

44

29

4

33

45

18

22

18

29

49

06

7

17

34

59

37

07

05

17

35

52

12

32

58

17

44

28

4

33

45

18

22

18

29

49

06

17

17

34

59

37

07

05

17

35

52

12

32

57

17

44

28

4

33

44

18

22

18

29

49

06

27

17

34

59 -37

07

04

17

35

52 +12

32

56

17

44

28

+4

33

43

18

22

17 -29

49

06

6

17

34

59

37

07

03

17

35

52

12

32

54

17

44

28

4

33

42

18

22

17

29

49

06

16

17

34

59

37

07

02

17

35

52

12

32

53

17

44

28

4

33

41

18

22

17

29

49

05

26

17

34

59

37

07

02

17

35

52

12

32

51

17

44

28

4

33

40

18

22

17

29

49

05

6

17

34

59

37

07

01

17

35

52

12

32

49

17

44

28

4

33

38

18

22

17

29

49

05

16

17

34

59

37

07

00

17

35

52

12

32

47

17

44

28

4

33

36

18

22

17

29

49

04

26

17

34

59 -37

07

01

17

35

52 +12

32

44

17

44

28

+4

33

35

18

22

17 -29

49

04

36

17

34

59 -37

06

59

17

35

52 +12

32

42

17

44

28

+4

33

33

18

22

18 -29

49

04

241

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name  Sagittarii Sagittarii Aquilae γ Aquilae 1.85 B9.5III 2.02 B2V 2.72 G9.5IV 2.99 A0 Vn Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 18 25 27 -34 22 22 18 56 28 -26 16 14 19 06 17 +13 53 39 19 47 10 +10 39 46

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

18

25

27

34

22

22

18

56

28

26

16

13

19

06

18

13

53

37

19

47

10

10

39

44

21

18

25

27

34

22

21

18

56

28

26

16

13

19

06

18

13

53

35

19

47

11

10

39

42

31

18

25

28

34

22

21

18

56

28

26

16

13

19

06

18

13

53

33

19

47

11

10

39

41

10

18

25

28

34

22

20

18

56

28

26

16

13

19

06

18

13

53

31

19

47

11

10

39

39

20

18

25

28

34

22

20

18

56

29

26

16

12

19

06

18

13

53

30

19

47

11

10

39

38

1

18

25

29 -34

22

20

18

56

29 -26

16

12

19

06

19 +13

53

28

19

47

11 +10

39

37

11

18

25

29

34

22

20

18

56

29

26

16

12

19

06

19

13

53

28

19

47

11

10

39

36

21

18

25

29

34

22

19

18

56

30

26

16

11

19

06

19

13

53

27

19

47

12

10

39

35

31

18

25

30

34

22

19

18

56

30

26

16

11

19

06

19

13

53

27

19

47

12

10

39

36

10

18

25

30

34

22

19

18

56

30

26

16

11

19

06

20

13

53

28

19

47

12

10

39

36

20

18

25

30

34

22

19

18

56

31

26

16

10

19

06

20

13

53

29

19

47

13

10

39

37

30

18

25

31 -34

22

19

18

56

31 -26

16

10

19

06

20 +13

53

30

19

47

13 +10

39

38

10

18

25

31

34

22

19

18

56

31

26

16

09

19

06

21

13

53

32

19

47

13

10

39

39

20

18

25

31

34

22

20

18

56

31

26

16

09

19

06

21

13

53

33

19

47

13

10

39

41

30

18

25

32

34

22

20

18

56

32

26

16

09

19

06

21

13

53

35

19

47

14

10

39

43

9

18

25

32

34

22

20

18

56

32

26

16

08

19

06

21

13

53

37

19

47

14

10

39

45

19

18

25

32

34

22

21

18

56

32

26

16

08

19

06

21

13

53

40

19

47

14

10

39

47

29

18

25

32 -34

22

22

18

56

32 -26

16

09

19

06

22 +13

53

42

19

47

14 +10

39

49

9

18

25

32

34

22

22

18

56

33

26

16

09

19

06

22

13

53

44

19

47

15

10

39

51

19

18

25

32

34

22

23

18

56

33

26

16

09

19

06

22

13

53

46

19

47

15

10

39

53

29

18

25

32

34

22

24

18

56

33

26

16

09

19

06

22

13

53

47

19

47

15

10

39

55

8

18

25

32

34

22

25

18

56

33

26

16

10

19

06

22

13

53

49

19

47

15

10

39

56

18

18

25

32

34

22

26

18

56

33

26

16

10

19

06

22

13

53

50

19

47

15

10

39

58

28

18

25

32 -34

22

26

18

56

32 -26

16

11

19

06

22 +13

53

52

19

47

15 +10

39

59

7

18

25

32

34

22

27

18

56

32

26

16

11

19

06

21

13

53

52

19

47

15

10

39

60

17

18

25

32

34

22

27

18

56

32

26

16

12

19

06

21

13

53

53

19

47

14

10

40

01

27

18

25

32

34

22

28

18

56

32

26

16

12

19

06

21

13

53

53

19

47

14

10

40

01

7

18

25

31

34

22

28

18

56

32

26

16

12

19

06

21

13

53

53

19

47

14

10

40

01

17

18

25

31

34

22

28

18

56

32

26

16

13

19

06

21

13

53

53

19

47

14

10

40

01

27

18

25

31 -34

22

27

18

56

31 -26

16

13

19

06

21 +13

53

52

19

47

14 +10

40

01

6

18

25

31

34

22

27

18

56

31

26

16

13

19

06

20

13

53

51

19

47

14

10

40

00

16

18

25

31

34

22

26

18

56

31

26

16

13

19

06

20

13

53

50

19

47

13

10

39

59

26

18

25

31

34

22

26

18

56

31

26

16

13

19

06

20

13

53

49

19

47

13

10

39

58

6

18

25

31

34

22

25

18

56

31

26

16

12

19

06

20

13

53

47

19

47

13

10

39

57

16

18

25

31

34

22

24

18

56

31

26

16

12

19

06

20

13

53

45

19

47

13

10

39

55

26

18

25

31 -34

22

24

18

56

31 -26

16

12

19

06

20 +13

53

43

19

47

13 +10

39

53

36

18

25

31 -34

22

23

18

56

31 -26

16

12

19

06

20 +13

53

41

19

47

13 +10

39

51

242

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Aquilae γ Cygni Cygni  Aquarii 0.77 A7 V 2.20 F8 I ab 2.91 A1.5V 1.25 A2 Iae Mag. Spect. Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 19 51 43 +8 55 19 20 22 55 +40 19 20 20 42 05 +45 21 13 21 32 35 -5 29 02

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

19

51

43

8

55

17

20

22

55

40

19

17

20

42

05

45

21

10

21

32

35

5

29

03

21

19

51

43

8

55

15

20

22

55

40

19

14

20

42

05

45

21

07

21

32

35

5

29

04

31

19

51

44

8

55

14

20

22

55

40

19

11

20

42

05

45

21

04

21

32

35

5

29

04

10 20

19 19

51 51

44 44

8 8

55 55

12 11

20 20

22 22

55 55

40 40

19 19

08 06

20 20

42 42

05 05

45 45

21 20

01 58

21 21

32 32

35 35

5 5

29 29

04 05

1

19

51

44

+8

55

10

20

22

55 +40

19

03

20

42

05 +45

20

55

21

32

35

-5

29

05

11

19

51

44

8

55

09

20

22

55

40

19

01

20

42

05

45

20

53

21

32

35

5

29

05

21

19

51

45

8

55

09

20

22

56

40

19

00

20

42

06

45

20

52

21

32

35

5

29

04

31

19

51

45

8

55

09

20

22

56

40

18

59

20

42

06

45

20

51

21

32

35

5

29

04

10

19

51

45

8

55

10

20

22

56

40

18

59

20

42

06

45

20

50

21

32

36

5

29

03

20

19

51

46

8

55

10

20

22

57

40

18

59

20

42

07

45

20

50

21

32

36

5

29

02

30

19

51

46

+8

55

12

20

22

57 +40

19

00

20

42

07 +45

20

51

21

32

36

-5

29

00

10

19

51

46

8

55

13

20

22

57

40

19

02

20

42

07

45

20

52

21

32

37

5

28

59

20

19

51

46

8

55

15

20

22

58

40

19

03

20

42

08

45

20

54

21

32

37

5

28

57

30

19

51

47

8

55

17

20

22

58

40

19

06

20

42

08

45

20

56

21

32

37

5

28

55

9

19

51

47

8

55

19

20

22

58

40

19

08

20

42

08

45

20

59

21

32

38

5

28

53

19

19

51

47

8

55

21

20

22

59

40

19

11

20

42

09

45

21

01

21

32

38

5

28

52

29

19

51

47

+8

55

23

20

22

59 +40

19

14

20

42

09 +45

21

04

21

32

38

-5

28

50

9

19

51

47

8

55

25

20

22

59

40

19

18

20

42

09

45

21

08

21

32

38

5

28

48

19

19

51

48

8

55

27

20

22

59

40

19

21

20

42

09

45

21

11

21

32

39

5

28

47

29

19

51

48

8

55

28

20

22

59

40

19

24

20

42

09

45

21

14

21

32

39

5

28

46

8

19

51

48

8

55

30

20

22

59

40

19

27

20

42

09

45

21

17

21

32

39

5

28

45

18

19

51

48

8

55

31

20

22

59

40

19

30

20

42

09

45

21

21

21

32

39

5

28

44

28

19

51

48

+8

55

32

20

22

59 +40

19

32

20

42

09 +45

21

23

21

32

39

-5

28

44

7

19

51

47

8

55

33

20

22

59

40

19

34

20

42

09

45

21

26

21

32

39

5

28

43

17

19

51

47

8

55

34

20

22

59

40

19

36

20

42

09

45

21

28

21

32

39

5

28

43

27

19

51

47

8

55

34

20

22

58

40

19

38

20

42

09

45

21

30

21

32

39

5

28

43

7

19

51

47

8

55

34

20

22

58

40

19

39

20

42

08

45

21

31

21

32

39

5

28

43

17

19

51

47

8

55

34

20

22

58

40

19

39

20

42

08

45

21

32

21

32

39

5

28

44

27

19

51

47

+8

55

34

20

22

58 +40

19

39

20

42

08 +45

21

33

21

32

38

-5

28

44

6

19

51

47

8

55

33

20

22

57

40

19

39

20

42

08

45

21

33

21

32

38

5

28

44

16

19

51

46

8

55

32

20

22

57

40

19

38

20

42

07

45

21

32

21

32

38

5

28

45

26

19

51

46

8

55

31

20

22

57

40

19

37

20

42

07

45

21

31

21

32

38

5

28

46

6

19

51

46

8

55

30

20

22

57

40

19

35

20

42

07

45

21

29

21

32

38

5

28

46

16

19

51

46

8

55

28

20

22

57

40

19

33

20

42

07

45

21

28

21

32

38

5

28

47

26

19

51

46

+8

55

27

20

22

57 +40

19

31

20

42

07 +45

21

25

21

32

38

-5

28

48

36

19

51

46

+8

55

25

20

22

57 +40

19

28

20

42

06 +45

21

22

21

32

38

-5

28

48

243

APPARENT PLACES OF STARS, 2020 FOR 0h TERRESTRIAL TIME Name Pegasi  Aquarii  Aquarii Pegasi K2 Ib 2.96 G2 Ib 2.49 B9III 3.27 A3 V Mag. Spect. 0.7 - 3.5 Right Declination Right Declination Right Declination Right Declination U.T. Ascension Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' " h m s º ' " Jan. 1 21 45 08 +9 57 60 22 06 47 -0 13 25 22 55 41 -15 43 02 23 05 44 +15 18 45

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

11

21

45

08

9

57

58

22

06

47

0

13

26

22

55

41

15

43

02

23

05

44

15

18

44

21 31

21 21

45 45

08 08

9 9

57 57

57 56

22 22

06 06

47 47

0 0

13 13

26 27

22 22

55 55

41 41

15 15

43 43

02 02

23 23

05 05

44 44

15 15

18 18

43 41

10 20

21 21

45 45

08 08

9 9

57 57

54 53

22 22

06 06

47 47

0 0

13 13

28 28

22 22

55 55

41 41

15 15

43 43

02 01

23 23

05 05

44 44

15 15

18 18

40 39

1

21

45

08

+9

57

52

22

06

47

-0

13

29

22

55

41 -15

43

01

23

05

44 +15

18

38

11

21

45

09

9

57

51

22

06

47

0

13

29

22

55

41

15

43

00

23

05

44

15

18

37

21

21

45

09

9

57

51

22

06

47

0

13

28

22

55

41

15

42

58

23

05

44

15

18

36

31

21

45

09

9

57

51

22

06

47

0

13

28

22

55

41

15

42

57

23

05

44

15

18

36

10

21

45

09

9

57

51

22

06

48

0

13

27

22

55

41

15

42

56

23

05

44

15

18

36

20

21

45

09

9

57

52

22

06

48

0

13

26

22

55

42

15

42

54

23

05

44

15

18

36

30

21

45

10

+9

57

53

22

06

48

-0

13

25

22

55

42 -15

42

52

23

05

45 +15

18

37

10

21

45

10

9

57

54

22

06

48

0

13

23

22

55

42

15

42

50

23

05

45

15

18

38

20

21

45

10

9

57

56

22

06

49

0

13

22

22

55

42

15

42

48

23

05

45

15

18

39

30

21

45

11

9

57

58

22

06

49

0

13

20

22

55

43

15

42

46

23

05

46

15

18

41

9

21

45

11

9

58

00

22

06

49

0

13

18

22

55

43

15

42

44

23

05

46

15

18

43

19

21

45

11

9

58

02

22

06

50

0

13

16

22

55

43

15

42

42

23

05

46

15

18

45

29

21

45

11

+9

58

04

22

06

50

-0

13

14

22

55

44 -15

42

41

23

05

47 +15

18

47

9

21

45

12

9

58

07

22

06

50

0

13

12

22

55

44

15

42

39

23

05

47

15

18

49

19

21

45

12

9

58

09

22

06

50

0

13

11

22

55

44

15

42

38

23

05

47

15

18

51

29

21

45

12

9

58

11

22

06

51

0

13

09

22

55

44

15

42

37

23

05

47

15

18

54

8

21

45

12

9

58

12

22

06

51

0

13

08

22

55

45

15

42

36

23

05

48

15

18

56

18

21

45

12

9

58

14

22

06

51

0

13

06

22

55

45

15

42

36

23

05

48

15

18

58

28

21

45

12

+9

58

16

22

06

51

-0

13

05

22

55

45 -15

42

36

23

05

48 +15

18

60

7

21

45

12

9

58

17

22

06

51

0

13

05

22

55

45

15

42

36

23

05

48

15

19

01

17

21

45

12

9

58

18

22

06

51

0

13

04

22

55

45

15

42

36

23

05

48

15

19

03

27

21

45

12

9

58

19

22

06

51

0

13

04

22

55

45

15

42

37

23

05

48

15

19

04

7

21

45

12

9

58

19

22

06

51

0

13

04

22

55

45

15

42

37

23

05

48

15

19

05

17

21

45

12

9

58

19

22

06

51

0

13

04

22

55

45

15

42

38

23

05

48

15

19

06

27

21

45

12

+9

58

20

22

06

51

-0

13

04

22

55

45 -15

42

39

23

05

48 +15

19

07

6

21

45

12

9

58

19

22

06

50

0

13

05

22

55

45

15

42

40

23

05

48

15

19

07

16

21

45

12

9

58

19

22

06

50

0

13

05

22

55

45

15

42

41

23

05

48

15

19

07

26

21

45

11

9

58

18

22

06

50

0

13

06

22

55

45

15

42

42

23

05

47

15

19

07

6

21

45

11

9

58

18

22

06

50

0

13

06

22

55

44

15

42

42

23

05

47

15

19

06

16

21

45

11

9

58

17

22

06

50

0

13

07

22

55

44

15

42

43

23

05

47

15

19

06

26

21

45

11

+9

58

15

22

06

50

-0

13

08

22

55

44 -15

42

43

23

05

47 +15

19

04

36

21

45

11

+9

58

14

22

06

50

-0

13

09

22

55

44 -15

42

44

23

05

47 +15

19

03

244

BESSELIAN DAY NUMBERS, 2020.5 FOR 0h TERRESTRIAL TIME 

Date

Jan.

Feb.

A

B

C

D

"

"

"

"

E s (0.0001)

d

d

0 1 2 3 4 5

-0.5041 0.5014 0.4986 0.4959 0.4932 0.4904

-16.652 16.608 16.573 16.541 16.508 16.466

+1.752 1.707 1.674 1.656 1.653 1.663

-3.025 3.355 3.684 4.012 4.338 4.662

+20.591 20.529 20.460 20.386 20.304 20.217

-21 21 22 22 22 22

+0.212 0.140 +0.046 -0.058 0.155 0.232

+0.042 0.071 0.088 0.089 0.075 +0.047

6 7 8 9 10 11

-0.4877 0.4849 0.4822 0.4795 0.4767 0.4740

-16.412 16.340 16.250 16.143 16.027 15.911

+1.683 1.706 1.725 1.730 1.716 1.677

-4.985 5.306 5.625 5.942 6.257 6.570

+20.124 20.024 19.919 19.808 19.691 19.569

-22 22 22 21 21 21

-0.274 0.272 0.224 0.134 -0.018 +0.098

+0.008 0.035 0.074 0.100 0.106 0.089

12 13 14 15 16 17

-0.4713 0.4685 0.4658 0.4630 0.4603 0.4576

-15.807 15.723 15.663 15.625 15.598 15.573

+1.616 1.542 1.468 1.406 1.365 1.350

-6.881 7.190 7.497 7.803 8.106 8.408

+19.441 19.307 19.168 19.023 18.873 18.716

-21 21 21 21 21 21

+0.187 0.225 0.203 0.129 +0.026 -0.076

-0.051 -0.000 +0.051 0.089 0.105 0.096

18 19 20 21 22 23

-0.4548 0.4521 0.4493 0.4466 0.4439 0.4411

-15.536 15.483 15.410 15.320 15.220 15.117

+1.355 1.374 1.394 1.406 1.402 1.378

-8.707 9.004 9.298 9.589 9.878 10.163

+18.553 18.385 18.210 18.029 17.843 17.650

-21 21 21 21 21 21

-0.152 0.183 0.163 0.099 -0.008 +0.092

+0.065 +0.021 -0.025 0.064 0.087 0.090

24 25 26 27 28 29

-0.4384 0.4357 0.4329 0.4302 0.4274 0.4247

-15.020 14.935 14.867 14.816 14.780 14.756

+1.335 1.278 1.212 1.146 1.085 1.036

-10.445 10.723 10.998 11.269 11.536 11.799

+17.452 17.247 17.038 16.822 16.602 16.376

-20 20 20 20 20 20

+0.178 0.235 0.252 0.227 0.165 +0.077

-0.075 0.045 -0.008 +0.030 0.063 0.083

30 31 1 2 3 4

-0.4220 0.4192 0.4165 0.4138 0.4110 0.4083

-14.738 14.720 14.696 14.662 14.612 14.546

+1.001 0.981 0.976 0.982 0.994 1.005

-12.058 12.312 12.563 12.809 13.051 13.288

+16.145 15.910 15.670 15.425 15.175 14.922

-21 21 21 21 21 21

-0.025 0.127 0.212 0.268 0.285 0.258

+0.090 0.081 0.057 +0.022 -0.019 0.060

5 6 7 8 9 10

-0.4055 0.4028 0.4001 0.3973 0.3946 0.3919

-14.463 14.367 14.266 14.171 14.093 14.039

+1.008 0.995 0.959 0.900 0.823 0.739

-13.521 13.750 13.974 14.194 14.410 14.622

+14.664 14.402 14.137 13.867 13.594 13.318

-21 21 20 20 20 20

-0.187 -0.082 +0.037 0.143 0.208 0.214

-0.092 0.108 0.101 0.071 -0.022 +0.033

11 12 13 14 15

-0.3891 0.3864 0.3836 0.3809 -0.3782

-14.010 13.998 13.991 13.976 -13.944

+0.664 0.610 0.583 0.582 +0.598

-14.829 15.032 15.231 15.426 -15.616

+13.038 12.754 12.466 12.175 +11.879

-20 20 21 21 -21

+0.158 +0.062 -0.045 0.130 -0.171

+0.080 0.105 0.104 0.077 +0.034

245

BESSELIAN DAY NUMBERS, 2020.5 FOR 0h TERRESTRIAL TIME 

Date

Feb.

Mar.

Apr.

A

B

C

D

"

"

"

"

E s (0.0001)

d

d

15 16 17 18 19 20

-0.3782 0.3754 0.3727 0.3700 0.3672 0.3645

-13.944 13.891 13.821 13.740 13.655 13.574

+0.598 0.618 0.633 0.633 0.614 0.578

-15.616 15.802 15.983 16.159 16.330 16.495

+11.879 11.580 11.277 10.970 10.660 10.346

-21 21 21 21 21 20

-0.171 0.160 0.103 -0.015 +0.083 0.172

+0.034 -0.014 0.055 0.082 0.090 0.079

21 22 23 24 25 26

-0.3617 0.3590 0.3563 0.3535 0.3508 0.3480

-13.504 13.450 13.412 13.390 13.380 13.377

+0.526 0.465 0.402 0.344 0.296 0.262

-16.656 16.811 16.960 17.104 17.242 17.374

+10.028 9.708 9.385 9.058 8.730 8.398

-20 20 20 21 21 21

+0.235 0.261 0.246 0.193 0.110 +0.009

-0.053 -0.017 +0.021 0.055 0.080 0.090

27 28 29 1 2 3

-0.3453 0.3426 0.3398 0.3371 0.3344 0.3316

-13.377 13.372 13.357 13.329 13.285 13.225

+0.244 0.242 0.252 0.270 0.290 0.305

-17.501 17.622 17.737 17.847 17.950 18.048

+8.065 7.729 7.391 7.051 6.710 6.367

-21 21 21 21 22 22

-0.094 0.185 0.252 0.283 0.273 0.221

+0.085 0.066 +0.034 -0.006 0.046 0.081

4 5 6 7 8 9

-0.3289 0.3261 0.3234 0.3207 0.3179 0.3152

-13.150 13.068 12.986 12.914 12.863 12.836

+0.308 0.292 0.255 0.196 0.126 0.056

-18.141 18.227 18.309 18.384 18.455 18.520

+6.023 5.678 5.332 4.985 4.638 4.289

-21 21 21 21 21 21

-0.134 -0.026 +0.083 0.167 0.200 0.171

-0.103 0.106 0.087 -0.046 +0.008 0.062

10 11 12 13 14 15

-0.3125 0.3097 0.3070 0.3042 0.3015 0.2988

-12.831 12.837 12.838 12.824 12.787 12.729

+0.003 -0.022 -0.018 +0.009 0.046 0.080

-18.580 18.635 18.684 18.729 18.768 18.802

+3.940 3.590 3.239 2.887 2.534 2.180

-21 22 22 22 22 22

+0.089 -0.019 0.117 0.173 0.174 0.121

+0.099 0.110 0.091 0.051 +0.000 -0.046

16 17 18 19 20 21

-0.2960 0.2933 0.2906 0.2878 0.2851 0.2823

-12.657 12.579 12.503 12.438 12.388 12.354

+0.101 0.102 0.085 0.052 +0.009 -0.037

-18.830 18.852 18.869 18.880 18.885 18.884

+1.826 1.470 1.114 0.758 0.402 +0.045

-22 22 22 22 22 22

-0.032 +0.072 0.169 0.240 0.275 0.269

-0.077 0.090 0.083 0.059 -0.025 +0.014

22 23 24 25 26 27

-0.2796 0.2769 0.2741 0.2714 0.2687 0.2659

-12.335 12.329 12.332 12.336 12.338 12.330

-0.080 0.114 0.133 0.137 0.126 0.100

-18.877 18.864 18.846 18.821 18.790 18.754

-0.312 0.668 1.024 1.379 1.734 2.087

-22 22 22 23 23 23

+0.223 0.146 +0.047 -0.057 0.154 0.228

+0.050 0.076 0.091 0.089 0.073 0.044

28 29 30 31 1

-0.2632 0.2604 0.2577 0.2550 -0.2522

-12.310 12.273 12.220 12.153 -12.076

-0.066 0.027 0.007 0.032 -0.040

-18.711 18.663 18.610 18.550 -18.485

-2.440 2.791 3.140 3.489 -3.835

-23 23 23 23 -23

-0.270 0.272 0.234 0.160 -0.063

+0.006 -0.035 0.071 0.097 -0.106

246

BESSELIAN DAY NUMBERS, 2020.5 FOR 0h TERRESTRIAL TIME 

Date

Apr.

May

A

B

C

D

"

"

"

"

E s (0.0001)

d

d

1 2 3 4 5 6

-0.2522 0.2495 0.2467 0.2440 0.2413 0.2385

-12.076 11.997 11.924 11.865 11.828 11.813

-0.040 0.029 0.002 0.049 0.101 0.144

-18.485 18.415 18.339 18.258 18.173 18.082

-3.835 4.179 4.522 4.862 5.200 5.537

-23 23 23 23 23 23

-0.063 +0.039 0.126 0.175 0.170 0.109

-0.106 0.095 0.063 -0.015 +0.038 0.084

7 8 9 10 11 12

-0.2358 0.2331 0.2303 0.2276 0.2248 0.2221

-11.813 11.816 11.807 11.775 11.718 11.641

-0.165 0.156 0.119 0.065 -0.009 +0.037

-17.986 17.886 17.782 17.672 17.558 17.439

-5.871 6.203 6.533 6.861 7.187 7.512

-23 23 24 24 24 24

+0.008 -0.100 0.179 0.202 0.163 -0.076

+0.108 0.103 0.070 +0.020 -0.032 0.072

13 14 15 16 17 18

-0.2194 0.2166 0.2139 0.2112 0.2084 0.2057

-11.554 11.467 11.390 11.326 11.280 11.249

+0.062 0.066 0.052 +0.026 -0.006 0.036

-17.315 17.186 17.051 16.912 16.768 16.618

-7.834 8.155 8.473 8.788 9.102 9.412

-23 23 23 23 23 23

+0.036 0.147 0.234 0.283 0.289 0.253

-0.091 0.089 0.068 -0.035 +0.005 0.042

19 20 21 22 23 24

-0.2029 0.2002 0.1975 0.1947 0.1920 0.1893

-11.232 11.224 11.220 11.213 11.198 11.171

-0.058 0.067 0.061 0.039 -0.003 +0.043

-16.464 16.304 16.140 15.970 15.796 15.617

-9.720 10.024 10.326 10.624 10.918 11.209

-23 24 24 24 24 24

+0.182 +0.086 -0.019 0.120 0.201 0.252

+0.073 0.090 0.093 0.080 0.054 +0.017

25 26 27 28 29 30

-0.1865 0.1838 0.1810 0.1783 0.1756 0.1728

-11.127 11.066 10.991 10.904 10.814 10.728

+0.094 0.142 0.182 0.205 0.210 0.195

-15.433 15.245 15.053 14.856 14.655 14.450

-11.497 11.780 12.059 12.335 12.606 12.873

-24 24 24 24 24 24

-0.264 0.235 0.170 -0.079 +0.020 0.107

-0.024 0.062 0.091 0.105 0.099 0.073

1 2 3 4 5 6

-0.1701 0.1674 0.1646 0.1619 0.1591 0.1564

-10.654 10.599 10.563 10.545 10.535 10.518

+0.164 0.124 0.087 0.066 0.070 0.102

-14.241 14.028 13.812 13.593 13.370 13.144

-13.135 13.393 13.647 13.896 14.141 14.382

-24 24 24 24 24 24

+0.162 0.171 0.126 +0.036 -0.073 0.170

-0.031 +0.019 0.067 0.099 0.106 0.085

7 8 9 10 11 12

-0.1537 0.1509 0.1482 0.1454 0.1427 0.1400

-10.483 10.423 10.337 10.236 10.129 10.029

+0.156 0.220 0.279 0.319 0.336 0.331

-12.915 12.683 12.448 12.209 11.967 11.721

-14.619 14.852 15.081 15.306 15.526 15.743

-24 24 24 24 24 24

-0.221 0.209 0.137 -0.026 +0.097 0.203

+0.041 -0.012 0.060 0.090 0.096 0.081

13 14 15 16 17

-0.1372 0.1345 0.1318 0.1290 -0.1263

-9.942 9.873 9.822 9.786 -9.761

+0.309 0.278 0.248 0.223 +0.210

-11.472 11.220 10.964 10.705 -10.443

-15.956 16.164 16.367 16.566 -16.760

-24 24 24 24 -24

+0.273 0.297 0.275 0.213 +0.123

-0.049 -0.009 +0.032 0.066 +0.088

247

BESSELIAN DAY NUMBERS, 2020.5 FOR 0h TERRESTRIAL TIME 

Date

May

June

July

A

B

C

D

"

"

"

"

E s (0.0001)

d

d

17 18 19 20 21 22

-0.1263 0.1235 0.1208 0.1181 0.1153 0.1126

-9.761 9.741 9.720 9.693 9.654 9.599

+0.210 0.211 0.228 0.260 0.303 0.351

-10.443 10.178 9.910 9.638 9.364 9.087

-16.760 16.949 17.133 17.313 17.486 17.655

-24 24 24 24 24 24

+0.123 +0.019 -0.085 0.174 0.234 0.257

+0.088 0.096 0.087 0.064 +0.029 -0.012

23 24 25 26 27 28

-0.1099 0.1071 0.1044 0.1016 0.0989 0.0962

-9.527 9.439 9.339 9.234 9.132 9.040

+0.399 0.438 0.463 0.468 0.452 0.419

-8.807 8.525 8.240 7.954 7.665 7.374

-17.818 17.976 18.128 18.274 18.415 18.550

-24 24 24 24 23 23

-0.237 0.179 -0.091 +0.010 0.101 0.164

-0.052 0.085 0.103 0.102 0.081 -0.042

29 30 31 1 2 3

-0.0934 0.0907 0.0880 0.0852 0.0825 0.0797

-8.967 8.913 8.877 8.852 8.826 8.786

+0.375 0.332 0.300 0.288 0.303 0.340

-7.082 6.788 6.492 6.196 5.898 5.600

-18.679 18.802 18.920 19.032 19.139 19.241

-23 23 23 23 24 24

+0.182 0.148 +0.069 -0.038 0.143 0.215

+0.006 0.054 0.090 0.105 0.093 0.058

4 5 6 7 8 9

-0.0770 0.0743 0.0715 0.0688 0.0661 0.0633

-8.724 8.637 8.529 8.411 8.294 8.188

+0.392 0.444 0.484 0.501 0.493 0.465

-5.300 4.999 4.697 4.394 4.090 3.784

-19.337 19.428 19.515 19.596 19.672 19.743

-24 23 23 23 23 23

-0.232 0.187 -0.091 +0.032 0.151 0.242

+0.008 -0.043 0.082 0.099 0.092 0.065

10 11 12 13 14 15

-0.0606 0.0578 0.0551 0.0524 0.0496 0.0469

-8.100 8.030 7.979 7.941 7.910 7.881

+0.424 0.379 0.338 0.307 0.290 0.288

-3.477 3.169 2.860 2.550 2.239 1.927

-19.809 19.869 19.924 19.974 20.017 20.055

-23 22 23 23 23 23

+0.287 0.284 0.237 0.155 +0.053 -0.053

-0.026 +0.017 0.056 0.083 0.096 0.093

16 17 18 19 20 21

-0.0441 0.0414 0.0387 0.0359 0.0332 0.0305

-7.848 7.805 7.747 7.673 7.582 7.478

+0.302 0.328 0.362 0.397 0.425 0.440

-1.614 1.301 0.987 0.673 0.358 -0.043

-20.088 20.114 20.135 20.150 20.158 20.161

-23 23 23 23 23 22

-0.148 0.218 0.253 0.245 0.196 0.113

+0.073 0.041 +0.001 -0.041 0.077 0.100

22 23 24 25 26 27

-0.0277 0.0250 0.0222 0.0195 0.0168 0.0140

-7.365 7.254 7.153 7.069 7.007 6.964

+0.435 0.409 0.364 0.305 0.244 0.192

+0.272 0.587 0.901 1.215 1.528 1.840

-20.157 20.148 20.132 20.110 20.082 20.048

-22 22 22 22 22 22

-0.010 +0.090 0.166 0.197 0.175 0.105

-0.105 0.088 0.053 -0.005 +0.044 0.084

28 29 30 1 2

-0.0113 0.0086 0.0058 0.0031 -0.0003

-6.934 6.906 6.869 6.814 -6.735

+0.160 0.151 0.166 0.197 +0.233

+2.151 2.461 2.770 3.077 +3.384

-20.009 19.964 19.913 19.857 -19.796

-22 22 22 22 -22

+0.002 -0.106 0.191 0.228 -0.207

+0.104 0.098 0.069 +0.024 -0.027

248

BESSELIAN DAY NUMBERS, 2020.5 FOR 0h TERRESTRIAL TIME 

Date

July

Aug.

A

B

C

D

"

"

"

"

E s (0.0001)

d

d

1 2 3 4 5 6

-0.0031 -0.0003 +0.0024 0.0051 0.0079 0.0106

-6.814 6.735 6.635 6.521 6.404 6.294

+0.197 0.233 0.260 0.269 0.254 0.217

+3.077 3.384 3.689 3.993 4.296 4.598

-19.857 19.796 19.730 19.658 19.582 19.500

-22 22 22 22 21 21

-0.228 0.207 0.132 -0.021 +0.100 0.202

+0.024 -0.027 0.070 0.095 0.098 0.078

7 8 9 10 11 12

+0.0133 0.0161 0.0188 0.0216 0.0243 0.0270

-6.199 6.124 6.068 6.028 5.999 5.974

+0.164 0.102 +0.041 -0.010 0.049 0.072

+4.899 5.199 5.498 5.795 6.091 6.386

-19.414 19.322 19.225 19.123 19.015 18.903

-21 21 21 21 21 21

+0.266 0.283 0.251 0.180 +0.084 -0.023

-0.042 +0.001 0.042 0.075 0.093 0.095

13 14 15 16 17 18

+0.0298 0.0325 0.0352 0.0380 0.0407 0.0435

-5.947 5.912 5.864 5.801 5.722 5.627

-0.079 0.072 0.056 0.036 0.020 0.014

+6.680 6.972 7.262 7.550 7.837 8.121

-18.784 18.660 18.531 18.397 18.256 18.111

-21 21 21 21 21 21

-0.123 0.203 0.250 0.257 0.222 0.148

+0.081 0.053 +0.015 -0.027 0.066 0.095

19 20 21 22 23 24

+0.0462 0.0489 0.0517 0.0544 0.0572 0.0599

-5.523 5.416 5.317 5.233 5.172 5.133

-0.027 0.060 0.115 0.186 0.263 0.333

+8.404 8.684 8.962 9.236 9.509 9.778

-17.959 17.803 17.640 17.472 17.299 17.121

-21 21 21 21 21 21

-0.048 +0.059 0.150 0.200 0.196 0.139

-0.106 0.097 0.066 -0.020 +0.032 0.077

25 26 27 28 29 30

+0.0626 0.0654 0.0681 0.0708 0.0736 0.0763

-5.110 5.092 5.068 5.028 4.966 4.884

-0.384 0.411 0.413 0.397 0.373 0.354

+10.043 10.306 10.565 10.821 11.074 11.323

-16.937 16.749 16.556 16.359 16.157 15.951

-21 21 21 21 21 21

+0.041 -0.068 0.160 0.210 0.205 0.146

+0.103 0.104 0.080 +0.037 -0.013 0.058

31 1 2 3 4 5

+0.0791 0.0818 0.0845 0.0873 0.0900 0.0927

-4.786 4.682 4.583 4.496 4.427 4.378

-0.351 0.369 0.409 0.467 0.535 0.605

+11.569 11.812 12.052 12.289 12.523 12.753

-15.741 15.527 15.309 15.087 14.860 14.630

-21 21 21 20 20 20

-0.047 +0.067 0.173 0.248 0.279 0.262

-0.089 0.098 0.085 0.054 -0.013 +0.029

6 7 8 9 10 11

+0.0955 0.0982 0.1010 0.1037 0.1064 0.1092

-4.347 4.328 4.315 4.303 4.285 4.257

-0.668 0.719 0.754 0.772 0.776 0.768

+12.980 13.204 13.425 13.642 13.856 14.066

-14.396 14.158 13.915 13.669 13.418 13.163

-20 21 21 21 21 21

+0.203 0.113 +0.008 -0.096 0.184 0.244

+0.065 0.089 0.096 0.087 0.063 +0.028

12 13 14 15 16

+0.1119 0.1146 0.1174 0.1201 +0.1229

-4.214 4.154 4.080 3.994 -3.902

-0.754 0.740 0.734 0.743 -0.771

+14.273 14.476 14.675 14.870 +15.061

-12.904 12.641 12.374 12.103 -11.828

-21 21 21 21 -21

-0.266 0.246 0.187 -0.096 +0.010

-0.013 0.054 0.087 0.105 -0.104

249

BESSELIAN DAY NUMBERS, 2020.5 FOR 0h TERRESTRIAL TIME 

Date

A

B

C

D

"

"

"

"

E s (0.0001)

d

d

Aug. 16 17 18 19 20 21

+0.1229 0.1256 0.1283 0.1311 0.1338 0.1366

-3.902 3.813 3.737 3.681 3.648 3.636

-0.771 0.821 0.889 0.968 1.044 1.104

+15.061 15.248 15.430 15.608 15.781 15.949

-11.828 11.549 11.266 10.979 10.688 10.394

-21 21 21 21 21 21

+0.010 0.110 0.180 0.200 0.162 +0.075

-0.104 0.081 -0.038 +0.014 0.065 0.099

22 23 24 25 26 27

+0.1393 0.1420 0.1448 0.1475 0.1502 0.1530

-3.633 3.626 3.605 3.562 3.498 3.417

-1.139 1.146 1.130 1.104 1.080 1.069

+16.112 16.271 16.424 16.572 16.715 16.854

-10.097 9.797 9.494 9.189 8.881 8.571

-21 21 21 21 21 21

-0.034 0.134 0.195 0.201 0.151 -0.059

+0.109 0.091 +0.050 -0.000 0.048 0.082

28 29 30 31 Sept. 1 2

+0.1557 0.1585 0.1612 0.1639 0.1667 0.1694

-3.329 3.243 3.168 3.109 3.069 3.047

-1.078 1.109 1.157 1.218 1.282 1.341

+16.987 17.116 17.240 17.360 17.475 17.586

-8.259 7.944 7.628 7.309 6.988 6.666

-21 21 21 21 21 21

+0.053 0.160 0.241 0.282 0.277 0.227

-0.096 0.089 0.062 -0.024 +0.019 0.057

3 4 5 6 7 8

+0.1721 0.1749 0.1776 0.1804 0.1831 0.1858

-3.039 3.039 3.041 3.038 3.026 3.000

-1.388 1.420 1.435 1.434 1.420 1.398

+17.691 17.792 17.889 17.980 18.067 18.149

-6.341 6.014 5.685 5.355 5.022 4.687

-21 21 22 22 22 22

+0.144 +0.041 -0.065 0.160 0.230 0.265

+0.084 0.096 0.092 0.072 +0.039 -0.000

9 10 11 12 13 14

+0.1886 0.1913 0.1940 0.1968 0.1995 0.2023

-2.959 2.902 2.833 2.755 2.677 2.606

-1.375 1.356 1.348 1.357 1.386 1.435

+18.226 18.298 18.364 18.426 18.482 18.533

-4.351 4.013 3.673 3.331 2.987 2.642

-22 22 22 22 22 22

-0.260 0.216 0.139 -0.041 +0.059 0.141

-0.041 0.077 0.100 0.107 0.092 0.058

15 16 17 18 19 20

+0.2050 0.2077 0.2105 0.2132 0.2159 0.2187

-2.551 2.519 2.508 2.512 2.517 2.510

-1.498 1.564 1.620 1.653 1.656 1.631

+18.578 18.617 18.651 18.678 18.700 18.716

-2.296 1.948 1.599 1.249 0.898 0.547

-22 22 22 22 22 23

+0.182 0.169 +0.100 -0.005 0.114 0.190

-0.009 +0.045 0.089 0.110 0.102 0.067

21 22 23 24 25 26

+0.2214 0.2242 0.2269 0.2296 0.2324 0.2351

-2.481 2.426 2.353 2.269 2.186 2.112

-1.590 1.547 1.515 1.503 1.514 1.543

+18.726 18.730 18.728 18.721 18.709 18.691

-0.196 +0.155 0.505 0.856 1.206 1.555

-23 23 23 22 22 22

-0.211 0.169 -0.079 +0.037 0.151 0.242

+0.016 -0.036 0.076 0.096 0.092 0.069

27 28 29 30 1

+0.2379 0.2406 0.2433 0.2461 +0.2488

-2.054 2.014 1.992 1.985 -1.986

-1.585 1.633 1.677 1.711 -1.730

+18.668 18.639 18.606 18.567 +18.523

+1.904 2.252 2.600 2.947 +3.294

-22 22 22 23 -23

+0.292 0.297 0.256 0.180 +0.079

-0.033 +0.010 0.049 0.080 +0.096

Oct.

250

BESSELIAN DAY NUMBERS, 2020.5 FOR 0h TERRESTRIAL TIME 

Date

Oct.

Nov.

A

B

C

D

"

"

"

"

E s (0.0001)

d

d

1 2 3 4 5 6

+0.2488 0.2515 0.2543 0.2570 0.2598 0.2625

-1.986 1.991 1.992 1.984 1.962 1.926

-1.730 1.732 1.718 1.689 1.651 1.610

+18.523 18.474 18.420 18.361 18.296 18.226

+3.294 3.640 3.985 4.330 4.673 5.016

-23 23 23 23 23 24

+0.079 -0.029 0.129 0.207 0.253 0.260

+0.096 0.096 0.080 0.050 +0.012 -0.029

7 8 9 10 11 12

+0.2652 0.2680 0.2707 0.2734 0.2762 0.2789

-1.873 1.807 1.732 1.653 1.579 1.516

-1.572 1.543 1.529 1.534 1.557 1.596

+18.151 18.070 17.985 17.893 17.797 17.694

+5.358 5.699 6.039 6.378 6.716 7.052

-24 24 23 23 23 23

-0.229 0.164 -0.076 +0.019 0.103 0.156

-0.067 0.094 0.106 0.099 0.073 -0.030

13 14 15 16 17 18

+0.2817 0.2844 0.2871 0.2899 0.2926 0.2953

-1.472 1.448 1.442 1.444 1.438 1.412

-1.644 1.688 1.715 1.714 1.684 1.630

+17.586 17.473 17.353 17.228 17.097 16.960

+7.387 7.721 8.052 8.382 8.709 9.034

-23 23 24 24 24 24

+0.162 0.115 +0.022 -0.091 0.187 0.232

+0.022 0.071 0.103 0.109 0.084 +0.037

19 20 21 22 23 24

+0.2981 0.3008 0.3036 0.3063 0.3090 0.3118

-1.358 1.280 1.185 1.088 0.998 0.924

-1.566 1.511 1.474 1.463 1.474 1.500

+16.818 16.670 16.518 16.360 16.197 16.029

+9.356 9.675 9.990 10.303 10.612 10.918

-24 24 24 24 24 24

-0.210 0.126 -0.004 +0.124 0.231 0.298

-0.019 0.067 0.096 0.099 0.079 0.044

25 26 27 28 29 30

+0.3145 0.3172 0.3200 0.3227 0.3255 0.3282

-0.869 0.832 0.810 0.799 0.792 0.782

-1.534 1.566 1.589 1.599 1.593 1.570

+15.857 15.680 15.498 15.313 15.122 14.927

+11.220 11.519 11.815 12.107 12.396 12.682

-24 24 24 24 24 24

+0.316 0.287 0.217 0.121 +0.012 -0.092

-0.001 +0.041 0.075 0.096 0.100 0.087

31 1 2 3 4 5

+0.3309 0.3337 0.3364 0.3392 0.3419 0.3446

-0.764 0.734 0.688 0.625 0.548 0.461

-1.532 1.484 1.431 1.380 1.338 1.310

+14.728 14.525 14.317 14.105 13.889 13.668

+12.964 13.242 13.517 13.789 14.056 14.320

-24 24 24 24 24 24

-0.178 0.233 0.250 0.229 0.172 -0.091

+0.060 +0.024 -0.018 0.057 0.088 0.104

6 7 8 9 10 11

+0.3474 0.3501 0.3528 0.3556 0.3583 0.3611

-0.369 0.279 0.199 0.135 0.089 0.062

-1.300 1.309 1.334 1.370 1.407 1.434

+13.443 13.214 12.980 12.742 12.499 12.253

+14.581 14.837 15.090 15.338 15.582 15.822

-24 24 24 24 24 24

+0.000 0.084 0.141 0.158 0.126 +0.048

-0.102 0.081 -0.044 +0.003 0.052 0.090

12 13 14 15 16

+0.3638 0.3665 0.3693 0.3720 +0.3747

-0.045 -0.028 +0.004 0.061 +0.148

-1.439 1.417 1.367 1.302 -1.236

+12.001 11.746 11.486 11.222 +10.954

+16.058 16.289 16.514 16.735 +16.950

-24 24 24 24 -24

-0.061 0.169 0.242 0.253 -0.193

+0.107 0.096 0.058 +0.004 -0.051

251

BESSELIAN DAY NUMBERS, 2020.5 FOR 0h TERRESTRIAL TIME 

Date

A

B

C

D

"

"

"

"

E s (0.0001)

d

d

Nov. 16 17 18 19 20 21

+0.3747 0.3775 0.3802 0.3830 0.3857 0.3884

+0.148 0.256 0.376 0.491 0.592 0.674

-1.236 1.186 1.161 1.163 1.186 1.220

+10.954 10.683 10.408 10.129 9.848 9.564

+16.950 17.160 17.363 17.562 17.754 17.941

-24 24 24 24 23 23

-0.193 -0.078 +0.062 0.191 0.282 0.322

-0.051 0.090 0.105 0.092 0.059 -0.015

22 23 24 25 26 27

+0.3912 0.3939 0.3966 0.3994 0.4021 0.4049

+0.735 0.778 0.809 0.834 0.860 0.892

-1.256 1.285 1.302 1.303 1.287 1.256

+9.277 8.987 8.695 8.400 8.103 7.803

+18.122 18.297 18.467 18.632 18.790 18.943

-23 23 23 23 24 24

+0.310 0.251 0.161 +0.053 -0.054 0.146

+0.030 0.068 0.093 0.102 0.094 0.070

28 29 30 1 2 3

+0.4076 0.4103 0.4131 0.4158 0.4185 0.4213

+0.936 0.995 1.070 1.161 1.263 1.371

-1.214 1.167 1.120 1.081 1.056 1.049

+7.501 7.197 6.891 6.582 6.272 5.959

+19.091 19.233 19.369 19.500 19.625 19.745

-24 24 24 24 23 23

-0.211 0.238 0.226 0.176 0.099 -0.008

+0.035 -0.006 0.047 0.080 0.101 0.104

4 5 6 7 8 9

+0.4240 0.4268 0.4295 0.4322 0.4350 0.4377

+1.478 1.576 1.659 1.723 1.770 1.803

-1.062 1.092 1.134 1.180 1.220 1.242

+5.645 5.328 5.009 4.689 4.366 4.042

+19.859 19.967 20.070 20.166 20.257 20.342

-23 23 23 23 23 23

+0.079 0.143 0.168 0.146 +0.078 -0.024

-0.087 0.054 -0.009 +0.039 0.079 0.102

10 11 12 13 14 15

+0.4405 0.4432 0.4459 0.4487 0.4514 0.4541

+1.833 1.871 1.929 2.015 2.126 2.254

-1.241 1.214 1.168 1.115 1.070 1.047

+3.715 3.387 3.057 2.726 2.394 2.061

+20.420 20.492 20.558 20.616 20.668 20.713

-23 23 23 23 23 22

-0.136 0.227 0.269 0.243 0.153 -0.020

+0.101 0.073 +0.026 -0.030 0.077 0.104

16 17 18 19 20 21

+0.4569 0.4596 0.4624 0.4651 0.4678 0.4706

+2.386 2.508 2.611 2.691 2.750 2.794

-1.051 1.082 1.130 1.184 1.235 1.274

+1.727 1.392 1.057 0.723 0.388 +0.053

+20.751 20.782 20.806 20.824 20.835 20.839

-22 22 22 22 22 22

+0.121 0.237 0.305 0.316 0.275 0.194

-0.104 0.078 -0.036 +0.012 0.056 0.087

22 23 24 25 26 27

+0.4733 0.4760 0.4788 0.4815 0.4843 0.4870

+2.829 2.862 2.899 2.945 3.006 3.082

-1.297 1.304 1.295 1.274 1.245 1.215

-0.281 0.615 0.949 1.282 1.614 1.946

+20.836 20.828 20.812 20.791 20.763 20.729

-22 22 22 22 22 22

+0.090 -0.019 0.117 0.190 0.229 0.228

+0.101 0.099 0.080 0.048 +0.007 -0.035

28 29 30 31 32

+0.4897 0.4925 0.4952 0.4979 +0.5007

+3.174 3.278 3.390 3.502 +3.607

-1.191 1.180 1.186 1.213 -1.259

-2.277 2.607 2.936 3.265 -3.592

+20.689 20.643 20.591 20.532 +20.468

-22 22 21 21 -21

-0.188 0.115 -0.023 +0.070 +0.145

-0.072 0.097 0.105 0.093 -0.063

Dec.

252

SECOND-ORDER DAY NUMBERS, 2020 J FOR NORTHERN DECLINATIONS FOR 0h TT AND EQUINOX J 2020.5 RIGHT ASCENSION Date Jan. Feb. Mar. Apr. May

June July Aug. Sept. Oct. Nov. Dec.

2 12 22 1 11 21 2 12 22 1 11 21 1 11 21 31 10 20 30 10 20 30 9 19 29 8 18 28 8 18 28 7 17 27 7 17 27 37

0h 12h

1h 13h

2h 14h

3h 15h

4h 16h

5h 17h

6h 18h

7h 19h

8h 20h

9h 21h

10h 22h

11h 23h

12h 24h

-2 -1 -1 -1 0 +1 +3 +5 +7 +9 +10 +11 +10 +9 +7 +5 +2 -1 -3 -5 -7 -8 -8 -7 -6 -5 -3 0 +2 +3 +5 +5 +5 +4 +2 0 -3 -6

+3 -1 -2 -2 -2 -1 +1 +2 +5 +7 +9 +11 +12 +12 +12 +10 +8 +6 +3 0 -2 -4 -6 -7 -7 -6 -5 -3 -1 +1 +3 +5 +6 +6 +5 +4 +2 -1

+7 -1 -2 -3 -3 -3 -2 -1 +1 +3 +6 +8 +10 +12 +13 +13 +12 +10 +8 +6 +3 0 -2 -4 -5 -6 -5 -4 -3 -1 +1 +3 +5 +7 +7 +7 +6 +4

+9 -1 -2 -3 -4 -5 -5 -5 -4 -2 0 +3 +5 +8 +10 +11 +12 +12 +11 +9 +7 +5 +2 0 -3 -4 -5 -5 -5 -3 -1 +1 +3 +5 +7 +8 +9 +8

+8 0 -1 -2 -4 -5 -6 -7 -7 -6 -5 -3 -1 +2 +5 +7 +9 +10 +11 +10 +9 +8 +5 +3 +1 -2 -3 -5 -5 -5 -4 -2 0 +2 +5 +7 +9 +9

+5 0 0 -1 -2 -4 -6 -8 -9 -9 -9 -9 -7 -5 -2 +1 +3 +6 +7 +8 +9 +8 +7 +6 +3 +1 -1 -3 -4 -5 -5 -5 -3 -1 +1 +4 +6 +8

+1 0 0 0 -1 -2 -4 -6 -8 -10 -11 -12 -11 -10 -8 -6 -3 0 +2 +4 +6 +7 +7 +6 +5 +4 +2 -1 -3 -4 -6 -6 -6 -5 -3 -1 +2 +5

-4 0 +1 +1 +1 0 -2 -3 -6 -8 -10 -12 -13 -13 -13 -11 -9 -7 -4 -1 +1 +3 +5 +6 +6 +5 +4 +2 0 -2 -4 -6 -7 -7 -6 -5 -3 0

-8 0 +1 +2 +2 +2 +1 0 -2 -4 -7 -9 -11 -13 -14 -14 -13 -11 -9 -7 -4 -1 +1 +3 +4 +5 +4 +3 +2 0 -2 -4 -6 -8 -8 -8 -7 -5

-10 0 +1 +2 +3 +4 +4 +4 +3 +1 -1 -4 -6 -9 -11 -12 -13 -13 -12 -10 -8 -6 -3 -1 +2 +3 +4 +4 +4 +2 0 -2 -4 -6 -8 -9 -10 -9

-9 -1 0 +1 +3 +4 +5 +6 +6 +5 +4 +2 0 -3 -6 -8 -10 -11 -12 -11 -10 -9 -6 -4 -2 +1 +2 +4 +4 +4 +3 +1 -1 -3 -6 -8 -10 -10

-6 -1 -1 0 +1 +3 +5 +7 +8 +8 +8 +8 +6 +4 +1 -2 -4 -7 -8 -9 -10 -9 -8 -7 -4 -2 0 +2 +3 +4 +4 +4 +2 0 -2 -5 -7 -9

-2 -1 -1 -1 0 +1 +3 +5 +7 +9 +10 +11 +10 +9 +7 +5 +2 -1 -3 -5 -7 -8 -8 -7 -6 -5 -3 0 +2 +3 +5 +5 +5 +4 +2 0 -3 -6

The second-order day number J given in this table in units of 0 s.00001 The apparent right ascension of a star is given by: 2 = 1+ 100 + Aa + Bb + Cc + Dd + E + J tan 1 Where the position (1,1) and centennial proper motion in right ascension () are referred to the mean equator and equinox of J 2020.5

253

SECOND-ORDER DAY NUMBERS, 2020 J' FOR NORTHERN DECLINATIONS FOR 0h TT AND EQUINOX J 2020.5 RIGHT ASCENSION Date

Jan. Feb. Mar. Apr. May

June July Aug. Sept. Oct. Nov. Dec.

2 12 22 1 11 21 2 12 22 1 11 21 1 11 21 31 10 20 30 10 20 30 9 19 29 8 18 28 8 18 28 7 17 27 7 17 27 37

0h 12h

1h 13h

2h 14h

3h 15h

4h 16h

5h 17h

6h 18h

7h 19h

8h 20h

9h 21h

10h 22h

11h 23h

12h 24h

-1 0 -1 -4 -5 -7 -8 -9 -9 -9 -8 -7 -5 -4 -2 -1 -1 -1 -1 -1 -2 -3 -5 -6 -7 -7 -8 -8 -7 -6 -5 -4 -3 -2 -1 -1 -1 -2

-1 0 -1 -3 -5 -7 -9 -11 -12 -12 -12 -11 -10 -8 -7 -5 -3 -2 -1 -1 -1 -1 -2 -3 -4 -5 -6 -7 -7 -7 -7 -6 -5 -4 -2 -1 -1 -1

-3 -1 0 -2 -4 -6 -9 -11 -13 -14 -15 -15 -15 -13 -12 -9 -7 -5 -3 -2 -1 -1 -1 -1 -2 -3 -5 -6 -7 -8 -8 -8 -7 -6 -5 -4 -3 -1

-6 -1 -1 -1 -3 -5 -8 -10 -13 -15 -17 -18 -18 -17 -16 -15 -12 -10 -7 -5 -3 -2 -1 -1 -1 -1 -3 -4 -6 -7 -8 -9 -9 -9 -8 -7 -6 -4

-10 -1 -1 0 -2 -3 -6 -8 -11 -13 -16 -18 -19 -20 -20 -18 -17 -14 -12 -9 -7 -4 -3 -1 -1 -1 -1 -2 -4 -5 -7 -9 -10 -11 -11 -11 -9 -8

-13 -1 -1 0 -1 -2 -3 -5 -8 -10 -13 -16 -18 -19 -20 -20 -19 -18 -16 -13 -10 -8 -5 -3 -2 -1 -1 -1 -2 -4 -6 -8 -10 -11 -12 -13 -12 -12

-14 -1 -1 -1 -1 -1 -2 -3 -4 -7 -9 -12 -14 -16 -18 -19 -19 -19 -18 -16 -14 -11 -8 -6 -4 -2 -1 -1 -1 -2 -4 -6 -8 -10 -12 -14 -14 -14

-14 0 -1 -1 -1 -1 -1 -1 -2 -3 -5 -7 -10 -12 -14 -16 -17 -18 -18 -17 -15 -13 -11 -8 -6 -4 -2 -1 -1 -1 -2 -3 -6 -8 -10 -13 -14 -15

-12 0 -2 -2 -1 -1 -1 -1 -1 -1 -2 -3 -5 -7 -9 -11 -13 -15 -15 -15 -15 -14 -12 -10 -8 -6 -4 -2 -1 -1 -1 -2 -3 -5 -8 -10 -12 -15

-9 0 -2 -2 -3 -2 -2 -2 -1 -1 -1 -1 -2 -3 -4 -6 -8 -10 -11 -12 -13 -13 -12 -11 -9 -8 -6 -4 -2 -1 -1 -1 -1 -3 -5 -7 -9 -12

-5 0 -2 -3 -4 -4 -4 -4 -3 -2 -1 -1 -1 -1 -1 -2 -4 -5 -7 -8 -9 -10 -10 -10 -10 -9 -7 -6 -4 -3 -1 -1 -1 -1 -2 -4 -6 -8

-2 0 -1 -4 -5 -6 -6 -6 -6 -5 -4 -3 -2 -1 -1 -1 -1 -2 -3 -4 -5 -7 -8 -8 -9 -9 -8 -7 -6 -4 -3 -2 -1 -1 -1 -1 -3 -4

-1 0 -1 -3 -5 -7 -8 -9 -9 -9 -8 -7 -5 -4 -2 -1 -1 -1 -1 -1 -2 -3 -5 -6 -7 -7 -8 -8 -7 -6 -5 -4 -3 -2 -1 -1 -1 -2

The second-order day number J' given in this table in units of 0".0001 The apparent declination of a star is given by:  = 1 + /100 + Aa' + Bb' + Cc' + J ' tan1 Where the declination (1) and centennial proper motion in declination () are referred to the mean equator and equinox of J 2020.5

254

SECOND-ORDER DAY NUMBERS, 2020 J FOR SOUTHERN DECLINATIONS FOR 0h TT AND EQUINOX J 2020.5 RIGHT ASCENSION Date

Jan. Feb. Mar. Apr. May

June July Aug. Sept. Oct. Nov. Dec.

2 12 22 1 11 21 2 12 22 1 11 21 1 11 21 31 10 20 30 10 20 30 9 19 29 8 18 28 8 18 28 7 17 27 7 17 27 37

0h 12h

1h 13h

2h 14h

3h 15h

4h 16h

5h 17h

6h 18h

7h 19h

8h 20h

9h 21h

10h 22h

11h 23h

12h 24h

-3 -10 -13 -14 -14 -14 -12 -10 -8 -5 -3 -1 +1 +2 +2 +2 +1 0 -2 -3 -4 -5 -5 -4 -3 -2 0 +2 +4 +6 +7 +7 +6 +5 +3 +1 -1 -2

-1 1 -3 -6 -8 -10 -10 -10 -9 -7 -5 -3 -1 0 +1 +2 +2 +1 0 -2 -3 -4 -5 -6 -5 -4 -3 -1 +1 +3 +5 +6 +6 +6 +5 +3 +2 0

+2 11 +7 +3 0 -3 -5 -7 -7 -7 -6 -4 -3 -1 0 +1 +2 +2 +1 0 -1 -3 -4 -6 -6 -6 -6 -5 -3 -1 +1 +3 +5 +6 +6 +5 +4 +2

+4 18 +15 +11 +7 +4 +1 -2 -4 -5 -5 -5 -4 -2 -1 0 +1 +2 +2 +2 +1 -1 -2 -4 -6 -7 -7 -7 -6 -4 -2 0 +2 +3 +4 +5 +5 +4

+5 21 +19 +16 +13 +10 +6 +3 0 -2 -3 -4 -4 -3 -2 -1 0 +2 +2 +3 +2 +1 0 -2 -3 -5 -7 -7 -7 -7 -6 -4 -2 0 +2 +3 +4 +4

+4 17 +18 +17 +15 +13 +10 +7 +4 +2 -1 -2 -3 -3 -3 -2 -1 0 +2 +3 +3 +3 +2 +1 -1 -3 -5 -6 -7 -8 -8 -7 -5 -3 -1 +1 +2 +3

+2 9 +12 +13 +13 +13 +11 +9 +7 +4 +2 0 -2 -3 -3 -3 -2 -1 +1 +2 +3 +4 +4 +3 +2 +1 -1 -3 -5 -7 -8 -8 -7 -6 -4 -2 0 +1

0 -2 +2 +5 +7 +9 +9 +9 +8 +6 +4 +2 0 -1 -2 -3 -3 -2 -1 +1 +2 +3 +4 +5 +4 +3 +2 0 -2 -4 -6 -7 -7 -7 -6 -4 -3 -1

-3 -12 -8 -4 -1 +2 +4 +6 +6 +6 +5 +3 +2 0 -1 -2 -3 -3 -2 -1 0 +2 +3 +5 +5 +5 +5 +4 +2 0 -2 -4 -6 -7 -7 -6 -5 -3

-5 -19 -16 -12 -8 -5 -2 +1 +3 +4 +4 +4 +3 +1 0 -1 -2 -3 -3 -3 -2 0 +1 +3 +5 +6 +6 +6 +5 +3 +1 -1 -3 -4 -5 -6 -6 -5

-6 -22 -20 -17 -14 -11 -7 -4 -1 +1 +2 +3 +3 +2 +1 0 -1 -3 -3 -4 -3 -2 -1 +1 +2 +4 +6 +6 +6 +6 +5 +3 +1 -1 -3 -4 -5 -5

-5 -18 -19 -18 -16 -14 -11 -8 -5 -3 0 +1 +2 +2 +2 +1 0 -1 -3 -4 -4 -4 -3 -2 0 +2 +4 +5 +6 +7 +7 +6 +4 +2 0 -2 -3 -4

-3 -10 -13 -14 -14 -14 -12 -10 -8 -5 -3 -1 +1 +2 +2 +2 +1 0 -2 -3 -4 -5 -5 -4 -3 -2 0 +2 +4 +6 +7 +7 +6 +5 +3 +1 -1 -2

s The second-order day number J given in this table in units of 0 .00001

The apparent right ascension of a star is given by:  = 1 + /100 + Aa + Bb + Cc + Dd + E + J tan21 Where the position (1,1) and centennial proper motion in right ascension () are referred to the mean equator and equinox of J 2020.5

255

SECOND-ORDER DAY NUMBERS, 2020 J' FOR SOUTHERN DECLINATIONS FOR 0h TT AND EQUINOX J 2020.5 RIGHT ASCENSION Date Jan. Feb. Mar. Apr. May

June July Aug. Sept. Oct. Nov. Dec.

2 12 22 1 11 21 2 12 22 1 11 21 1 11 21 31 10 20 30 10 20 30 9 19 29 8 18 28 8 18 28 7 17 27 7 17 27 37

0h 12h

1h 13h

2h 14h

3h 15h

4h 16h

5h 17h

6h 18h

7h 19h

8h 20h

9h 21h

10h 22h

11h 23h

12h 24h

-1 -2 -4 -5 -6 -8 -9 -9 -9 -9 -8 -7 -6 -4 -3 -2 -1 -1 -1 -1 -2 -4 -6 -7 -9 -10 -11 -10 -10 -9 -7 -6 -4 -2 -1 -1 -1 -1

-1 -1 -1 -1 -2 -3 -4 -5 -6 -7 -7 -6 -6 -5 -4 -3 -2 -1 -1 -1 -1 -2 -4 -5 -7 -9 -10 -11 -11 -11 -10 -8 -7 -5 -3 -2 -1 -1

-1 -3 -2 -1 -1 -1 -1 -2 -3 -4 -5 -5 -5 -5 -4 -3 -3 -2 -1 -1 -1 -1 -2 -3 -5 -7 -9 -10 -11 -12 -11 -10 -9 -7 -5 -4 -2 -1

-2 -9 -6 -4 -2 -1 -1 -1 -1 -2 -3 -3 -4 -4 -4 -4 -3 -3 -2 -1 -1 -1 -1 -2 -3 -4 -6 -8 -9 -11 -11 -11 -11 -9 -8 -6 -4 -2

-4 -17 -13 -10 -6 -4 -2 -1 -1 -1 -1 -2 -3 -3 -4 -4 -4 -4 -3 -2 -1 -1 -1 -1 -1 -2 -4 -5 -7 -9 -10 -11 -11 -10 -9 -8 -6 -4

-6 -25 -21 -17 -12 -9 -6 -3 -2 -1 -1 -1 -1 -2 -3 -4 -4 -4 -4 -4 -3 -2 -1 -1 -1 -1 -2 -3 -4 -6 -7 -9 -10 -10 -10 -9 -7 -6

-7 -31 -27 -23 -18 -14 -10 -7 -4 -2 -1 -1 -1 -1 -2 -3 -4 -4 -5 -5 -4 -3 -3 -2 -1 -1 -1 -1 -2 -3 -5 -6 -7 -8 -9 -9 -8 -7

-8 -32 -30 -27 -23 -18 -15 -11 -7 -4 -2 -1 -1 -1 -1 -2 -3 -4 -5 -5 -5 -5 -4 -4 -3 -2 -1 -1 -1 -1 -2 -3 -5 -6 -7 -8 -8 -7

-8 -30 -29 -27 -24 -21 -17 -14 -10 -7 -4 -2 -1 -1 -1 -1 -2 -3 -4 -5 -6 -6 -6 -6 -5 -4 -2 -2 -1 -1 -1 -1 -2 -3 -5 -6 -6 -7

-7 -24 -24 -24 -22 -21 -18 -15 -12 -9 -6 -4 -2 -1 -1 -1 -1 -2 -3 -5 -6 -7 -7 -7 -7 -6 -5 -4 -2 -1 -1 -1 -1 -1 -2 -4 -5 -5

-5 -16 -17 -18 -18 -18 -17 -15 -13 -10 -8 -6 -4 -2 -1 -1 -1 -1 -2 -4 -5 -6 -8 -8 -8 -8 -7 -6 -5 -3 -2 -1 -1 -1 -1 -2 -3 -4

-3 -8 -10 -11 -12 -13 -13 -12 -11 -10 -8 -7 -5 -3 -2 -1 -1 -1 -1 -2 -4 -5 -7 -8 -9 -10 -10 -9 -8 -6 -5 -3 -2 -1 -1 -1 -1 -2

-1 -2 -4 -5 -6 -8 -9 -9 -9 -9 -8 -7 -6 -4 -3 -2 -1 -1 -1 -1 -2 -4 -6 -7 -9 -10 -11 -10 -10 -9 -7 -6 -4 -2 -1 -1 -1 -1

The second-order day number J' given in this table in units of 0".0001 The apparent declination of a star is given by: = 1 + /100 + Aa ' + Bb ' + Cc ' + J ' tan1 Where the declination (1) and centennial proper motion in declination () are referred to the mean equator and equinox of J 2020.5

256

POSITION AND VELOCITY OF THE EARTH, 2020 ORIGIN AT SOLAR SYSTEM BARYCENTRE MEAN EQUATOR AND EQUINOX J 2000.0 Date 0h T.D.B. Jan.

Feb.

X

Y

Z

. X

. Y

. Z

0 1 2 3 4 5

-0.152 0.170 0.187 0.204 0.221 0.238

871 144 364 525 623 651

14 +0.898 582 71 +0.389 562 63 39 0.895 983 83 0.388 436 66 42 0.893 107 92 0.387 190 45 83 0.889 956 13 0.385 824 50 30 0.886 529 71 0.384 339 34 57 0.882 829 99 0.382 735 57

-1729 1724 1719 1713 1706 1699

8043 7546 1615 320 3736 1940

-245 273 301 328 356 383

9990 7580 4054 9322 3296 5892

-106 118 130 142 154 166

5702 6171 6168 5646 4564 2880

6 7 8 9 10 11

-0.255 0.272 0.289 0.305 0.322 0.339

605 479 269 970 576 084

47 +0.878 858 40 +0.381 013 80 91 0.874 616 42 0.379 174 68 90 0.870 105 58 0.377 218 92 53 0.865 327 48 0.375 147 22 97 0.860 283 70 0.372 960 31 48 0.854 975 86 0.370 658 94

-1691 1683 1674 1665 1655 1645

5013 3042 6119 4332 7764 6471

-410 437 464 491 517 543

7039 6671 4738 1210 6076 9343

-178 189 201 212 224 235

0556 7555 3853 9426 4264 8369

12 13 14 15 16 17

-0.355 0.371 0.387 0.404 0.419 0.435

488 783 966 031 973 787

35 +0.849 405 54 +0.368 243 82 89 0.843 574 31 0.365 715 68 38 0.837 483 73 0.363 075 24 05 0.831 135 36 0.360 323 21 05 0.824 530 83 0.357 460 30 45 0.817 671 80 0.354 487 24

-1635 1623 1612 1600 1587 1574

0486 9804 4379 4148 9031 8948

-570 596 621 647 673 698

1033 1164 9737 6726 2072 5683

-247 258 269 280 291 302

1746 4405 6355 7594 8108 7869

18 19 20 21 22 23

-0.451 0.467 0.482 0.497 0.512 0.527

469 013 414 668 769 712

27 +0.810 560 08 +0.351 404 82 44 0.803 197 59 0.348 213 86 89 0.795 586 42 0.344 915 22 54 0.787 728 80 0.341 509 85 31 0.779 627 13 0.337 998 75 19 0.771 283 97 0.334 383 00

-1561 1547 1532 1517 1502 1486

3839 3662 8396 8050 2658 2275

-723 748 773 798 822 846

7435 7187 4783 0060 2855 3008

-313 324 335 345 356 366

6836 4954 2166 8407 3608 7701

24 25 26 27 28 29

-0.542 0.557 0.571 0.585 0.599 0.613

492 104 544 807 888 783

22 +0.762 702 05 +0.330 663 74 54 0.753 884 21 0.326 842 17 37 0.744 833 46 0.322 919 56 07 0.735 552 91 0.318 897 24 10 0.726 045 76 0.314 776 56 05 0.716 315 32 0.310 558 96

-1469 1452 1435 1417 1398 1380

6977 6861 2033 2612 8716 0469

-870 893 916 939 961 984

0369 4802 6179 4394 9352 0970

-377 387 397 407 416 426

0621 2304 2692 1732 9378 5590

30 31 1 2 3 4

-0.627 0.640 0.654 0.667 0.680 0.693

487 997 309 418 320 013

63 +0.706 364 96 +0.306 245 87 67 0.696 198 12 0.301 838 80 11 0.685 818 32 0.297 339 26 03 0.675 229 10 0.292 748 80 62 0.664 434 08 0.288 069 00 21 0.653 436 90 0.283 301 45

-1360 1341 1321 1300 1279 1258

7991 1404 0826 6380 8191 6384

-1005 1027 1048 1069 1089 1109

9176 3907 5106 2722 6713 7045

-436 445 454 463 472 481

0329 3562 5261 5396 3944 0884

5 6 7 8 9 10

-0.705 0.717 0.729 0.741 0.753 0.764

492 754 796 614 205 568

23 +0.642 241 22 +0.278 447 77 27 0.630 850 72 0.273 509 59 02 0.619 269 07 0.268 488 52 30 0.607 499 91 0.263 386 20 99 0.595 546 82 0.258 204 21 03 0.583 413 33 0.252 944 13

-1237 1215 1193 1170 1147 1124

1090 2436 0540 5499 7375 6189

-1129 1148 1167 1186 1204 1222

3701 6681 6006 1718 3874 2523

-489 497 506 514 522 529

6203 9895 1962 2420 1294 8610

11 12 13 14 15

-0.775 0.786 0.797 0.807 -0.817 . X,

697 590 245 657 824

34 +0.571 102 93 +0.247 607 50 -1101 1919 82 0.558 619 09 0.242 195 86 1077 4515 31 0.545 965 29 0.236 710 72 1053 3916 57 0.533 145 11 0.231 153 63 1029 0075 37 +0.520 162 21 +0.225 526 16 -1004 2967 . . are in units of 10-9 a.u. per day Y, Z

-1239 1256 1273 1290 -1306

7702 9407 7590 2165 3013

-537 544 552 559 -566

4390 8647 1373 2544 2120

257

FRAME BIAS, PRECESSION AND NUTATION, 2020 MATRIX ELEMENTS FOR CONVERSION FROM GCRS TO TRUE EQUINOX OF DATE Date 0h TT Jan.

Feb.

M11 - 1

M12

M13

M21

M22 - 1

M23

M31

M32 M33 - 1

0 -1150 1 1150 2 1150 3 1150 4 1151 5 1151

-439 439 439 439 439 440

823 873 912 947 984 030

-191 191 191 191 191 191

099 +439 825 121 439 874 138 439 913 153 439 948 169 439 986 190 440 032

-967 967 968 968 968 968

+432 +191 096 411 191 117 395 191 134 386 191 150 384 191 166 389 191 186

-1273 1251 1236 1227 1225 1230

-183 183 183 183 183 183

6 -1151 7 1152 8 1152 9 1153 10 1153 11 1154

-440 440 440 440 440 440

091 171 272 391 520 650

-191 191 191 191 191 191

216 +440 093 251 440 173 295 440 274 346 440 392 402 440 522 459 440 652

-968 969 969 970 970 971

+398 +191 213 409 191 247 418 191 291 421 191 342 413 191 399 394 191 455

-1240 1251 1260 1263 1257 1238

-183 183 183 183 183 183

12 -1155 13 1155 14 1156 15 1156 16 1156 17 1156

-440 440 440 440 441 441

767 861 928 971 000 029

-191 191 191 191 191 191

509 +440 769 550 440 862 579 440 929 598 440 972 611 441 001 623 441 030

-971 972 972 972 972 973

+365 +191 506 329 191 547 292 191 576 262 191 595 242 191 608 235 191 620

-1209 1173 1137 1107 1087 1080

-183 183 184 184 184 184

18 -1156 19 1157 20 1157 21 1158 22 1158 23 1159

-441 441 441 441 441 441

069 128 209 310 422 537

-191 191 191 191 191 191

640 +441 070 666 441 129 702 441 211 745 441 311 794 441 423 844 441 539

-973 973 973 974 974 975

+238 +191 638 246 191 663 256 191 699 262 191 742 259 191 791 248 191 841

-1083 1092 1102 1108 1106 1095

-184 184 184 184 184 184

24 -1159 25 1160 26 1160 27 1161 28 1161 29 1161

-441 441 441 441 441 441

646 740 817 873 913 940

-191 191 191 191 192 192

891 +441 647 932 441 742 965 441 818 990 441 874 007 441 914 019 441 941

-975 976 976 976 976 977

+227 +191 888 199 191 929 167 191 963 135 191 987 105 192 005 81 192 017

-1074 1047 1015 0983 0954 0930

-184 184 184 184 184 184

30 -1161 31 1161 1 1161 2 1161 3 1162 4 1162

-441 441 442 442 442 442

960 980 007 045 100 174

-192 192 192 192 192 192

028 +441 961 036 441 981 048 442 008 065 442 046 089 442 101 121 442 175

-977 977 977 977 977 978

+64 +192 026 55 192 034 52 192 046 55 192 063 60 192 086 66 192 119

-0913 0903 0901 0904 0910 0915

-184 184 184 184 184 185

5 -1163 6 1163 7 1164 8 1164 9 1165 10 1165

-442 442 442 442 442 442

267 374 487 593 680 741

-192 192 192 192 192 192

161 +442 268 207 442 375 256 442 487 302 442 594 340 442 681 367 442 741

-978 978 979 979 980 980

+67 +192 159 61 192 205 43 192 254 +15 192 301 -23 192 339 64 192 365

-0917 0911 0894 0866 0828 0788

-185 185 185 185 185 185

11 -1165 12 1165 13 1165 14 1165 15 -1166

-442 442 442 442 -442

773 786 794 811 846

-192 381 +442 774 -980 192 387 442 787 980 192 390 442 795 980 192 397 442 811 980 -192 413 +442 847 -981 Values are in units of 10 -8

-100 +192 379 127 192 385 140 192 389 140 192 396 -133 +192 411

-0751 0725 0712 0712 -0720

-185 185 185 185 -185

258

POSITION AND VELOCITY OF THE EARTH, 2020 ORIGIN AT SOLAR SYSTEM BARYCENTRE MEAN EQUATOR AND EQUINOX J 2000.0 Date h 0 T.D.B. Feb.

Mar.

Apr.

X

Y

. X

Z

. Y

. Z

15 16 17 18 19 20

-0.817 0.827 0.837 0.846 0.855 0.864

824 742 408 819 972 863

37 +0.520 162 21 +0.225 526 16 42 0.507 020 37 0.219 829 94 50 0.493 723 53 0.214 066 63 43 0.480 275 75 0.208 237 96 10 0.466 681 22 0.202 345 70 53 0.452 944 24 0.196 391 70

-1004 979 953 928 902 875

2967 2604 9028 2310 2539 9825

-1306 1322 1337 1352 1366 1380

3013 0002 2996 1863 6481 6738

-566 573 579 586 592 598

2120 0051 6283 0763 3437 4256

21 22 23 24 25 26

-0.873 0.881 0.889 0.897 0.905 0.912

490 851 942 760 305 573

81 +0.439 069 23 +0.190 377 83 21 0.425 060 69 0.184 306 00 09 0.410 923 20 0.178 178 19 97 0.396 661 42 0.171 996 38 53 0.382 280 05 0.165 762 60 57 0.367 783 85 0.159 478 91

-849 822 795 768 740 712

4289 6062 5283 2096 6650 9092

-1394 1407 1420 1432 1443 1455

2536 3788 0416 2364 9580 2028

-604 610 615 620 625 630

3174 0149 5146 8131 9079 7967

27 28 29 1 2 3

-0.919 0.926 0.932 0.938 0.944 0.950

563 272 698 842 699 271

05 +0.353 177 59 +0.153 147 36 10 0.338 466 09 0.146 770 05 95 0.323 654 16 0.140 349 07 01 0.308 746 62 0.133 886 51 80 0.293 748 30 0.127 384 50 03 0.278 664 00 0.120 845 13

-684 656 628 600 571 542

9569 8227 5210 0659 4718 7527

-1465 1476 1486 1495 1504 1512

9680 2519 0538 3732 2111 5691

-635 639 644 648 652 655

4777 9498 2119 2634 1043 7346

4 5 6 7 8 9

-0.955 0.960 0.965 0.969 0.973 0.977

554 549 254 668 791 623

49 +0.263 498 51 +0.114 270 51 16 0.248 256 57 0.107 662 72 11 0.232 942 87 0.101 023 85 56 0.217 562 04 0.094 355 92 80 0.202 118 60 0.087 660 94 16 0.186 616 97 0.080 940 88

-513 484 455 426 397 368

9227 9953 9828 8956 7405 5201

-1520 1527 1534 1541 1547 1552

4504 8594 8026 2885 3266 9259

-659 662 665 668 670 673

1550 3674 3740 1782 7842 1967

10 11 12 13 14 15

-0.981 0.984 0.987 0.990 0.992 0.994

161 407 359 015 377 441

98 +0.171 061 51 +0.074 197 64 56 0.155 456 52 0.067 433 10 17 0.139 806 27 0.060 649 13 98 0.124 115 10 0.053 847 58 17 0.108 387 42 0.047 030 36 91 0.092 627 75 0.040 199 38

-339 309 280 250 221 191

2325 8726 4345 9140 3100 6260

-1558 1562 1567 1571 1574 1577

0939 8338 1436 0168 4438 4139

-675 677 679 680 682 683

4200 4565 3071 9703 4428 7207

16 17 18 19 20 21

-0.996 0.997 0.998 0.999 1.000 1.000

209 679 850 722 295 569

45 +0.076 840 71 +0.033 09 0.061 031 01 0.026 29 0.045 203 48 0.019 58 0.029 362 98 0.012 68 +0.013 514 42 0.005 41 -0.002 337 22 +0.000

356 504 643 777 908 962

61 05 77 83 34 58

-161 132 102 72 42 -12

8695 0504 1807 2736 3429 4027

-1579 1581 1583 1584 1585 1585

9162 9420 4835 5352 0926 1526

-684 685 686 686 687 687

7999 6761 3461 8068 0562 0923

22 23 24 25 26 27

-1.000 1.000 0.999 0.998 0.997 0.995

543 218 594 672 451 933

75 82 89 37 83 96

-0.018 0.034 0.049 0.065 0.081 0.097

186 029 860 674 467 232

96 82 78 85 05 43

-0.007 0.014 0.021 0.028 0.035 0.042

832 700 562 417 263 097

79 14 47 62 43 74

+17 47 77 107 136 166

5327 4486 3304 1636 9335 6259

-1584 1583 1582 1580 1577 1575

7135 7742 3347 3964 9611 0322

-686 686 685 685 684 682

9139 5199 9098 0837 0418 7849

28 29 30 31 1

-0.994 0.992 0.989 0.986 -0.983 . X,

119 009 605 908 919

62 78 57 24 16

-0.112 0.128 0.144 0.159 -0.175 . Y,

966 06 663 08 318 66 928 05 486 56 . Z

-0.048 0.055 0.062 0.069 -0.076

918 723 510 277 022

41 32 34 40 42

+196 225 255 284 +313

2266 7221 0990 3446 4467

-1571 1567 1563 1558 -1553

6135 7099 3273 4724 1534

-681 679 677 675 -673

3143 6315 7386 6380 3330

are in units of 10-9 a.u. per day

259

FRAME BIAS, PRECESSION AND NUTATION, 2020 MATRIX ELEMENTS FOR CONVERSION FROM GCRS TO TRUE EQUINOX OF DATE Date 0h TT Feb.

Mar.

Apr.

M11 - 1

M12

M13

M21

M22 - 1

M23

M31

M32 M33 - 1

15 -1166 16 1166 17 1166 18 1167 19 1167 20 1168

-442 442 442 443 443 443

846 905 983 074 169 259

-192 192 192 192 192 192

413 +442 847 438 442 905 472 442 983 511 443 074 553 443 169 592 443 259

-981 981 981 982 982 982

-133 +192 411 123 192 437 116 192 471 116 192 510 125 192 551 143 192 591

-0720 0730 0737 0737 0728 0711

-185 185 185 185 185 185

21 -1168 22 1169 23 1169 24 1169 25 1169 26 1169

-443 443 443 443 443 443

337 398 440 465 476 478

-192 192 192 192 192 192

626 +443 337 652 443 398 671 443 441 681 443 465 686 443 476 687 443 479

-983 983 983 983 983 983

-168 +192 625 198 192 651 228 192 670 257 192 681 280 192 686 296 192 687

-0686 0656 0626 0598 0574 0558

-186 186 186 186 186 186

27 -1169 28 1169 29 1169 1 1169 2 1170 3 1170

-443 443 443 443 443 443

479 485 501 532 581 649

-192 192 192 192 192 192

688 +443 479 690 443 485 697 443 501 711 443 532 732 443 582 762 443 649

-983 983 983 984 984 984

-305 +192 687 306 192 690 301 192 697 292 192 710 283 192 732 276 192 761

-0550 0548 0553 0562 0572 0580

-186 186 186 186 186 186

4 -1170 5 1171 6 1171 7 1172 8 1172 9 1172

-443 443 443 443 444 444

731 823 915 995 052 082

-192 192 192 192 192 192

797 +443 732 837 443 824 877 443 915 912 443 995 937 444 052 950 444 082

-984 985 985 986 986 986

-274 +192 797 282 192 837 301 192 877 329 192 911 363 192 937 397 192 950

-0581 0574 0556 0528 0494 0460

-186 186 186 186 186 186

10 -1172 11 1172 12 1172 13 1172 14 1172 15 1173

-444 444 444 444 444 444

088 082 080 096 137 201

-192 192 192 192 192 193

953 +444 088 950 444 082 949 444 080 956 444 096 974 444 137 002 444 202

-986 986 986 986 986 987

-423 +192 953 435 192 950 433 192 949 420 192 956 402 192 974 385 193 002

-0434 0422 0424 0437 0455 0472

-186 186 186 186 186 186

16 -1173 17 1174 18 1174 19 1175 20 1175 21 1175

-444 444 444 444 444 444

282 369 453 526 582 620

-193 193 193 193 193 193

037 +444 282 075 444 369 111 444 453 143 444 526 167 444 582 184 444 620

-987 987 988 988 988 988

-376 +193 037 375 193 075 383 193 111 399 193 143 420 193 167 443 193 184

-0482 0483 0475 0459 0438 0416

-186 186 186 187 187 187

22 -1175 23 1175 24 1175 25 1175 26 1175 27 1175

-444 444 444 444 444 444

641 648 645 639 638 646

-193 193 193 193 193 193

193 +444 641 196 444 648 195 444 645 192 444 639 192 444 638 195 444 646

-989 989 989 989 989 989

-464 +193 193 480 193 196 490 193 195 492 193 193 486 193 192 474 193 196

-0395 0379 0369 0367 0373 0385

-187 187 187 187 187 187

28 -1175 29 1176 30 1176 31 1176 1 -1177

-444 444 444 444 -444

669 710 769 844 930

-193 205 +444 669 -989 193 223 444 710 989 193 249 444 769 989 193 281 444 844 989 -193 319 +444 930 -990 Values are in units of 10 -8

-457 +193 206 438 193 223 422 193 249 410 193 281 -406 +193 318

-0402 0421 0438 0450 -0454

-187 187 187 187 -187

260

POSITION AND VELOCITY OF THE EARTH, 2020 ORIGIN AT SOLAR SYSTEM BARYCENTRE MEAN EQUATOR AND EQUINOX J 2000.0 Date h 0 T.D.B. Apr.

May

X

Y

. X

Z

. Y

. Z

1 2 3 4 5 6

-0.983 0.980 0.977 0.973 0.969 0.964

919 639 071 216 076 653

16 82 83 86 68 04

-0.175 0.190 0.206 0.221 0.237 0.252

486 989 432 811 121 358

56 60 67 37 44 75

-0.076 0.082 0.089 0.096 0.102 0.109

022 743 438 105 742 347

42 39 31 24 31 68

+313 342 371 399 428 456

4467 3939 1766 7870 2208 4772

-1553 1547 1541 1534 1527 1519

1534 3792 1605 5089 4372 9570

-673 670 668 665 662 658

3330 8271 1248 2310 1517 8928

7 8 9 10 11 12

-0.959 0.954 0.949 0.944 0.938 0.932

947 962 698 158 342 253

71 40 75 33 68 35

-0.267 0.282 0.297 0.312 0.327 0.342

519 599 594 500 314 031

26 01 08 55 41 61

-0.115 0.122 0.128 0.135 0.141 0.148

919 456 956 417 838 217

58 30 13 40 39 40

+484 512 540 567 595 622

5597 4747 2294 8290 2754 5652

-1512 1503 1495 1486 1476 1466

0781 8066 1431 0838 6215 7478

-655 651 648 644 640 635

4593 8555 0831 1416 0292 7424

13 14 15 16 17 18

-0.925 0.919 0.912 0.905 0.897 0.890

891 260 359 192 760 066

93 11 70 63 95 86

-0.356 0.371 0.385 0.399 0.414 0.428

647 159 561 849 020 068

97 30 32 74 28 66

-0.154 0.160 0.167 0.173 0.179 0.185

552 842 084 277 420 509

65 36 72 90 07 40

+649 676 703 729 756 782

6909 6424 4073 9729 3259 4537

-1456 1445 1434 1423 1411 1398

4553 7385 5937 0197 0169 5868

-631 626 621 616 611 606

2781 6339 8076 7981 6053 2289

19 20 21 22 23 24

-0.882 0.873 0.865 0.856 0.847 0.838

112 900 433 714 745 530

67 83 91 59 71 19

-0.441 0.455 0.469 0.482 0.496 0.509

990 781 438 955 330 557

60 89 32 76 11 33

-0.191 0.197 0.203 0.209 0.215 0.220

544 522 442 301 099 833

04 18 01 73 54 71

+808 833 859 884 909 933

3433 9821 3578 4579 2701 7822

-1385 1372 1358 1344 1330 1315

7319 4556 7623 6568 1449 2337

-600 594 589 582 576 570

6696 9287 0069 9062 6284 1759

25 26 27 28 29 30

-0.829 0.819 0.809 0.799 0.788 0.778

071 371 435 264 864 236

10 62 02 70 12 84

-0.522 0.535 0.548 0.560 0.573 0.585

633 554 317 917 351 615

47 67 14 20 30 99

-0.226 0.232 0.237 0.243 0.248 0.253

502 104 637 099 490 807

49 18 12 69 30 43

+957 981 1005 1028 1051 1073

9825 8596 4033 6039 4528 9433

-1299 1284 1268 1251 1234 1217

9310 2453 1869 7665 9958 8875

-563 556 549 542 535 527

5517 7591 8020 6846 4119 9892

1 2 3 4 5 6

-0.767 0.756 0.745 0.733 0.721 0.709

386 316 031 533 827 916

46 66 08 39 19 02

-0.597 0.609 0.621 0.632 0.644 0.655

707 624 361 916 287 470

97 05 21 54 24 61

-0.259 0.264 0.269 0.274 0.279 0.284

049 215 303 312 241 089

60 +1096 0701 -1200 4548 41 1117 8301 1182 7116 52 1139 2238 1164 6715 63 1160 2540 1146 3469 53 1180 9268 1127 7482 04 1201 2509 1108 8816

-520 512 504 496 488 480

4224 7178 8817 9204 8398 6436

7 8 9 10 11 12

-0.697 0.685 0.672 0.660 0.647 0.634

803 492 986 289 403 333

31 44 71 45 99 75

-0.666 0.677 0.687 0.698 0.708 0.718

463 264 870 277 483 486

98 70 06 30 60 11

-0.288 0.293 0.298 0.302 0.307 0.311

854 535 131 642 065 401

02 +1221 2346 -1089 7494 35 1240 8849 1070 3493 89 1260 2047 1050 6764 48 1279 1924 1030 7243 95 1297 8427 1010 4883 10 1316 1464 989 9649

-472 463 455 446 437 429

3344 9122 3759 7230 9511 0587

13 14 15 16 17

-0.621 0.607 0.594 0.580 -0.566 . X,

082 653 050 276 337

25 11 07 97 74

-0.728 0.737 0.747 0.756 -0.765 . Y,

281 94 868 22 242 10 400 78 341 49 . Z

-0.315 0.319 0.323 0.327 -0.331

646 801 864 834 709

72 +1334 0933 59 1351 6722 50 1368 8722 25 1385 6829 65 +1402 0944

-420 410 401 392 -382

0446 9090 6528 2771 7839

-969 948 926 905 -883

1534 0554 6742 0148 0822

are in units of 10-9 a.u. per day

261

FRAME BIAS, PRECESSION AND NUTATION, 2020 MATRIX ELEMENTS FOR CONVERSION FROM GCRS TO TRUE EQUINOX OF DATE Date 0h TT Apr.

May

M11 - 1

M12

M13

M21

M22 - 1

M23

M31

M32 M33 - 1

1 -1177 2 1177 3 1178 4 1178 5 1178 6 1178

-444 445 445 445 445 445

930 018 100 165 207 224

-193 193 193 193 193 193

319 +444 930 357 445 018 392 445 100 421 445 165 439 445 207 446 445 224

-990 990 991 991 991 991

-406 +193 318 411 193 357 427 193 392 449 193 421 474 193 439 495 193 447

-0454 0449 0434 0412 0387 0366

-187 187 187 187 187 187

7 -1178 8 1178 9 1178 10 1178 11 1179 12 1179

-445 445 445 445 445 445

224 220 230 266 329 415

-193 193 193 193 193 193

446 +445 224 445 445 220 449 445 230 465 445 266 492 445 329 530 445 415

-991 991 991 991 992 992

-506 +193 447 502 193 445 484 193 450 457 193 465 430 193 492 408 193 530

-0356 0360 0378 0404 0432 0454

-187 187 187 187 187 187

13 -1180 14 1180 15 1181 16 1181 17 1181 18 1182

-445 445 445 445 445 445

512 609 696 767 819 853

-193 193 193 193 193 193

572 +445 512 614 445 609 652 445 696 682 445 767 705 445 819 720 445 853

-992 993 993 994 994 994

-396 +193 572 394 193 614 401 193 651 414 193 682 430 193 705 444 193 720

-0466 0469 0462 0449 0434 0419

-187 187 188 188 188 188

19 -1182 20 1182 21 1182 22 1182 23 1182 24 1182

-445 445 445 445 445 445

872 880 885 893 909 940

-193 193 193 193 193 193

728 +445 872 732 445 880 734 445 885 737 445 893 744 445 909 758 445 940

-994 994 994 994 994 994

-455 +193 728 460 193 732 457 193 734 446 193 737 429 193 744 406 193 758

-0409 0404 0407 0418 0435 0458

-188 188 188 188 188 188

25 -1182 26 1183 27 1183 28 1184 29 1184 30 1185

-445 446 446 446 446 446

989 056 141 237 338 434

-193 193 193 193 193 193

779 +445 989 808 446 056 845 446 141 887 446 237 931 446 338 972 446 434

-995 995 995 996 996 997

-382 +193 779 358 193 808 339 193 845 328 193 886 326 193 930 333 193 972

-0483 0506 0526 0537 0540 0533

-188 188 188 188 188 188

1 -1185 2 1185 3 1186 4 1186 5 1186 6 1186

-446 446 446 446 446 446

516 579 618 638 650 668

-194 194 194 194 194 194

008 +446 517 035 446 579 052 446 618 061 446 639 066 446 650 074 446 668

-997 997 997 997 997 998

-348 +194 008 368 194 035 386 194 052 396 194 061 395 194 066 379 194 074

-0518 0499 0481 0470 0472 0488

-188 188 188 188 188 188

7 -1186 8 1186 9 1187 10 1188 11 1188 12 1189

-446 446 446 446 447 447

707 774 870 983 102 215

-194 194 194 194 194 194

091 +446 707 120 446 775 162 446 870 211 446 984 263 447 103 311 447 215

-998 998 998 999 1000 1000

-353 +194 091 322 194 120 294 194 161 274 194 210 266 194 262 269 194 311

-0514 0545 0574 0594 0602 0600

-188 188 188 189 189 189

13 -1189 14 1190 15 1190 16 1190 17 -1190

-447 447 447 447 -447

311 388 445 486 514

-194 353 +447 312 -1000 194 387 447 389 1001 194 412 447 446 1001 194 429 447 486 1001 -194 441 +447 514 -1001 Values are in units of 10 -8

-280 +194 353 295 194 386 310 194 411 322 194 429 -328 +194 441

-0590 0575 0560 0548 -0542

-189 189 189 189 -189

262

POSITION AND VELOCITY OF THE EARTH, 2020 ORIGIN AT SOLAR SYSTEM BARYCENTRE MEAN EQUATOR AND EQUINOX J 2000.0 Date 0h T.D.B. May

June

July

X

Y

. X

Z

. Y

. Z

17 18 19 20 21 22

-0.566 0.552 0.537 0.523 0.509 0.494

337 236 977 564 001 294

74 44 20 24 89 56

-0.765 0.774 0.782 0.790 0.798 0.806

341 061 558 829 871 683

49 53 28 16 70 50

-0.331 0.335 0.339 0.342 0.346 0.349

709 489 172 758 244 631

65 +1402 0944 54 1418 0968 78 1433 6812 25 1448 8381 86 1463 5582 55 1477 8328

-883 860 838 815 792 769

0822 8828 4237 7121 7562 5653

-382 373 363 353 343 333

7839 1753 4537 6219 6827 6397

23 24 25 26 27 28

-0.479 0.464 0.449 0.434 0.418 0.403

446 463 348 106 743 263

75 04 08 61 37 18

-0.814 0.821 0.828 0.835 0.842 0.848

262 605 712 578 204 588

26 78 00 96 87 07

-0.352 0.356 0.359 0.362 0.365 0.367

917 101 182 159 032 799

32 +1491 6533 17 1505 0116 18 1517 9007 47 1530 3152 23 1542 2513 69 1553 7070

-746 722 698 674 650 626

1496 5204 6903 6727 4819 1325

-323 313 302 292 282 271

4967 2582 9293 5155 0231 4582

29 30 31 1 2 3

-0.387 0.371 0.356 0.340 0.324 0.308

670 971 168 268 274 192

83 12 77 49 86 39

-0.854 0.860 0.866 0.871 0.876 0.881

727 620 266 665 815 715

04 42 97 58 23 00

-0.370 0.373 0.375 0.377 0.380 0.382

461 016 463 803 035 159

17 +1564 6828 05 1575 1817 76 1585 2086 82 1594 7714 78 1603 8794 23 1612 5426

-601 577 552 527 502 477

6390 0157 2754 4294 4863 4511

-260 250 239 228 217 206

8278 1383 3963 6076 7770 9082

4 5 6 7 8 9

-0.292 0.275 0.259 0.243 0.226 0.210

025 778 455 060 598 073

46 39 41 77 69 46

-0.886 0.890 0.894 0.898 0.902 0.905

363 761 905 796 433 813

96 20 81 78 12 77

-0.384 0.386 0.387 0.389 0.391 0.392

173 079 874 560 136 600

82 +1620 7712 17 1628 5727 93 1635 9512 70 1642 9074 10 1649 4377 70 1655 5358

-452 427 401 376 350 325

3258 1085 7956 3829 8666 2452

-196 185 174 163 152 140

0029 0615 0828 0654 0072 9073

10 11 12 13 14 15

-0.193 0.176 0.160 0.143 0.126 0.109

489 851 162 429 655 845

44 07 88 47 51 74

-0.908 0.911 0.914 0.916 0.918 0.920

937 803 411 758 846 671

68 82 21 92 07 87

-0.393 0.395 0.396 0.397 0.398 0.399

954 195 325 342 247 038

10 +1661 1940 87 1666 4039 60 1671 1574 90 1675 4472 40 1679 2662 76 1682 6080

-299 273 247 221 195 169

5197 6930 7698 7566 6603 4884

-129 118 107 96 84 73

7652 5816 3579 0961 7985 4681

16 17 18 19 20 21

-0.093 0.076 0.059 0.042 0.025 -0.008

004 138 249 345 429 507

96 03 86 44 79 99

-0.922 0.923 0.924 0.925 0.925 0.926

235 536 574 348 858 104

61 66 48 61 73 62

-0.399 0.400 0.400 0.401 0.401 0.401

716 280 730 066 288 395

66 +1685 4670 82 1687 8370 99 1689 7124 96 1691 0878 55 1691 9579 63 1692 3179

-143 116 90 64 37 -11

2493 9514 6041 2176 8030 3731

-62 50 39 27 16 -4

1076 7204 3100 8801 4354 9806

22 +0.008 414 86 23 0.025 333 60 24 0.042 243 09 25 0.059 138 21 26 0.076 013 90 27 0.092 865 14

-0.926 0.925 0.925 0.924 0.923 0.922

086 803 256 446 372 036

19 50 75 32 72 60

-0.401 0.401 0.401 0.400 0.400 0.399

388 266 029 678 213 634

14 +1692 1649 07 1691 4972 46 1690 3158 44 1688 6243 20 1686 4288 00 1683 7379

+15 41 67 94 120 146

0584 4766 8661 2114 4982 7132

+6 17 29 40 52 63

4786 9358 3842 8169 2270 6079

438 73 579 99 461 31 083 67 448 07 . Z

-0.398 0.398 0.397 0.396 -0.395

941 135 216 184 041

15 +1680 5622 +172 05 1676 9136 198 09 1672 8045 224 71 1668 2464 250 39 +1663 2500 +276

8457 +74 8872 86 8324 97 6786 108 4257 +119

9541 2606 5243 7426 9147

28 +0.109 687 04 -0.920 29 0.126 474 81 0.918 30 0.143 223 77 0.916 1 0.159 929 40 0.914 2 +0.176 587 24 -0.911 . . Y, X,

are in units of 10-9 a.u. per day

263

FRAME BIAS, PRECESSION AND NUTATION, 2020 MATRIX ELEMENTS FOR CONVERSION FROM GCRS TO TRUE EQUINOX OF DATE Date 0h TT May

June

July

M11 - 1

M12

M13

M21

M22 - 1

M23

M31

M32 M33 - 1

17 -1190 18 1191 19 1191 20 1191 21 1191 22 1191

-447 447 447 447 447 447

514 536 559 589 633 693

-194 194 194 194 194 194

441 +447 514 -1001 451 447 536 1001 461 447 559 1002 474 447 589 1002 493 447 633 1002 520 447 694 1002

-328 +194 441 328 194 451 320 194 461 304 194 474 284 194 493 260 194 519

-0542 0542 0551 0566 0587 0611

-189 189 189 189 189 189

23 -1192 24 1192 25 1193 26 1194 27 1194 28 1195

-447 447 447 448 448 448

774 872 983 101 215 317

-194 194 194 194 194 194

554 +447 774 -1003 597 447 872 1003 646 447 984 1003 697 448 101 1004 746 448 216 1004 790 448 317 1005

-237 +194 554 218 194 596 206 194 645 204 194 695 212 194 745 228 194 789

-0634 0653 0666 0668 0661 0645

-189 189 189 190 190 190

29 -1195 30 1195 31 1196 1 1196 2 1196 3 1196

-448 448 448 448 448 448

400 459 499 528 557 600

-194 194 194 194 194 194

826 +448 400 -1005 852 448 460 1006 870 448 500 1006 882 448 528 1006 894 448 557 1006 913 448 601 1006

-250 +194 825 271 194 851 287 194 869 292 194 881 286 194 894 267 194 913

-0624 0603 0587 0582 0589 0607

-190 190 190 190 190 190

4 -1197 5 1197 6 1198 7 1198 8 1199 9 1200

-448 448 448 449 449 449

669 766 887 019 150 268

-194 194 195 195 195 195

943 +448 669 -1007 986 448 767 1007 038 448 887 1008 095 449 019 1008 152 449 150 1009 203 449 269 1009

-242 +194 942 217 194 985 198 195 037 190 195 094 194 195 151 208 195 202

-0632 0658 0677 0686 0682 0669

-190 190 190 190 190 191

10 -1200 11 1201 12 1201 13 1201 14 1201 15 1202

-449 449 449 449 449 449

367 444 502 544 578 610

-195 195 195 195 195 195

246 +449 367 -1010 280 449 445 1010 305 449 502 1010 323 449 545 1010 338 449 578 1011 352 449 610 1011

-228 +195 245 250 195 279 270 195 304 285 195 323 294 195 337 294 195 351

-0649 0628 0608 0593 0585 0584

-191 191 191 191 191 191

16 -1202 17 1202 18 1202 19 1203 20 1203 21 1204

-449 449 449 449 449 450

647 695 759 842 943 060

-195 195 195 195 195 195

368 +449 647 -1011 389 449 695 1011 417 449 759 1011 453 449 842 1012 497 449 944 1012 547 450 061 1013

-288 +195 367 275 195 388 259 195 416 243 195 452 229 195 496 222 195 546

-0591 0603 0620 0637 0651 0658

-191 191 191 191 191 191

22 -1205 23 1205 24 1206 25 1206 26 1207 27 1207

-450 450 450 450 450 450

185 310 423 516 586 634

-195 195 195 195 195 195

602 +450 186 -1013 656 450 310 1014 705 450 423 1014 745 450 516 1015 776 450 586 1015 796 450 634 1015

-224 +195 601 237 195 655 259 195 704 288 195 745 318 195 775 343 195 796

-0656 0644 0622 0594 0564 0539

-191 191 192 192 192 192

28 -1207 29 1207 30 1208 1 1208 2 -1208

-450 450 450 450 -450

667 698 739 800 888

-195 811 +450 667 -1016 195 824 450 698 1016 195 842 450 739 1016 195 869 450 801 1016 -195 907 +450 888 -1017 Values are in units of 10 -8

-359 +195 811 363 195 824 356 195 842 341 195 868 -324 +195 906

-0524 0519 0527 0542 -0559

-192 192 192 192 -192

264

POSITION AND VELOCITY OF THE EARTH, 2020 ORIGIN AT SOLAR SYSTEM BARYCENTRE MEAN EQUATOR AND EQUINOX J 2000.0 Date h 0 T.D.B. July

Aug.

X

Y

. X

Z

. Y

. Z

1 +0.159 929 40 2 0.176 587 24 3 0.193 192 96 4 0.209 742 29 5 0.226 230 98 6 0.242 654 79

-0.914 0.911 0.908 0.905 0.902 0.898

083 448 555 406 003 345

67 07 48 87 14 20

-0.396 0.395 0.393 0.392 0.390 0.389

184 041 786 420 944 357

71 +1668 2464 +250 6786 +108 7426 39 1663 2500 276 4257 119 9147 57 1657 8232 302 0757 131 0408 72 1651 9712 327 6320 142 1221 28 1645 6957 353 0979 153 1600 66 1638 9955 378 4758 164 1558

7 +0.259 009 46 8 0.275 290 69 9 0.291 494 12 10 0.307 615 34 11 0.323 649 91 12 0.339 593 32

-0.894 0.890 0.885 0.881 0.876 0.871

433 270 854 188 273 109

92 18 88 97 46 42

-0.387 0.385 0.383 0.381 0.379 0.377

661 855 940 917 786 547

30 +1631 8672 +403 7661 +175 1103 59 1624 3060 428 9676 186 0236 96 1616 3067 454 0768 196 8950 84 1607 8642 479 0883 207 7230 66 1598 9742 503 9959 218 5052 89 1589 6330 528 7922 229 2393

13 +0.355 441 06 14 0.371 188 55 15 0.386 831 22 16 0.402 364 46 17 0.417 783 64 18 0.433 084 12

-0.865 0.860 0.854 0.847 0.841 0.834

698 040 138 992 604 976

01 46 09 30 61 61

-0.375 0.372 0.370 0.367 0.364 0.361

202 749 191 527 758 886

04 +1579 8372 +553 4692 +239 9223 63 1569 5846 578 0189 250 5513 21 1558 8725 602 4322 261 1229 37 1547 6985 626 7000 271 6334 75 1536 0607 650 8122 282 0793 02 1523 9569 674 7575 292 4560

19 +0.448 261 22 20 0.463 310 28 21 0.478 226 65 22 0.493 005 70 23 0.507 642 89 24 0.522 133 77

-0.828 0.821 0.813 0.806 0.798 0.790

110 006 668 098 297 269

05 79 82 33 61 13

-0.358 0.355 0.352 0.349 0.345 0.342

909 831 650 369 987 507

88 +1511 3862 +698 5235 +302 7584 12 1498 3489 722 0961 312 9808 55 1484 8474 745 4604 323 1167 09 1470 8869 768 6007 333 1592 71 1456 4764 791 5020 343 1011 43 1441 6272 814 1511 352 9359

25 +0.536 474 02 26 0.550 659 48 27 0.564 686 14 28 0.578 550 15 29 0.592 247 78 30 0.605 775 43

-0.782 0.773 0.764 0.755 0.746 0.737

015 539 843 930 803 464

46 29 34 37 14 41

-0.338 0.335 0.331 0.327 0.323 0.319

929 254 484 620 662 613

37 +1426 3538 +836 5369 +362 6578 66 1410 6717 858 6521 372 2624 52 1394 5964 880 4923 381 7465 14 1378 1426 902 0558 391 1086 76 1361 3232 923 3436 400 3480 59 1344 1488 944 3583 409 4654

31 +0.619 129 59 1 0.632 306 84 2 0.645 303 75 3 0.658 116 96 4 0.670 743 07 5 0.683 178 69

-0.727 0.718 0.708 0.698 0.687 0.677

916 163 206 048 691 140

88 23 12 16 97 15

-0.315 0.311 0.306 0.302 0.298 0.293

473 244 927 523 033 458

85 +1326 6273 +965 1032 +418 4620 75 1308 7643 985 5817 427 3391 46 1290 5624 1005 7970 436 0981 17 1272 0225 1025 7511 444 7406 04 1253 1437 1045 4442 453 2671 22 1233 9242 1064 8750 461 6778

6 +0.695 420 41 7 0.707 464 79 8 0.719 308 37 9 0.730 947 69 10 0.742 379 28 11 0.753 599 68

-0.666 0.655 0.644 0.633 0.621 0.609

395 460 337 030 540 872

35 24 54 04 60 14

-0.288 0.284 0.279 0.274 0.269 0.264

799 059 237 335 354 296

87 +1214 3623 +1084 0406 +469 9721 17 1194 4555 1102 9364 478 1487 29 1174 2028 1121 5567 486 2058 45 1153 6035 1139 8952 494 1413 88 1132 6573 1157 9447 501 9526 83 1111 3647 1175 6976 509 6369

027 66 010 25 823 08 469 41 952 62 . Z

-0.259 0.253 0.248 0.243 -0.237

162 953 670 315 890

58 +1089 7266 +1193 1464 +517 45 1067 7436 1210 2826 524 78 1045 4171 1227 0973 531 97 1022 7486 1243 5803 539 43 +999 7400 +1259 7202 +546

12 +0.764 605 43 -0.598 13 0.775 393 06 0.586 14 0.785 959 15 0.573 15 0.796 300 27 0.561 16 +0.806 412 99 -0.548 . . X, Y,

are in units of 10-9 a.u. per day

1912 6126 8974 0417 0409

265

FRAME BIAS, PRECESSION AND NUTATION, 2020 MATRIX ELEMENTS FOR CONVERSION FROM GCRS TO TRUE EQUINOX OF DATE Date 0h TT July

Aug.

M11 - 1

M12

M13

M21

M22 - 1

M23

M31

M32 M33 - 1

1 -1208 2 1208 3 1209 4 1210 5 1210 6 1211

-450 450 450 451 451 451

800 888 999 127 258 381

-195 195 195 196 196 196

869 +450 801 -1016 907 450 888 1017 955 451 000 1017 011 451 127 1018 068 451 258 1018 121 451 381 1019

-341 +195 868 324 195 906 311 195 955 307 196 010 314 196 067 332 196 120

-0542 0559 0573 0577 0571 0553

-192 192 192 192 192 192

7 -1212 8 1212 9 1212 10 1213 11 1213 12 1213

-451 451 451 451 451 451

487 571 633 677 710 738

-196 196 196 196 196 196

167 +451 487 -1019 203 451 571 1020 230 451 633 1020 249 451 677 1020 264 451 710 1020 276 451 738 1020

-359 +196 166 388 196 203 418 196 230 443 196 249 462 196 264 473 196 276

-0527 0498 0468 0443 0425 0414

-192 192 193 193 193 193

13 -1213 14 1213 15 1214 16 1214 17 1214 18 1215

-451 451 451 451 452 452

768 806 859 929 018 123

-196 196 196 196 196 196

289 +451 768 -1020 306 451 806 1021 329 451 859 1021 359 451 929 1021 398 452 018 1022 443 452 123 1022

-477 +196 289 473 196 306 466 196 329 456 196 359 449 196 398 446 196 443

-0410 0413 0421 0431 0439 0442

-193 193 193 193 193 193

19 -1216 20 1216 21 1217 22 1217 23 1218 24 1218

-452 452 452 452 452 452

240 359 470 563 632 675

-196 196 196 196 196 196

494 +452 240 -1023 546 452 359 1023 594 452 470 1024 634 452 563 1024 664 452 632 1024 683 452 675 1025

-452 +196 494 469 196 546 495 196 594 530 196 635 567 196 665 601 196 684

-0436 0420 0394 0360 0323 0289

-193 193 193 193 193 193

25 -1218 26 1218 27 1218 28 1219 29 1219 30 1219

-452 452 452 452 452 452

701 721 747 792 861 953

-196 196 196 196 196 196

694 +452 701 -1025 703 452 720 1025 714 452 747 1025 734 452 792 1025 764 452 860 1025 804 452 952 1026

-627 +196 695 640 196 704 641 196 715 633 196 735 621 196 764 613 196 804

-0264 0251 0250 0258 0270 0279

-193 193 193 194 194 194

31 -1220 1 1221 2 1221 3 1222 4 1222 5 1223

-453 453 453 453 453 453

062 178 289 386 463 517

-196 196 196 196 197 197

851 +453 062 -1026 901 453 177 1027 949 453 288 1027 992 453 385 1028 025 453 462 1028 049 453 517 1028

-611 +196 852 620 196 902 639 196 950 668 196 993 701 197 026 735 197 050

-0281 0272 0253 0225 0193 0159

-194 194 194 194 194 194

6 -1223 7 1223 8 1223 9 1223 10 1223 11 1223

-453 453 453 453 453 453

552 573 587 600 620 652

-197 197 197 197 197 197

064 +453 552 -1029 073 453 573 1029 079 453 586 1029 085 453 600 1029 094 453 619 1029 108 453 651 1029

-766 +197 065 790 197 075 807 197 081 816 197 087 818 197 095 814 197 109

-0128 0103 0086 0078 0076 0080

-194 194 194 194 194 194

12 -1224 13 1224 14 1224 15 1225 16 -1225

-453 453 453 453 -454

700 766 849 945 048

-197 128 +453 699 -1029 197 157 453 765 1030 197 193 453 848 1030 197 235 453 944 1030 -197 279 +454 047 -1031 Values are in units of 10 -8

-808 +197 130 801 197 158 799 197 194 803 197 236 -817 +197 281

-0087 0093 0096 0092 -0079

-194 194 194 195 -195

266

POSITION AND VELOCITY OF THE EARTH, 2020 ORIGIN AT SOLAR SYSTEM BARYCENTRE MEAN EQUATOR AND EQUINOX J 2000.0 Date h 0 T.D.B. Aug.

Sept.

Oct.

X

Y

. Y

. X

Z

. Z

16 +0.806 412 99 17 0.816 293 95 18 0.825 939 79 19 0.835 347 28 20 0.844 513 25 21 0.853 434 70

-0.548 0.536 0.523 0.510 0.497 0.484

952 276 443 459 326 048

62 19 76 09 09 79

-0.237 0.232 0.226 0.221 0.215 0.209

890 395 833 204 511 755

43 65 16 55 50 73

+999 976 952 928 904 879

7400 3952 7201 7240 4199 8247

+1259 1275 1290 1305 1320 1334

7202 +546 0409 5045 552 8897 9191 559 5819 9498 566 1111 5831 572 4706 8079 578 6545

22 +0.862 108 83 23 0.870 533 01 24 0.878 704 79 25 0.886 621 94 26 0.894 282 35 27 0.901 684 03

-0.470 0.457 0.443 0.429 0.415 0.401

631 077 392 579 643 587

32 86 60 72 35 57

-0.203 0.198 0.192 0.186 0.180 0.174

939 063 130 141 099 005

01 17 04 45 23 18

+854 829 804 778 753 727

9571 8370 4832 9119 1365 1674

+1348 1362 1374 1387 1399 1411

6166 +584 6584 0058 590 4795 9761 596 1166 5308 601 5707 6751 606 8432 4148 611 9362

28 +0.908 825 08 29 0.915 703 66 30 0.922 317 99 31 0.928 666 30 1 0.934 746 85 2 0.940 557 89

-0.387 0.373 0.358 0.344 0.329 0.314

416 133 743 249 656 967

39 78 66 94 48 16

-0.167 0.161 0.155 0.149 0.142 0.136

861 668 429 146 819 450

09 72 79 04 16 85

+701 674 648 621 594 567

0117 6752 1612 4718 6085 5721

+1422 1433 1444 1454 1464 1473

7553 +616 8523 7013 621 5938 2567 626 1626 4237 630 5602 2034 634 7878 5957 638 8460

3 +0.946 097 71 4 0.951 364 58 5 0.956 356 80 6 0.961 072 66 7 0.965 510 49 8 0.969 668 64

-0.300 0.285 0.270 0.255 0.240 0.225

185 316 362 329 219 037

86 49 98 30 50 64

-0.130 0.123 0.117 0.110 0.104 0.097

042 596 114 597 047 466

80 72 31 28 37 34

+540 512 485 457 429 401

3632 9826 4316 7121 8265 7776

+1482 1491 1499 1507 1514 1521

5990 +642 7346 2103 646 4532 4260 650 0008 2413 653 3758 6515 656 5766 6510 659 6013

9 +0.973 545 51 10 0.977 139 50 11 0.980 449 08 12 0.983 472 75 13 0.986 209 06 14 0.988 656 61

-0.209 0.194 0.179 0.163 0.148 0.132

787 474 101 673 194 669

87 38 44 38 62 69

-0.090 0.084 0.077 0.070 0.064 0.057

855 217 554 866 157 427

94 98 28 69 08 38

+373 345 316 288 259 230

5690 2042 6872 0225 2154 2726

+1528 1534 1540 1545 1550 1554

2337 +662 4478 3933 665 1135 1230 667 5959 4151 669 8919 2607 671 9978 6495 673 9094

15 +0.990 814 09 16 0.992 680 28 17 0.994 254 13 18 0.995 534 74 19 0.996 521 44 20 0.997 213 79

-0.117 0.101 0.085 0.070 0.054 0.038

103 499 864 202 517 816

19 87 56 21 81 35

-0.050 0.043 0.037 0.030 0.023 0.016

679 915 137 347 548 741

55 63 67 82 22 07

+201 172 142 113 83 54

2028 0185 7358 3748 9581 5082

+1558 1562 1564 1567 1569 1570

5708 +675 6216 0130 677 1291 9657 678 4263 4212 679 5088 3763 680 3737 8324 681 0203

21 +0.997 611 56 -0.023 102 80 -0.009 928 54 22 0.997 714 72 -0.007 382 05 -0.003 112 78 23 0.997 523 39 +0.008 341 11 +0.003 704 09 24 0.997 037 78 0.024 062 00 0.010 520 00 25 0.996 258 20 0.039 776 01 0.017 332 90 26 0.995 185 00 0.055 478 63 0.024 140 82

+25 -4 33 63 92 121

0459 4117 8518 2651 6452 9877

+1571 1572 1572 1571 1570 1569

7955 +681 4502 2747 681 6663 2799 681 6729 8210 681 4742 9064 681 0740 5431 680 4761

27 +0.993 818 58 +0.071 28 0.992 159 36 0.086 29 0.990 207 79 0.102 30 0.987 964 34 0.118 1 +0.985 429 51 +0.133 . . X, Y,

165 40 +0.030 941 78 -151 2893 +1567 7366 +679 6833 831 90 0.037 733 84 180 5472 1565 4910 678 6980 473 76 0.044 515 10 209 7589 1562 8090 677 5221 086 63 0.051 283 65 238 9222 1559 6925 676 1570 666 17 +0.058 037 61 -268 0347 +1556 1424 +674 6038 . Z are in units of 10-9 a.u. per day

267

FRAME BIAS, PRECESSION AND NUTATION, 2020 MATRIX ELEMENTS FOR CONVERSION FROM GCRS TO TRUE EQUINOX OF DATE Date 0h TT

M11 - 1

M12

M13

M21

M22 - 1

M23

M31

M32 M33 - 1

Aug. 16 -1225 17 1226 18 1226 19 1227 20 1227 21 1227

-454 454 454 454 454 454

048 147 233 295 331 345

-197 197 197 197 197 197

279 +454 047 -1031 322 454 146 1031 360 454 232 1032 387 454 294 1032 402 454 330 1032 409 454 344 1032

-817 +197 281 841 197 324 874 197 361 913 197 389 950 197 405 979 197 411

-0079 0055 -0022 +0016 0053 0082

-195 195 195 195 195 195

22 -1227 23 1227 24 1227 25 1227 26 1228 27 1228

-454 454 454 454 454 454

348 355 378 426 498 588

-197 197 197 197 197 197

410 +454 347 -1032 413 454 354 1032 423 454 377 1032 444 454 425 1033 475 454 497 1033 514 454 587 1033

-996 +197 412 999 197 415 991 197 426 979 197 446 967 197 477 962 197 516

+0099 0102 0094 0082 0070 0064

-195 195 195 195 195 195

28 -1229 29 1229 30 1230 31 1230 Sept. 1 1230 2 1231

-454 454 454 454 454 455

686 782 866 932 977 001

-197 197 197 197 197 197

557 +454 685 -1034 598 454 781 1034 635 454 865 1035 663 454 931 1035 683 454 975 1035 694 455 000 1035

-967 +197 559 982 197 601 1006 197 637 1035 197 666 1066 197 686 1095 197 697

+0069 0083 0107 0136 0167 0195

-195 195 195 195 195 195

3 -1231 4 1231 5 1231 6 1231 7 1231 8 1231

-455 455 455 455 455 455

010 010 008 011 024 053

-197 197 197 197 197 197

698 +455 009 -1035 698 455 009 1035 697 455 006 1035 698 455 009 1035 704 455 023 1035 716 455 052 1035

-1118 +197 701 1134 197 701 1141 197 700 1140 197 701 1134 197 707 1123 197 719

+0218 0234 0241 0241 0234 0223

-195 195 195 195 195 195

9 -1231 10 1231 11 1232 12 1232 13 1233 14 1233

-455 455 455 455 455 455

099 162 240 326 414 493

-197 197 197 197 197 197

736 +455 098 -1036 764 455 161 1036 797 455 238 1036 835 455 325 1037 873 455 413 1037 908 455 492 1037

-1112 +197 739 1103 197 767 1099 197 800 1103 197 838 1118 197 876 1142 197 911

+0212 0202 0198 0203 0217 0240

-196 196 196 196 196 196

15 -1234 16 1234 17 1234 18 1234 19 1234 20 1234

-455 455 455 455 455 455

555 591 603 598 592 600

-197 197 197 197 197 197

934 +455 553 -1038 950 455 590 1038 955 455 601 1038 953 455 597 1038 951 455 590 1038 954 455 598 1038

-1172 +197 938 1205 197 954 1232 197 959 1248 197 957 1249 197 954 1237 197 958

+0271 0303 0330 0346 0347 0335

-196 196 196 196 196 196

21 -1234 22 1234 23 1235 24 1235 25 1236 26 1236

-455 455 455 455 455 456

633 693 775 869 962 044

-197 197 198 198 198 198

968 +455 631 -1038 995 455 692 1038 030 455 774 1039 071 455 867 1039 111 455 960 1040 147 456 042 1040

-1217 +197 972 1196 197 998 1181 198 034 1176 198 074 1181 198 115 1195 198 150

+0315 0294 0279 0273 0277 0292

-196 196 196 196 196 196

27 -1237 28 1237 29 1237 30 1237 1 -1237

-456 456 456 456 -456

109 153 178 186 185

-198 175 +456 107 -1040 198 195 456 152 1040 198 205 456 176 1040 198 209 456 185 1041 -198 208 +456 183 -1041 Values are in units of 10 -8

-1216 +198 179 1239 198 198 1260 198 209 1277 198 213 -1286 +198 212

+0312 0335 0356 0373 +0382

-196 196 196 196 -196

Oct.

268

POSITION AND VELOCITY OF THE EARTH, 2020 ORIGIN AT SOLAR SYSTEM BARYCENTRE MEAN EQUATOR AND EQUINOX J 2000.0 Date 0h T.D.B. Oct.

Nov.

X

Y

Z

. X

. Y

. Z

1 +0.985 429 51 +0.133 666 17 +0.058 037 61 2 0.982 603 82 0.149 208 03 0.064 775 10 3 0.979 487 82 0.164 707 89 0.071 494 25 4 0.976 082 08 0.180 161 39 0.078 193 17 5 0.972 387 22 0.195 564 16 0.084 870 00 6 0.968 403 88 0.210 911 80 0.091 522 84

-268 297 326 355 383 412

0347 0940 0971 0407 9213 7346

+1556 1552 1547 1542 1537 1531

1424 +674 6038 1587 672 8628 7405 670 9346 8862 668 8188 5939 666 5151 8609 664 0227

7 +0.964 132 77 +0.226 199 90 +0.098 149 82 8 0.959 574 63 0.241 424 00 0.104 749 02 9 0.954 730 26 0.256 579 61 0.111 318 53 10 0.949 600 53 0.271 662 21 0.117 856 43 11 0.944 186 37 0.286 667 21 0.124 360 75 12 0.938 488 79 0.301 589 99 0.130 829 53

-441 470 498 527 555 583

4756 1393 7198 2106 6047 8932

+1525 1519 1511 1504 1496 1488

6843 +661 3406 0608 658 4679 9865 655 4027 4569 652 1435 4666 648 6882 0098 645 0338

13 +0.932 508 89 +0.316 425 83 +0.137 260 75 14 0.926 247 91 0.331 169 98 0.143 652 38 15 0.919 707 24 0.345 817 59 0.150 002 34 16 0.912 888 44 0.360 363 81 0.156 308 52 17 0.905 793 34 0.374 803 73 0.162 568 80 18 0.898 423 95 0.389 132 53 0.168 781 06

-612 640 668 695 723 750

0654 1072 0014 7271 2606 5790

+1479 1469 1459 1449 1438 1427

0795 +641 1770 6692 637 1143 7730 632 8423 3881 628 3585 5163 623 6621 1643 618 7548

19 +0.890 782 54 +0.403 345 46 +0.174 943 21 20 0.882 871 56 0.417 437 89 0.181 053 20 21 0.874 693 58 0.431 405 37 0.187 109 05 22 0.866 251 28 0.445 243 57 0.193 108 85 23 0.857 547 38 0.458 948 33 0.199 050 74 24 0.848 584 63 0.472 515 56 0.204 932 94

-777 804 831 857 883 909

6616 4920 0590 3558 3786 1249

+1415 1403 1390 1377 1363 1349

3435 +613 6403 0687 608 3244 3550 602 8139 2168 597 1152 6663 591 2341 7134 585 1755

25 +0.839 365 81 +0.485 941 28 +0.210 753 68 26 0.829 893 70 0.499 221 60 0.216 511 25 27 0.820 171 10 0.512 352 65 0.222 203 98 28 0.810 200 85 0.525 330 64 0.227 830 21 29 0.799 985 77 0.538 151 82 0.233 388 32 30 0.789 528 73 0.550 812 46 0.238 876 69

-934 959 984 1009 1033 1057

5932 7820 6898 3142 6536 7057

+1335 1320 1305 1290 1274 1257

3664 +578 9439 6319 572 5428 5150 565 9753 0207 559 2438 1527 552 3507 9143 545 2981

31 +0.778 832 62 +0.563 308 88 +0.244 293 75 1 0.767 900 35 0.575 637 41 0.249 637 92 2 0.756 734 86 0.587 794 40 0.254 907 64 3 0.745 339 12 0.599 776 22 0.260 101 36 4 0.733 716 15 0.611 579 24 0.265 217 54 5 0.721 868 99 0.623 199 83 0.270 254 64

-1081 1104 1128 1150 1173 1195

4678 9373 1114 9863 5580 8219

+1241 1224 1207 1189 1171 1152

3083 +538 0875 3368 530 7205 0012 523 1979 3024 515 5207 2410 507 6892 8167 499 7036

6 +0.709 800 75 +0.634 634 36 +0.275 211 10 7 0.697 514 61 0.645 879 20 0.280 085 40 8 0.685 013 79 0.656 930 68 0.284 875 97 9 0.672 301 61 0.667 785 17 0.289 581 27 10 0.659 381 48 0.678 438 96 0.294 199 72 11 0.646 256 95 0.688 888 37 0.298 729 74

-1217 1239 1260 1281 1302 1322

7723 4029 7060 6729 2927 5519

+1134 1114 1095 1075 1055 1034

0289 +491 5639 8771 483 2694 3597 474 8196 4752 466 2136 2219 457 4499 5984 448 5273

12 +0.632 931 70 +0.699 13 0.619 409 59 0.709 14 0.605 694 67 0.718 15 0.591 791 22 0.728 16 +0.577 703 68 +0.737 . . Y, X,

129 69 +0.303 169 73 -1342 4343 +1013 6049 +439 4448 159 24 0.307 518 10 1361 9209 992 2444 430 2023 973 38 0.311 773 25 1380 9913 970 5237 420 8016 568 55 0.315 933 62 1399 6252 948 4544 411 2463 941 36 +0.319 997 68 -1417 8049 +926 0529 +401 5426 . Z are in units of 10-9 a.u. per day

269

FRAME BIAS, PRECESSION AND NUTATION, 2020 MATRIX ELEMENTS FOR CONVERSION FROM GCRS TO TRUE EQUINOX OF DATE Date 0h TT Oct.

Nov.

M11 - 1

M12

M13

M21

M22 - 1

M23

M31

M32 M33 - 1

1 -1237 2 1237 3 1237 4 1237 5 1237 6 1237

-456 456 456 456 456 456

185 180 179 187 211 252

-198 198 198 198 198 198

208 +456 183 -1041 206 456 178 1041 206 456 177 1041 210 456 186 1041 220 456 209 1041 238 456 250 1041

-1286 +198 212 1288 198 210 1281 198 210 1267 198 213 1248 198 224 1228 198 241

+0382 0383 0376 0363 0344 0324

-196 196 196 196 196 196

7 -1238 8 1238 9 1239 10 1239 11 1239 12 1240

-456 456 456 456 456 456

310 384 468 556 639 710

-198 198 198 198 198 198

263 +456 309 -1041 295 456 382 1041 332 456 467 1042 370 456 555 1042 406 456 638 1043 437 456 708 1043

-1210 +198 267 1196 198 298 1190 198 335 1192 198 373 1203 198 409 1223 198 440

+0305 0291 0284 0286 0297 0316

-197 197 197 197 197 197

13 -1240 14 1240 15 1240 16 1240 17 1240 18 1240

-456 456 456 456 456 456

759 786 792 790 796 826

-198 198 198 198 198 198

458 +456 758 -1043 470 456 784 1043 472 456 790 1043 472 456 789 1043 474 456 795 1043 487 456 824 1043

-1246 +198 462 1267 198 473 1281 198 476 1281 198 476 1266 198 478 1239 198 491

+0339 0361 0374 0374 0359 0332

-197 197 197 197 197 197

19 -1241 20 1241 21 1242 22 1242 23 1243 24 1243

-456 456 457 457 457 457

885 973 079 187 287 370

-198 198 198 198 198 198

513 +456 884 -1044 551 456 972 1044 597 457 077 1045 644 457 186 1045 688 457 286 1046 724 457 369 1046

-1209 +198 517 1182 198 555 1165 198 600 1159 198 647 1165 198 691 1177 198 727

+0302 0275 0257 0251 0256 0269

-197 197 197 197 197 197

25 -1244 26 1244 27 1244 28 1244 29 1244 30 1244

-457 457 457 457 457 457

432 473 497 510 518 529

-198 198 198 198 198 198

750 +457 431 -1046 768 457 472 1046 779 457 496 1047 785 457 509 1047 788 457 517 1047 793 457 527 1047

-1194 +198 754 1210 198 772 1221 198 782 1226 198 788 1223 198 792 1212 198 796

+0285 0300 0312 0317 0314 0302

-198 198 198 198 198 198

31 -1244 1 1245 2 1245 3 1245 4 1246 5 1246

-457 457 457 457 457 457

549 583 634 704 790 887

-198 198 198 198 198 198

801 +457 547 -1047 816 457 581 1047 839 457 633 1047 869 457 703 1047 906 457 788 1048 948 457 886 1048

-1194 +198 805 1170 198 819 1145 198 842 1120 198 872 1100 198 909 1087 198 951

+0284 0261 0235 0210 0190 0176

-198 198 198 198 198 198

6 -1247 7 1247 8 1248 9 1248 10 1248 11 1249

-457 458 458 458 458 458

990 090 180 252 303 334

-198 199 199 199 199 199

993 +457 989 -1049 036 458 089 1049 075 458 178 1050 107 458 250 1050 129 458 301 1050 142 458 332 1050

-1082 +198 996 1087 199 039 1099 199 078 1117 199 110 1135 199 132 1148 199 145

+0171 0175 0187 0204 0222 0235

-198 198 198 198 198 198

12 -1249 13 1249 14 1249 15 1249 16 -1250

-458 458 458 458 -458

352 371 406 470 567

-199 150 +458 351 -1050 199 159 458 370 1051 199 174 458 405 1051 199 202 458 469 1051 -199 244 +458 565 -1051 Values are in units of 10 -8

-1151 +199 153 1140 199 162 1116 199 177 1084 199 205 -1053 +199 246

+0238 0227 0203 0171 +0139

-198 198 198 198 -198

270

POSITION AND VELOCITY OF THE EARTH, 2020 ORIGIN AT SOLAR SYSTEM BARYCENTRE MEAN EQUATOR AND EQUINOX J 2000.0 Date h 0 T.D.B. Nov.

Dec.

.

X

Y

. X

Z

. Y

. Z

16 +0.577 703 68 +0.737 941 36 +0.319 997 68 17 0.563 436 68 0.747 088 57 0.323 964 00 18 0.548 994 91 0.756 007 14 0.327 831 21 19 0.534 383 16 0.764 694 23 0.331 598 02 20 0.519 606 19 0.773 147 18 0.335 263 26 21 0.504 668 77 0.781 363 43 0.338 825 77

-1417 1435 1452 1469 1485 1501

8049 +926 0529 +401 5426 5176 903 3380 391 6983 7555 880 3293 381 7218 5157 857 0450 371 6217 7986 833 5011 361 4056 6060 809 7104 351 0799

22 +0.489 575 65 +0.789 340 60 +0.342 284 51 23 0.474 331 54 0.797 076 35 0.345 638 45 24 0.458 941 16 0.804 568 46 0.348 886 61 25 0.443 409 19 0.811 814 77 0.352 028 08 26 0.427 740 31 0.818 813 20 0.355 061 94 27 0.411 939 22 0.825 561 71 0.357 987 33

-1516 1531 1546 1560 1573 1586

9400 +785 6836 +340 6503 8028 761 4297 330 1212 1959 736 9565 319 4969 1202 712 2711 308 7809 5764 687 3800 297 9765 5650 662 2892 287 0872

28 +0.396 010 57 +0.832 058 33 +0.360 803 41 29 0.379 959 05 0.838 301 17 0.363 509 37 30 0.363 789 31 0.844 288 34 0.366 104 44 1 0.347 506 03 0.850 018 02 0.368 587 84 2 0.331 113 88 0.855 488 42 0.370 958 84 3 0.314 617 56 0.860 697 77 0.373 216 69

-1599 1611 1622 1633 1644 1654

0864 +637 0045 +276 1156 1409 611 5309 265 0644 7287 585 8727 253 9361 8492 560 0337 242 7323 5020 534 0168 231 4546 6850 507 8243 220 1042

4 +0.298 021 76 +0.865 644 32 +0.375 360 68 5 0.281 331 24 0.870 326 36 0.377 390 09 6 0.264 550 78 0.874 742 15 0.379 304 20 7 0.247 685 25 0.878 890 02 0.381 102 31 8 0.230 739 57 0.882 768 27 0.382 783 71 9 0.213 718 79 0.886 375 28 0.384 347 70

-1664 1673 1682 1690 1698 1705

3954 +481 4581 +208 6818 6294 454 9198 197 1880 3810 428 2112 185 6231 6434 401 3338 173 9872 4077 374 2904 162 2811 6631 347 0844 150 5051

10 +0.196 628 05 +0.889 709 44 +0.385 793 59 11 0.179 472 64 0.892 769 21 0.387 120 69 12 0.162 257 99 0.895 553 16 0.388 328 37 13 0.144 989 67 0.898 059 97 0.389 416 03 14 0.127 673 39 0.900 288 52 0.390 383 13 15 0.110 314 93 0.902 237 87 0.391 229 21

-1712 1718 1724 1729 1733 1737

3968 +319 7212 +138 6605 5948 292 2088 126 7497 2424 264 5586 114 7764 3259 236 7857 102 7460 8340 208 9089 90 6661 7597 180 9490 78 5454

16 +0.092 920 14 +0.903 907 30 +0.391 953 93 17 0.075 494 85 0.905 296 28 0.392 557 01 18 0.058 044 84 0.906 404 49 0.393 038 27 19 0.040 575 84 0.907 231 76 0.393 397 61 20 0.023 093 50 0.907 778 05 0.393 635 00 21 0.005 603 39 0.908 043 42 0.393 750 46

-1741 1743 1746 1747 1748 1749

1013 +152 9272 8612 124 8638 0451 96 7757 6604 68 6775 7149 40 5811 2158 +12 4961

22 23 24 25 26 27

-0.011 0.029 0.046 0.064 0.081 0.099

889 378 858 325 773 196

00 +0.908 028 04 +0.393 744 05 21 0.907 732 14 0.393 615 89 87 0.907 156 03 0.393 366 12 66 0.906 300 11 0.392 994 93 29 0.905 164 82 0.392 502 53 53 0.903 750 68 0.391 889 17

-1749 1748 1747 1745 1743 1740

1699 5832 4608 8081 6301 9317

-15 43 71 99 127 155

28 29 30 31 32

-0.116 0.133 0.151 0.168 -0.185 . X,

590 949 268 542 767

20 +0.902 058 26 +0.391 18 0.900 088 17 0.390 38 0.897 841 07 0.389 75 0.895 317 64 0.388 25 +0.892 518 59 +0.387 . . Y, Z

-1737 1733 1729 1725 -1719

7179 9934 7623 0273 7901

-183 210 238 266 -293

155 300 326 231 018

12 69 18 93 28

+66 54 42 29 17 +5

3933 2191 0312 8366 6415 4510

5689 6060 6082 5685 4803 3380

-6 18 31 43 55 67

7304 8992 0513 1834 2924 3752

1362 8707 5382 1361 6627

-79 91 103 115 -127

4293 4526 4435 4006 3237

are in units of 10-9 a.u. per day

271

FRAME BIAS, PRECESSION AND NUTATION, 2020 MATRIX ELEMENTS FOR CONVERSION FROM GCRS TO TRUE EQUINOX OF DATE Date 0h TT

M11 - 1

M12

M13

M21

M22 - 1

M23

M31

M32 M33 - 1

Nov. 16 -1250 17 1251 18 1251 19 1252 20 1253 21 1253

-458 458 458 458 459 459

567 688 822 951 064 155

-199 199 199 199 199 199

244 +458 565 -1051 296 458 687 1052 354 458 821 1053 410 458 950 1053 459 459 063 1054 499 459 154 1054

-1053 +199 246 1029 199 299 1017 199 357 1018 199 413 1029 199 462 1046 199 502

+0139 0114 0102 0103 0114 0130

-198 199 199 199 199 199

22 -1253 23 1254 24 1254 25 1254 26 1254 27 1254

-459 459 459 459 459 459

223 271 306 334 363 398

-199 199 199 199 199 199

528 +459 222 -1054 549 459 270 1055 565 459 305 1055 577 459 333 1055 589 459 361 1055 605 459 397 1055

-1064 +199 531 1078 199 552 1086 199 567 1087 199 580 1079 199 592 1064 199 608

+0147 0161 0170 0170 0162 0147

-199 199 199 199 199 199

28 -1255 29 1255 30 1256 1 1256 2 1257 3 1257

-459 459 459 459 459 459

447 513 597 698 812 933

-199 199 199 199 199 199

626 +459 446 -1055 655 459 512 1056 691 459 596 1056 735 459 697 1057 785 459 811 1057 837 459 932 1058

-1044 +199 629 1021 199 657 999 199 694 980 199 737 968 199 787 965 199 839

+0127 0104 0081 0062 0049 0046

-199 199 199 199 200 200

4 -1258 5 1259 6 1259 7 1260 8 1260 9 1260

-460 460 460 460 460 460

052 162 255 327 379 416

-199 199 199 200 200 200

889 +460 051 -1058 936 460 161 1059 977 460 254 1059 008 460 326 1060 030 460 378 1060 047 460 415 1060

-971 +199 891 986 199 939 1007 199 979 1029 200 011 1049 200 033 1060 200 049

+0052 0066 0086 0109 0128 0139

-200 200 200 200 200 200

10 -1260 11 1260 12 1261 13 1261 14 1262 15 1263

-460 460 460 460 460 460

449 492 557 652 776 919

-200 200 200 200 200 200

061 +460 448 -1060 080 460 491 1060 108 460 556 1061 149 460 650 1061 203 460 775 1062 265 460 918 1062

-1059 +200 064 1046 200 082 1024 200 110 998 200 151 977 200 205 966 200 267

+0138 0125 0103 0076 0054 0043

-200 200 200 200 200 201

16 -1264 17 1264 18 1265 19 1265 20 1266 21 1266

-461 461 461 461 461 461

067 203 318 408 474 523

-200 200 200 200 200 200

329 +461 065 -1063 388 461 202 1064 438 461 317 1064 477 461 406 1064 506 461 473 1065 527 461 522 1065

-969 +200 331 984 200 391 1007 200 441 1034 200 480 1058 200 509 1077 200 530

+0045 0059 0082 0109 0133 0152

-201 201 201 201 201 201

22 -1266 23 1266 24 1267 25 1267 26 1267 27 1268

-461 461 461 461 461 461

562 598 639 691 759 844

-200 200 200 200 200 200

544 +461 560 -1065 560 461 597 1065 578 461 638 1066 600 461 690 1066 630 461 758 1066 667 461 843 1067

-1089 +200 547 1092 200 563 1088 200 581 1078 200 603 1064 200 632 1050 200 669

+0163 0167 0162 0152 0138 0123

-201 201 201 201 201 201

28 -1268 29 1269 30 1270 31 1270 32 -1271

-461 462 462 462 -462

946 063 188 313 430

-200 711 +461 945 -1067 200 762 462 062 1068 200 816 462 187 1068 200 870 462 312 1069 -200 921 +462 429 -1069 Values are in units of 10 -8

-1038 +200 714 1033 200 764 1036 200 819 1049 200 873 -1072 +200 924

+0111 0105 0108 0121 +0143

-201 202 202 202 -202

Dec.

272

APPARENT PLACES OF POLARIS, 2020

Date

FOR 0h TERRESTRIAL TIME Mag. 2.02  Ursae Minoris FEBRUARY MARCH JANUARY Right Declination Right Declination Right Declination Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' "

Sp. F8v APRIL Right Declination Ascension h m s º ' "

1

2

57

56 +89

21

04

2

57

02 +89

21

09

2

56

08 +89

21

08

2

55

25 +89

21

01

2

2

57

54 +89

21

04

2

57

01 +89

21

09

2

56

06 +89

21

08

2

55

24 +89

21

01

3

2

57

53 +89

21

04

2

56

59 +89

21

09

2

56

04 +89

21

07

2

55

23 +89

21

01

4

2

57

51 +89

21

05

2

56

57 +89

21

09

2

56

03 +89

21

07

2

55

22 +89

21

01

5

2

57

50 +89

21

05

2

56

55 +89

21

09

2

56

02 +89

21

07

2

55

21 +89

21

00

6

2

57

48 +89

21

05

2

56

54 +89

21

09

2

55

60 +89

21

07

2

55

20 +89

21

00

7

2

57

47 +89

21

05

2

56

52 +89

21

09

2

55

58 +89

21

07

2

55

19 +89

20

60

8

2

57

46 +89

21

05

2

56

50 +89

21

09

2

55

56 +89

21

07

2

55

18 +89

20

60

9

2

57

44 +89

21

06

2

56

48 +89

21

09

2

55

55 +89

21

07

2

55

17 +89

20

59

10

2

57

43 +89

21

06

2

56

46 +89

21

09

2

55

53 +89

21

07

2

55

17 +89

20

59

11

2

57

42 +89

21

06

2

56

44 +89

21

09

2

55

51 +89

21

06

2

55

16 +89

20

59

12

2

57

40 +89

21

06

2

56

41 +89

21

09

2

55

49 +89

21

06

2

55

16 +89

20

58

13

2

57

38 +89

21

07

2

56

39 +89

21

09

2

55

48 +89

21

06

2

55

16 +89

20

58

14

2

57

36 +89

21

07

2

56

37 +89

21

09

2

55

47 +89

21

06

2

55

15 +89

20

58

15

2

57

34 +89

21

07

2

56

36 +89

21

09

2

55

45 +89

21

05

2

55

15 +89

20

58

16

2

57

32 +89

21

07

2

56

34 +89

21

09

2

55

44 +89

21

05

2

55

14 +89

20

57

17

2

57

30 +89

21

07

2

56

32 +89

21

09

2

55

43 +89

21

05

2

55

14 +89

20

57

18

2

57

29 +89

21

07

2

56

31 +89

21

09

2

55

42 +89

21

05

2

55

13 +89

20

57

19

2

57

27 +89

21

07

2

56

29 +89

21

09

2

55

40 +89

21

05

2

55

13 +89

20

56

20

2

57

25 +89

21

08

2

56

27 +89

21

09

2

55

39 +89

21

05

2

55

12 +89

20

56

21

2

57

24 +89

21

08

2

56

25 +89

21

09

2

55

37 +89

21

04

2

55

11 +89

20

56

22

2

57

22 +89

21

08

2

56

23 +89

21

09

2

55

36 +89

21

04

2

55

11 +89

20

55

23

2

57

21 +89

21

08

2

56

21 +89

21

09

2

55

34 +89

21

04

2

55

11 +89

20

55

24

2

57

19 +89

21

08

2

56

19 +89

21

09

2

55

33 +89

21

04

2

55

11 +89

20

55

25

2

57

17 +89

21

08

2

56

17 +89

21

08

2

55

31 +89

21

03

2

55

11 +89

20

54

26

2

57

15 +89

21

08

2

56

15 +89

21

08

2

55

30 +89

21

03

2

55

11 +89

20

54

27

2

57

13 +89

21

09

2

56

13 +89

21

08

2

55

29 +89

21

03

2

55

11 +89

20

54

28

2

57

11 +89

21

09

2

56

11 +89

21

08

2

55

28 +89

21

02

2

55

11 +89

20

53

29

2

57

09 +89

21

09

2

56 9.2

21 7.9

2

55

27 +89

21

02

2

55

11 +89

20

53

30

2

57

06 +89

21

09

2

55

26 +89

21

02

2

55

11 +89

20

53

31

2

57

04 +89

21

09

2

55

25 +89

21

02

89

273

APPARENT PLACES OF POLARIS, 2020

Date

FOR 0h TERRESTRIAL TIME Mag. 2.02  Ursae Minoris MAY JUNE JULY Declination Right Right Declination Right Declination Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' "

Sp. F8v AUGUST Right Declination Ascension h m s º ' "

1

2

55

11 +89

20

53

2

55

30 +89

20

44

2

56

13 +89

20

39

2

57

14 +89

20

38

2

2

55

11 +89

20

52

2

55

31 +89

20

44

2

56

15 +89

20

39

2

57

16 +89

20

38

3

2

55

11 +89

20

52

2

55

32 +89

20

44

2

56

17 +89

20

38

2

57

18 +89

20

38

4

2

55

11 +89

20

52

2

55

33 +89

20

43

2

56

20 +89

20

38

2

57

20 +89

20

38

5

2

55

11 +89

20

52

2

55

35 +89

20

43

2

56

22 +89

20

38

2

57

22 +89

20

38

6

2

55

11 +89

20

51

2

55

36 +89

20

43

2

56

23 +89

20

38

2

57

24 +89

20

38

7

2

55

12 +89

20

51

2

55

38 +89

20

43

2

56

25 +89

20

38

2

57

25 +89

20

38

8

2

55

12 +89

20

51

2

55

39 +89

20

42

2

56

27 +89

20

38

2

57

27 +89

20

38

9

2

55

13 +89

20

50

2

55

40 +89

20

42

2

56

29 +89

20

38

2

57

29 +89

20

38

10

2

55

14 +89

20

50

2

55

42 +89

20

42

2

56

30 +89

20

38

2

57

31 +89

20

38

11

2

55

14 +89

20

50

2

55

43 +89

20

42

2

56

32 +89

20

38

2

57

33 +89

20

38

12

2

55

15 +89

20

49

2

55

44 +89

20

42

2

56

33 +89

20

38

2

57

35 +89

20

38

13

2

55

15 +89

20

49

2

55

45 +89

20

42

2

56

35 +89

20

38

2

57

38 +89

20

39

14

2

55

16 +89

20

49

2

55

46 +89

20

41

2

56

37 +89

20

38

2

57

40 +89

20

39

15

2

55

16 +89

20

49

2

55

47 +89

20

41

2

56

39 +89

20

38

2

57

42 +89

20

39

16

2

55

16 +89

20

48

2

55

49 +89

20

41

2

56

41 +89

20

38

2

57

44 +89

20

39

17

2

55

17 +89

20

48

2

55

50 +89

20

41

2

56

43 +89

20

37

2

57

46 +89

20

39

18

2

55

17 +89

20

48

2

55

52 +89

20

40

2

56

46 +89

20

37

2

57

48 +89

20

39

19

2

55

18 +89

20

47

2

55

54 +89

20

40

2

56

48 +89

20

37

2

57

50 +89

20

39

20

2

55

18 +89

20

47

2

55

55 +89

20

40

2

56

50 +89

20

37

2

57

52 +89

20

40

21

2

55

19 +89

20

47

2

55

57 +89

20

40

2

56

52 +89

20

37

2

57

54 +89

20

40

22

2

55

20 +89

20

47

2

55

59 +89

20

40

2

56

54 +89

20

38

2

57

55 +89

20

40

23

2

55

21 +89

20

46

2

56

01 +89

20

40

2

56

56 +89

20

38

2

57

57 +89

20

40

24

2

55

22 +89

20

46

2

56

02 +89

20

40

2

56

57 +89

20

38

2

57

59 +89

20

40

25

2

55

23 +89

20

46

2

56

04 +89

20

40

2

56

59 +89

20

38

2

58

01 +89

20

40

26

2

55

24 +89

20

45

2

56

05 +89

20

39

2

57

01 +89

20

38

2

58

04 +89

20

40

27

2

55

25 +89

20

45

2

56

07 +89

20

39

2

57

03 +89

20

38

2

58

06 +89

20

41

28

2

55

26 +89

20

45

2

56

08 +89

20

39

2

57

05 +89

20

38

2

58

08 +89

20

41

29

2

55

27 +89

20

45

2

56

10 +89

20

39

2

57

07 +89

20

38

2

58

10 +89

20

41

30

2

55

28 +89

20

45

2

56

11 +89

20

39

2

57

09 +89

20

38

2

58

12 +89

20

41

31

2

55

29 +89

20

44

2

57

12 +89

20

38

2

58

14 +89

20

41

274

APPARENT PLACES OF POLARIS, 2020

Date

FOR 0h TERRESTRIAL TIME Mag. 2.02  Ursae Minoris SEPTEMBER OCTOBER NOVEMBER Declination Right Declination Right Declination Right Ascension Ascension Ascension h m s º ' " h m s º ' " h m s º ' "

Sp. F8v DECEMBER Right Declination Ascension h m s º ' "

1

2

58

15 +89

20

42

2

59

05 +89

20

49

2

59

36 +89

20

60

2

59

38 +89

21

11

2

2

58

17 +89

20

42

2

59

06 +89

20

50

2

59

36 +89

21

00

2

59

38 +89

21

11

3

2

58

19 +89

20

42

2

59

07 +89

20

50

2

59

37 +89

21

01

2

59

38 +89

21

12

4

2

58

20 +89

20

42

2

59

09 +89

20

50

2

59

38 +89

21

01

2

59

37 +89

21

12

5

2

58

22 +89

20

42

2

59

10 +89

20

50

2

59

39 +89

21

01

2

59

37 +89

21

12

6

2

58

24 +89

20

43

2

59

11 +89

20

51

2

59

39 +89

21

02

2

59

36 +89

21

13

7

2

58

26 +89

20

43

2

59

13 +89

20

51

2

59

40 +89

21

02

2

59

35 +89

21

13

8

2

58

28 +89

20

43

2

59

14 +89

20

51

2

59

40 +89

21

03

2

59

34 +89

21

14

9

2

58

29 +89

20

43

2

59

16 +89

20

52

2

59

40 +89

21

03

2

59

33 +89

21

14

10

2

58

31 +89

20

43

2

59

17 +89

20

52

2

59

40 +89

21

03

2

59

33 +89

21

14

11

2

58

33 +89

20

44

2

59

18 +89

20

52

2

59

40 +89

21

04

2

59

32 +89

21

14

12

2

58

35 +89

20

44

2

59

19 +89

20

53

2

59

40 +89

21

04

2

59

31 +89

21

15

13

2

58

37 +89

20

44

2

59

20 +89

20

53

2

59

40 +89

21

04

2

59

31 +89

21

15

14

2

58

39 +89

20

44

2

59

21 +89

20

54

2

59

40 +89

21

05

2

59

30 +89

21

15

15

2

58

41 +89

20

45

2

59

22 +89

20

54

2

59

41 +89

21

05

2

59

29 +89

21

16

16

2

58

42 +89

20

45

2

59

23 +89

20

54

2

59

41 +89

21

05

2

59

29 +89

21

16

17

2

58

43 +89

20

45

2

59

24 +89

20

54

2

59

41 +89

21

06

2

59

28 +89

21

16

18

2

58

45 +89

20

46

2

59

25 +89

20

55

2

59

42 +89

21

06

2

59

27 +89

21

17

19

2

58

46 +89

20

46

2

59

26 +89

20

55

2

59

42 +89

21

07

2

59

26 +89

21

17

20

2

58

48 +89

20

46

2

59

27 +89

20

55

2

59

42 +89

21

07

2

59

24 +89

21

17

21

2

58

50 +89

20

46

2

59

29 +89

20

56

2

59

42 +89

21

07

2

59

23 +89

21

18

22

2

58

52 +89

20

46

2

59

30 +89

20

56

2

59

41 +89

21

08

2

59

22 +89

21

18

23

2

58

54 +89

20

47

2

59

31 +89

20

57

2

59

41 +89

21

08

2

59

20 +89

21

18

24

2

58

55 +89

20

47

2

59

31 +89

20

57

2

59

41 +89

21

09

2

59

19 +89

21

18

25

2

58

57 +89

20

47

2

59

32 +89

20

57

2

59

40 +89

21

09

2

59

18 +89

21

19

26

2

58

59 +89

20

48

2

59

33 +89

20

58

2

59

40 +89

21

09

2

59

17 +89

21

19

27

2

58

60 +89

20

48

2

59

33 +89

20

58

2

59

39 +89

21

10

2

59

16 +89

21

19

28

2

59

01 +89

20

48

2

59

34 +89

20

59

2

59

39 +89

21

10

2

59

15 +89

21

19

29

2

59

02 +89

20

49

2

59

34 +89

20

59

2

59

39 +89

21

10

2

59

13 +89

21

20

30

2

59

04 +89

20

49

2

59

35 +89

20

59

2

59

39 +89

21

11

2

59

12 +89

21

20

2

59

35 +89

20

60

2 2

59 59

11 +89 10 +89

21 21

20 21

31 32

275

POLARIS TABLE, 2020 LST

0 a0

h

1h b0

a0

2h b0

a0

3h b0

a0

4h b0

a0

5h b0

a0

b0

m             0 -27.8 +27.6 -34.0 +19.4 -37.8 +9.8 -39.1 -0.5 -37.6 -10.7 -33.5 -20.2 3 28.2 27.2 34.3 18.9 38.0 9.3 39.1 1.0 37.5 11.2 33.3 20.6 6 28.5 26.8 34.5 18.5 38.1 8.8 39.0 1.5 37.3 11.7 33.0 21.0 9 28.9 26.5 34.7 18.0 38.2 8.3 39.0 2.0 37.2 12.2 32.7 21.5 12 29.2 26.1 35.0 17.5 38.3 7.8 39.0 2.5 37.0 12.7 32.4 21.9 15 18 21 24 27

-29.6 29.9 30.2 30.6 30.9

+25.7 25.3 24.9 24.5 24.1

-35.2 35.4 35.6 35.8 36.0

+17.1 16.6 16.1 15.7 15.2

-38.4 38.5 38.6 38.7 38.7

+7.3 6.8 6.3 5.7 5.2

-39.0 38.9 38.9 38.8 38.7

-3.1 3.6 4.1 4.6 5.1

-36.8 36.6 36.5 36.3 36.1

-13.2 13.6 14.1 14.6 15.1

-32.2 31.9 31.6 31.2 30.9

-22.3 22.8 23.2 23.6 24.0

30 33 36 39 42

-31.2 31.5 31.8 32.1 32.4

+23.7 23.3 22.8 22.4 22.0

-36.2 36.4 36.6 36.8 37.0

+14.7 14.2 13.7 13.3 12.8

-38.8 38.9 38.9 39.0 39.0

+4.7 4.2 3.7 3.2 2.6

-38.7 38.6 38.5 38.4 38.3

-5.6 6.1 6.7 7.2 7.7

-35.9 35.7 35.5 35.2 35.0

-15.6 16.0 16.5 17.0 17.4

-30.6 30.3 30.0 29.6 29.3

-24.4 24.8 25.2 25.6 26.0

45 48 51 54 57 60

-32.7 32.9 33.2 33.5 33.7 -34.0

+21.6 21.1 20.7 20.3 19.8 +19.4

-37.1 37.3 37.4 37.6 37.7 -37.8

+12.3 11.8 11.3 10.8 10.3 +9.8

-39.0 39.0 39.1 39.1 39.1 -39.1

+2.1 1.6 1.1 +0.6 0.1 -0.5

-38.2 38.1 38.0 37.9 37.7 -37.6

-8.2 8.7 9.2 9.7 10.2 -10.7

-34.8 34.6 34.3 34.1 33.8 -33.5

-17.9 18.4 18.8 19.3 19.7 -20.2

-29.0 28.6 28.3 27.9 27.5 -27.2

-26.4 26.7 27.1 27.5 27.9 -28.2

Lat. ° 0 10 20 30

a1

b1

a1

b1

a1

b1

a1

b1

a1

b1

a1

b1

-.1 -.1 -.1 -.1

-.3 -.2 -.2 -.1

-.1 -.1 .0 .0

-.2 -.2 -.2 -.1

.0 .0 .0 .0

-.1 -.1 -.1 -.1

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

+.1 +.1 +.1 +.1

-.1 -.1 .0 .0

+.2 +.2 +.2 +.1

40 45 50 55

.0 .0 .0 .0

-.1 .0 .0 +.1

.0 .0 .0 .0

-.1 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

+.1 .0 .0 .0

60 62 64 66

+.1 +.1 +.1 +.1

+.1 +.2 +.2 +.2

.0 .0 .0 +.1

+.1 +.1 +.2 +.2

.0 .0 .0 .0

+.1 +.1 +.1 +.1

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

-.1 -.1 -.1 -.1

.0 .0 +.0 +.1

-.1 -.1 -.2 -.2

Month

a2

b2

a2

b2

a2

b2

a2

b2

a2

b2

a2

b2

Jan. Feb. Mar.

+.2 +.1 -.1

-.1 -.2 -.3

+.2 +.1 .0

-.1 -.2 -.3

+.2 +.2 +.1

.0 -.2 -.3

+.2 +.2 +.2

.0 -.1 -.3

+.2 +.2 +.2

+.1 -.1 -.2

+.1 +.3 +.3

+.1 .0 -.1

Apr. May June

-.2 -.3 -.3

-.3 -.2 .0

-.1 -.3 -.3

-.3 -.2 -.1

-.1 -.2 -.3

-.3 -.3 -.2

.0 -.1 -.2

-.3 -.3 -.3

+.1 .0 -.2

-.3 -.4 -.3

+.2 +.1 -.1

-.3 -.4 -.3

July Aug. Sept.

-.3 -.1 .0

+.1 +.2 +.3

-.3 -.2 .0

.1 +.2 +.3

-.3 -.2 -.1

.0 +.1 +.3

-.3 -.3 -.2

-.1 +.1 +.2

-.3 -.3 -.2

-.2 .0 +.2

-.2 -.3 -.3

-.2 -.1 +.1

Oct. Nov. Dec.

+.2 +.4 +.5

+.3 +.2 .0

+.2 +.3 +.5

+.3 +.3 +.1

+.1 +.3 +.4

+.3 +.3 +.3

.0 +.2 +.3

+.3 +.4 +.4

-.1 .1 +.2

+.3 +.4 +.4

-.2 -.1 +.1

+.3 +.4 +.5

Latitude = Corrected observed altitude of Polaris + a 0 + a 1 + a 2 Azimuth of Polaris = (b 0 + b 1 + b 2)/ cos (latitude)

276

POLARIS TABLE, 2020 LST

6 a0

h

h

h

7 b0

a0

h

8 b0

a0

9 b0

a0

10 b0

a0

h

h

11 b0

a0

b0

m             0 -27.2 -28.2 -18.9 -34.3 -9.4 -38.0 +0.7 -39.1 +10.8 -37.5 +20.1 -33.4 3 26.8 28.6 18.5 34.5 8.9 38.1 1.2 39.1 11.3 37.3 20.6 33.1 6 26.4 28.9 18.0 34.8 8.4 38.2 1.7 39.0 11.8 37.2 21.0 32.8 9 26.0 29.3 17.6 35.0 7.9 38.3 2.3 39.0 12.3 37.0 21.4 32.6 12 25.7 29.6 17.1 35.2 7.4 38.4 2.8 39.0 12.7 36.9 21.8 32.3 15 18 21 24 27

-25.3 24.9 24.5 24.1 23.7

-29.9 30.3 30.6 30.9 31.2

-16.7 16.2 15.7 15.3 14.8

-35.5 35.7 35.9 36.1 36.3

-6.9 6.4 5.9 5.4 4.9

-38.5 38.6 38.7 38.7 38.8

+3.3 3.8 4.3 4.8 5.3

-38.9 38.9 38.8 38.8 38.7

+13.2 13.7 14.2 14.7 15.1

-36.7 36.5 36.3 36.1 35.9

+22.3 22.7 23.1 23.5 23.9

-32.0 31.7 31.4 31.1 30.8

30 33 36 39 42

-23.3 22.8 22.4 22.0 21.6

-31.5 31.8 32.1 32.4 32.7

-14.3 13.8 13.3 12.9 12.4

-36.5 36.6 36.8 37.0 37.1

-4.4 3.9 3.4 2.9 2.3

-38.9 38.9 39.0 39.0 39.0

+5.8 6.3 6.8 7.3 7.8

-38.6 38.5 38.4 38.3 38.2

+15.6 16.1 16.5 17.0 17.4

-35.7 35.5 35.3 35.1 34.9

+24.3 24.7 25.1 25.5 25.9

-30.5 30.1 29.8 29.5 29.2

45 48 51 54 57 60

-21.1 20.7 20.3 19.8 19.4 -18.9

-33.0 33.3 33.5 33.8 34.0 -34.3

-11.9 11.4 10.9 10.4 9.9 -9.4

-37.3 37.5 37.6 37.7 37.9 -38.0

-1.8 1.3 -0.8 -+0.3 0.2 +0.7

-39.0 39.1 39.1 39.1 39.1 -39.1

+8.3 8.8 9.3 9.8 10.3 +10.8

-38.1 38.0 37.9 37.8 37.6 -37.5

+17.9 18.4 18.8 19.2 19.7 +20.1

-34.6 34.4 34.1 33.9 33.6 -33.4

+26.3 26.6 27.0 27.4 27.7 +28.1

-28.8 28.5 28.1 27.8 27.4 -27.0

Lat. ° 0 10 20 30

a1

b1

a1

b1

a1

b1

a1

b1

a1

b1

a1

b1

-.1 -.1 -.1 -.1

+.3 +.2 +.2 +.1

-.2 -.2 -.1 -.1

+.2 +.2 +.2 +.1

-.2 -.2 -.2 -.1

+.1 +.1 +.1 +.1

-.3 -.2 -.2 -.1

.0 .0 .0 .0

-.2 -.2 -.2 -.1

-.1 -.1 -.1 -.1

-.2 -.2 -.1 -.1

-.2 -.2 -.2 -.1

40 45 50 55

.0 .0 .0 .0

+.1 .0 .0 -.1

-.1 .0 .0 .0

+.1 .0 .0 .0

-.1 .0 .0 +.0

.0 .0 .0 .0

-.1 .0 .0 +.1

.0 .0 .0 .0

-.1 .0 .0 .0

.0 .0 .0 .0

-.1 .0 .0 .0

-.1 .0 .0 .0

60 62 64 66

+.1 +.1 +.1 +.1

-.1 -.2 -.2 -.2

+.1 +.1 +.1 +.2

-.1 -.1 -.2 -.2

+.1 +.1 +.2 +.2

-.1 -.1 -.1 -.1

+.1 +.2 +.2 +.2

.0 .0 .0 .0

+.1 +.1 +.2 +.2

+.1 +.1 +.1 +.1

+.1 +.1 +.1 +.2

+.1 +.1 +.2 +.2

Month

a2

b2

a2

b2

a2

b2

a2

b2

a2

b2

a2

b2

Jan. Feb. Mar.

+.1 +.2 +.3

+.2 +.1 -.1

+.1 +.2 +.3

+.2 +.1 -.1

.0 +.2 +.3

+.2 +.2 +.1

.0 +.1 +.3

+.2 +.2 +.2

-.1 +.1 +.2

+.2 +.2 +.2

-.1 .0 +.1

+.1 +.3 +.3

Apr. May June

+.3 +.2 .0

-.2 -.3 -.3

+.3 +.2 +.1

-.2 -.3 -.3

+.3 +.3 +.2

-.1 -.2 -.3

+.4 +.3 +.3

.0 -.1 -.2

+.3 +.4 +.3

+.1 .0 -.2

+.3 +.4 +.3

+.2 +.1 -.1

July Aug. Sept.

-.1 -.2 -.3

-.3 -.1 .0

-.1 -.2 -.3

-.3 -.1 .0

.0 -.1 -.3

-.3 -.2 -.1

+.1 -.1 -.2

-.3 -.3 -.2

+.2 .0 -.2

-.3 -.3 -.2

+.2 +.1 -.1

-.2 -.3 -.3

Oct. Nov. Dec.

-.3 -.2 .0

+.2 +.4 +.5

-.3 -.3 -.1

+.2 +.4 +.5

-.3 -.3 -.3

+.1 +.3 +.4

-.3 -.4 -.4

.0 +.2 +.3

-.3 -.4 -.4

-.1 .1 +.2

-.3 -.4 -.5

-.2 -.1 +.1

Latitude = Corrected observed altitude of Polaris + a 0 + a 1 + a 2 Azimuth of Polaris = (b 0 + b 1 + b 2)/ cos (latitude)

277

POLARIS TABLE, 2020 h

LST

13h

12 a0

b0

a0

14h b0

a0

15h b0

a0

16h b0

a0

17h b0

a0

b0

m             0 +28.1 -27.0 +34.1 -18.9 +37.9 -9.5 +39.1 +0.5 +37.6 +10.4 +33.7 +19.7 3 28.4 26.7 34.4 18.5 38.0 9.1 39.1 1.0 37.5 10.9 33.4 20.1 6 28.8 26.3 34.6 18.0 38.1 8.6 39.0 1.5 37.4 11.4 33.2 20.6 9 29.1 25.9 34.8 17.6 38.2 8.1 39.0 2.0 37.2 11.9 32.9 21.0 12 29.5 25.5 35.1 17.1 38.3 7.6 39.0 2.5 37.0 12.3 32.6 21.4 15 18 21 24 27

+29.8 30.1 30.4 30.8 31.1

-25.2 24.8 24.4 24.0 23.6

+35.3 35.5 35.7 35.9 36.1

-16.7 16.2 15.7 15.3 14.8

+38.4 38.5 38.6 38.7 38.7

-7.1 6.6 6.1 5.6 5.1

+39.0 38.9 38.9 38.8 38.8

+3.0 3.5 4.0 4.5 5.0

+36.9 36.7 36.5 36.4 36.2

+12.8 13.3 13.8 14.2 14.7

+32.3 32.0 31.7 31.4 31.1

+21.8 22.3 22.7 23.1 23.5

30 33 36 39 42

+31.4 31.7 32.0 32.3 32.5

-23.2 22.8 22.3 21.9 21.5

+36.3 36.5 36.7 36.8 37.0

-14.3 13.9 13.4 12.9 12.5

+38.8 38.9 38.9 39.0 39.0

-4.6 4.1 3.6 3.1 2.6

+38.7 38.6 38.5 38.4 38.3

+5.5 6.0 6.5 7.0 7.5

+36.0 35.8 35.6 35.3 35.1

+15.2 15.6 16.1 16.6 17.0

+30.8 30.5 30.2 29.9 29.5

+23.9 24.3 24.7 25.1 25.5

45 48 51 54 57 60

+32.8 33.1 33.4 33.6 33.9 +34.1

-21.1 20.7 20.2 19.8 19.4 -18.9

+37.2 37.3 37.5 37.6 37.7 +37.9

-12.0 11.5 11.0 10.5 10.0 -9.5

+39.0 39.0 39.1 39.1 39.1 +39.1

-2.1 1.6 1.1 -0.6 -+0.1 +0.5

+38.2 38.1 38.0 37.9 37.8 +37.6

+8.0 8.5 8.9 9.4 9.9 +10.4

+34.9 34.7 34.4 34.2 33.9 +33.7

+17.5 17.9 18.4 18.8 19.3 +19.7

+29.2 28.9 28.5 28.2 27.8 +27.4

+25.8 26.2 26.6 27.0 27.3 +27.7

Lat. ° 0 10 20 30

a1

b1

a1

b1

a1

b1

a1

b1

a1

b1

a1

b1

-.1 -.1 -.1 -.1

-.3 -.2 -.2 -.1

-.1 -.1 .0 .0

-.2 -.2 -.2 -.1

.0 .0 .0 .0

-.1 -.1 -.1 -.1

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

+.1 +.1 +.1 +.1

-.1 -.1 .0 .0

+.2 +.2 +.2 +.1

40 45 50 55

.0 .0 .0 .0

-.1 .0 .0 +.1

.0 .0 .0 .0

-.1 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

+.1 .0 .0 .0

60 62 64 66

+.1 +.1 +.1 +.1

+.1 +.2 +.2 +.2

.0 .0 .0 +.1

+.1 +.1 +.2 +.2

.0 .0 .0 .0

+.1 +.1 +.1 +.1

.0 .0 .0 .0

.0 .0 .0 .0

.0 .0 .0 .0

-.1 -.1 -.1 -.1

.0 .0 +.0 +.1

-.1 -.1 -.2 -.2

Month

a2

b2

a2

b2

a2

b2

a2

b2

a2

b2

a2

b2

Jan. Feb. Mar.

-.2 -.1 +.1

+.1 +.2 +.3

-.2 -.1 .0

+.1 +.2 +.3

-.2 -.2 -.1

.0 +.2 +.3

-.2 -.2 -.2

.0 +.1 +.3

-.2 -.2 -.2

-.1 +.1 +.2

-.1 -.3 -.3

-.1 .0 +.1

Apr. May June

+.2 +.3 +.3

+.3 +.2 .0

+.1 +.3 +.3

+.3 +.2 +.1

.1 +.2 +.3

+.3 +.3 +.2

.0 +.1 +.2

+.4 +.3 +.3

-.1 .0 +.2

+.3 +.4 +.3

-.2 -.1 +.1

+.3 +.4 +.3

July Aug. Sept.

+.3 +.1 .0

-.1 -.2 -.3

+.3 +.2 .0

-.1 -.2 -.3

+.3 +.2 +.1

.0 -.1 -.3

+.3 +.3 +.2

+.1 -.1 -.2

+.3 +.3 +.2

+.2 .0 -.2

+.2 +.3 +.3

+.2 +.1 -.1

Oct. Nov. Dec.

-.2 -.4 -.5

-.3 -.2 .0

-.2 -.3 -.5

-.3 -.3 -.1

-.1 -.3 -.4

-.3 -.3 -.3

.0 -.2 -.3

-.3 -.4 -.4

+.1 -.1 -.2

-.3 -.4 -.4

+.2 +.1 -.1

-.3 -.4 -.5

Latitude = Corrected observed altitude of Polaris + a 0 + a 1 + a 2 Azimuth of Polaris = (b 0 + b 1 + b 2)/ cos (latitude)

278

POLARIS TABLE, 2020 h

LST

19h

18 a0

b0

a0

20h b0

a0

21 b0

a0

h

22h b0

a0

23h b0

a0

b0

m             0 +27.4 +27.7 +19.3 +33.8 +9.9 +37.7 -0.2 +39.1 -10.3 +37.8 -19.7 +33.8 3 27.1 28.0 18.9 34.1 9.4 37.9 0.7 39.1 10.8 37.6 20.2 33.6 6 26.7 28.4 18.5 34.3 8.9 38.0 1.2 39.1 11.3 37.5 20.6 33.3 9 26.3 28.7 18.0 34.6 8.4 38.1 1.7 39.1 11.8 37.3 21.1 33.0 12 26.0 29.1 17.5 34.8 7.9 38.2 2.2 39.0 12.3 37.2 21.5 32.8 15 18 21 24 27

+25.6 25.2 24.8 24.4 24.0

+29.4 29.7 30.1 30.4 30.7

+17.1 16.6 16.2 15.7 15.2

+35.0 35.3 35.5 35.7 35.9

+7.4 6.9 6.4 5.9 5.4

+38.3 38.4 38.5 38.6 38.7

-2.7 3.3 3.8 4.3 4.8

+39.0 39.0 38.9 38.9 38.8

-12.8 13.2 13.7 14.2 14.7

+37.0 36.9 36.7 36.5 36.3

-21.9 22.3 22.8 23.2 23.6

+32.5 32.2 31.9 31.6 31.3

30 33 36 39 42

+23.6 23.2 22.8 22.4 21.9

+31.0 31.3 31.6 31.9 32.2

+14.8 14.3 13.8 13.3 12.9

+36.1 36.3 36.5 36.7 36.8

+4.9 4.4 3.9 3.4 2.9

+38.7 38.8 38.9 38.9 39.0

-5.3 5.8 6.3 6.8 7.3

+38.8 38.7 38.6 38.5 38.4

-15.2 15.6 16.1 16.6 17.0

+36.1 35.9 35.7 35.5 35.3

-24.0 24.4 24.8 25.2 25.6

+31.0 30.7 30.3 30.0 29.7

45 48 51 54 57 60

+21.5 21.1 20.7 20.2 19.8 +19.3

+32.5 32.8 33.1 33.3 33.6 +33.8

+12.4 11.9 11.4 10.9 10.4 +9.9

+37.0 37.2 37.3 37.5 37.6 +37.7

+2.4 1.9 1.3 0.8 +0.3 -0.2

+39.0 39.0 39.0 39.1 39.1 +39.1

-7.8 8.3 8.8 9.3 9.8 -10.3

+38.3 38.2 38.1 38.0 37.9 +37.8

-17.5 17.9 18.4 18.8 19.3 -19.7

+35.1 34.8 34.6 34.3 34.1 +33.8

-26.0 26.3 26.7 27.1 27.5 -27.8

+29.3 29.0 28.6 28.3 27.9 +27.6

Lat. ° 0 10 20 30

a1

b1

a1

b1

a1

b1

a1

b1

a1

b1

a1

b1

-.1 -.1 -.1 -.1

+.3 +.2 +.2 +.1

-.2 -.2 -.1 -.1

+.2 +.2 +.2 +.1

-.2 -.2 -.2 -.1

+.1 +.1 +.1 +.1

-.3 -.2 -.2 -.1

.0 .0 .0 .0

-.2 -.2 -.2 -.1

-.1 -.1 -.1 -.1

-.2 -.2 -.1 -.1

-.2 -.2 -.2 -.1

40 45 50 55

.0 .0 .0 .0

+.1 .0 .0 -.1

-.1 .0 .0 .0

+.1 .0 .0 .0

-.1 .0 .0 +.0

.0 .0 .0 .0

-.1 .0 .0 +.1

.0 .0 .0 .0

-.1 .0 .0 .0

.0 .0 .0 .0

-.1 .0 .0 .0

-.1 .0 .0 .0

60 62 64 66

+.1 +.1 +.1 +.1

-.1 -.2 -.2 -.2

+.1 +.1 +.1 +.2

-.1 -.1 -.2 -.2

+.1 +.1 +.2 +.2

-.1 -.1 -.1 -.1

+.1 +.2 +.2 +.2

.0 .0 .0 .0

+.1 +.1 +.2 +.2

+.1 +.1 +.1 +.1

+.1 +.1 +.1 +.2

+.1 +.1 +.2 +.2

Month

a2

b2

a2

b2

a2

b2

a2

b2

a2

b2

a2

b2

Jan. Feb. Mar.

-.1 -.2 -.3

-.2 -.1 +.1

-.1 -.2 -.3

-.2 -.1 .0

.0 -.2 -.3

-.2 -.2 -.1

.0 -.1 -.3

-.2 -.2 -.2

+.1 -.1 -.2

-.2 -.2 -.2

+.1 .0 -.1

-.1 -.3 -.3

Apr. May June

-.3 -.2 .0

+.2 +.3 +.3

-.3 -.2 -.1

+.1 +.3 +.3

-.3 -.3 -.2

.1 +.2 +.3

-.4 -.3 -.3

.0 +.1 +.2

-.3 -.4 -.3

-.1 .0 +.2

-.3 -.4 -.3

-.2 -.1 +.1

July Aug. Sept.

+.1 +.2 +.3

+.3 +.1 .0

.1 +.2 +.3

+.3 +.2 .0

.0 +.1 +.3

+.3 +.2 +.1

-.1 +.1 +.2

+.3 +.3 +.2

-.2 .0 +.2

+.3 +.3 +.2

-.2 -.1 +.1

+.2 +.3 +.3

Oct. Nov. Dec.

+.3 +.2 .0

-.2 -.4 -.5

+.3 +.3 +.1

-.2 -.3 -.5

+.3 +.3 +.3

-.1 -.3 -.4

+.3 +.4 +.4

.0 -.2 -.3

+.3 +.4 +.4

+.1 -.1 -.2

+.3 +.4 +.5

+.2 +.1 -.1

Latitude = Corrected observed altitude of Polaris + a 0 + a 1 + a 2 Azimuth of Polaris = (b 0 + b 1 + b 2)/ cos (latitude)

PART - III SUNRISE, SUNSET AND MOONRISE, MOONSET

280

SUNRISE, 2020 LOCAL MEAN TIME OF SUNRISE (SUN'S UPPER LIMB) AND BEGINNING OF MORNING TWILIGHT ON THE MERIDIAN OF GREENWICH To obtain the standard time at any station, add four minutes for each degree if the station is west of the standard meridian, or deduct four minutes for each degree if the station is east of the standard meridian. In India, to obtain I.S.T., add 4 x ( 82º.5 -  ) mins. or deduct 4 x (  - 82º.5 ) mins. as the station is west or east of 82º.5 E. Longitude. Lat. 0º

10º

30º

20º

35º

40º

45º

50º

52º

54º

56º

58º

60º

Date h m h m h m h m h m h m h m h m h m h m h m h m h m Jan.

1 5 9 13 17 21

6 6 6 6 6 6

00 01 03 05 06 08

6 6 6 6 6 6

17 18 20 21 22 22

6 6 6 6 6 6

35 36 37 38 38 38

6 6 6 6 6 6

56 57 57 57 56 55

7 7 7 7 7 7

08 08 09 08 07 06

7 7 7 7 7 7

22 22 22 21 19 17

7 7 7 7 7 7

38 38 37 36 34 31

7 7 7 7 7 7

59 58 57 54 51 48

8 8 8 8 8 7

08 07 06 03 00 56

8 8 8 8 8 8

19 18 16 13 09 04

8 8 8 8 8 8

31 30 27 24 19 14

8 8 8 8 8 8

46 44 41 37 31 25

9 9 8 8 8 8

02 00 56 51 45 38

25 29 2 6 10 14

6 6 6 6 6 6

09 09 10 11 11 11

6 6 6 6 6 6

23 23 22 22 21 20

6 6 6 6 6 6

37 36 35 34 32 30

6 6 6 6 6 6

54 52 50 47 45 41

7 7 6 6 6 6

04 01 59 55 52 48

7 7 7 7 7 6

15 12 08 04 00 55

7 7 7 7 7 7

28 24 19 14 09 03

7 7 7 7 7 7

43 38 33 27 20 13

7 7 7 7 7 7

51 45 39 33 26 18

7 7 7 7 7 7

59 53 46 39 31 23

8 8 7 7 7 7

08 01 54 46 38 29

8 8 8 7 7 7

18 11 03 54 45 35

8 8 8 8 7 7

30 22 13 03 53 42

18 22 26 Mar. 1 5 9

6 6 6 6 6 6

11 10 10 09 08 07

6 6 6 6 6 6

19 18 16 14 12 10

6 6 6 6 6 6

28 25 22 20 16 13

6 6 6 6 6 6

38 34 30 26 21 17

6 6 6 6 6 6

43 39 34 29 24 18

6 6 6 6 6 6

50 44 39 33 27 21

6 6 6 6 6 6

57 51 44 37 30 23

7 6 6 6 6 6

06 59 51 43 34 26

7 7 6 6 6 6

10 02 54 45 36 27

7 7 6 6 6 6

15 06 57 48 38 28

7 7 7 6 6 6

20 10 00 51 40 30

7 7 7 6 6 6

25 15 04 54 43 32

7 7 7 6 6 6

31 20 09 57 46 34

13 17 21 25 29 Apr. 2

6 6 6 6 6 6

06 05 04 03 01 00

6 6 6 6 5 5

08 06 03 01 59 57

6 6 6 5 5 5

10 06 03 59 56 53

6 6 6 5 5 5

12 07 02 57 53 48

6 6 6 5 5 5

13 07 02 56 51 45

6 6 6 5 5 5

14 08 01 55 48 42

6 6 6 5 5 5

16 08 01 53 46 38

6 6 6 5 5 5

17 09 00 51 42 34

6 6 6 5 5 5

18 09 00 50 41 32

6 6 5 5 5 5

19 09 59 49 39 30

6 6 5 5 5 5

20 09 59 48 38 27

6 6 5 5 5 5

21 09 58 47 36 24

6 6 5 5 5 5

22 10 57 45 33 21

Feb.

BEGINNING OF MORNING TWILIGHT h m h m h m h m h m h m h m h m h m h m h m h m h m Jan.

1 9 17 25 2 10

4 4 4 4 4 5

45 49 53 56 58 00

5 5 5 5 5 5

01 05 07 09 10 10

5 5 5 5 5 5

16 19 21 21 20 17

5 5 5 5 5 5

31 32 33 31 28 24

5 5 5 5 5 5

37 39 38 36 32 26

5 5 5 5 5 5

45 45 44 41 35 28

5 5 5 5 5 5

52 52 50 45 39 30

6 5 5 5 5 5

00 59 56 50 42 31

6 6 5 5 5 5

03 02 58 52 43 31

6 6 6 5 5 5

06 05 01 54 44 31

6 6 6 5 5 5

10 08 04 56 45 31

6 6 6 5 5 5

14 12 06 58 46 31

6 6 6 6 5 5

18 16 09 00 47 30

18 26 Mar. 5 13 21 29 Apr. 6

5 5 4 4 4 4 4

00 00 59 57 55 53 50

5 5 5 4 4 4 4

08 06 02 58 54 49 44

5 5 5 4 4 4 4

14 09 03 57 50 42 35

5 5 5 4 4 4 4

18 10 02 52 43 32 21

5 5 5 4 4 4 4

19 10 00 49 37 25 13

5 5 4 4 4 4 4

19 09 57 44 30 16 02

5 5 4 4 4 4 3

19 07 53 38 22 05 47

5 5 4 4 4 3 3

18 03 47 29 10 50 29

5 5 4 4 4 3 3

17 01 44 25 04 42 19

5 4 4 4 3 3 3

16 59 40 20 58 34 08

5 4 4 4 3 3 2

15 57 36 14 50 24 56

5 4 4 4 3 3 2

13 54 32 08 41 12 40

5 4 4 4 3 2 2

12 50 26 00 31 59 21

Feb.

281

SUNSET, 2020 LOCAL MEAN TIME OF SUNSET (SUN'S UPPER LIMB) AND ENDING OF EVENING TWILIGHT ON THE MERIDIAN OF GREENWICH To obtain the standard time at any station, add four minutes for each degree if the station is west of the standard meridian, or deduct four minutes for each degree if the station is east of the standard meridian. In India, to obtain I.S.T., add 4 x ( 82º.5 - O ) mins. or deduct 4 x ( O - 82º.5 ) mins. as the station is west or east of 82º.5 E. Longitude. Lat. 0º

10º

20º

30º

35º

40º

45º

50º

52º

54º

56º

58º

60º

Date h m h m h m h m h m h m h m h m h m h m h m h m h m Jan.

1 5 9 13 17 21

18 18 18 18 18 18

07 09 11 12 14 15

17 17 17 17 17 18

50 52 54 56 58 00

17 17 17 17 17 17

32 34 37 40 42 45

17 17 17 17 17 17

11 14 17 20 24 27

16 17 17 17 17 17

59 02 05 09 13 17

16 16 16 16 17 17

45 48 52 56 01 05

16 16 16 16 16 16

29 32 37 41 46 52

16 16 16 16 16 16

08 13 17 23 29 35

15 16 16 16 16 16

59 03 08 14 20 27

15 15 15 16 16 16

48 53 58 04 11 18

15 15 15 15 16 16

36 41 47 54 01 09

15 15 15 15 15 15

21 27 34 41 49 58

15 15 15 15 15 15

04 11 18 26 35 45

25 29 2 6 10 14

18 18 18 18 18 18

16 17 17 18 18 18

18 18 18 18 18 18

02 04 05 06 07 08

17 17 17 17 17 17

47 50 52 54 57 59

17 17 17 17 17 17

31 34 38 41 44 47

17 17 17 17 17 17

21 25 29 33 37 41

17 17 17 17 17 17

10 15 20 24 29 34

16 17 17 17 17 17

57 03 08 14 20 26

16 16 16 17 17 17

41 48 55 02 09 16

16 16 16 16 17 17

34 41 49 56 04 11

16 16 16 16 16 17

26 34 42 50 58 06

16 16 16 16 16 17

17 25 34 43 52 00

16 16 16 16 16 16

07 16 25 35 45 54

15 16 16 16 16 16

55 05 15 26 36 47

18 22 26 Mar. 1 5 9

18 18 18 18 18 18

17 17 16 16 15 14

18 18 18 18 18 18

09 10 10 11 11 11

18 18 18 18 18 18

00 02 04 05 07 08

17 17 17 17 18 18

51 54 57 59 02 05

17 17 17 17 17 18

45 49 52 56 59 03

17 17 17 17 17 18

39 43 48 52 57 01

17 17 17 17 17 17

31 37 42 48 53 59

17 17 17 17 17 17

23 29 36 43 49 56

17 17 17 17 17 17

18 26 33 40 48 55

17 17 17 17 17 17

14 22 30 38 46 53

17 17 17 17 17 17

09 18 26 35 44 52

17 17 17 17 17 17

04 13 23 32 41 50

16 17 17 17 17 17

58 08 18 28 39 49

13 17 21 25 29 Apr. 2

18 18 18 18 18 18

13 11 10 09 08 07

18 18 18 18 18 18

11 11 11 11 11 11

18 18 18 18 18 18

09 10 11 13 14 15

18 18 18 18 18 18

07 10 12 15 17 20

18 18 18 18 18 18

06 10 13 16 19 22

18 18 18 18 18 18

05 09 13 18 22 26

18 18 18 18 18 18

04 09 14 19 24 29

18 18 18 18 18 18

02 09 15 21 28 34

18 18 18 18 18 18

02 09 16 23 29 36

18 18 18 18 18 18

01 09 16 24 31 39

18 18 18 18 18 18

00 08 17 25 33 41

17 18 18 18 18 18

59 08 17 26 35 44

17 18 18 18 18 18

58 08 18 28 38 47

Feb.

END OF EVENING TWILIGHT h m h m h m h m h m h m h m h m h m h m h m h m h m Jan.

1 9 17 25 2 10

19 19 19 19 19 19

22 25 27 29 29 29

19 19 19 19 19 19

05 09 12 15 17 19

18 18 18 19 19 19

50 55 59 04 08 11

18 18 18 18 18 19

36 42 48 54 59 05

18 18 18 18 18 19

29 35 42 49 56 03

18 18 18 18 18 19

22 29 36 44 52 01

18 18 18 18 18 18

15 22 30 40 49 59

18 18 18 18 18 18

07 15 24 35 46 58

18 18 18 18 18 18

04 12 22 33 45 58

18 18 18 18 18 18

00 09 19 31 44 58

17 18 18 18 18 18

57 06 17 29 43 58

17 18 18 18 18 18

53 02 14 28 43 59

17 17 18 18 18 18

49 59 11 26 42 59

18 26 Mar. 5 13 21 29 Apr. 6

19 19 19 19 19 19 19

27 26 24 21 19 17 15

19 19 19 19 19 19 19

20 20 21 21 21 21 21

19 19 19 19 19 19 19

14 17 20 22 25 27 30

19 19 19 19 19 19 19

11 16 21 27 32 38 44

19 19 19 19 19 19 19

10 17 24 30 38 45 53

19 19 19 19 19 19 20

09 18 27 35 45 54 04

19 19 19 19 19 20 20

10 20 31 42 54 06 19

19 19 19 19 20 20 20

11 24 37 51 05 21 38

19 19 19 19 20 20 20

12 26 40 55 11 29 47

19 19 19 20 20 20 20

13 28 44 00 18 37 58

19 19 19 20 20 20 21

14 31 48 06 26 48 12

19 19 19 20 20 20 21

16 34 53 13 35 59 27

19 19 19 20 20 21 21

18 37 58 21 46 14 47

Feb.

282

SUNRISE, 2020 LOCAL MEAN TIME OF SUNRISE (SUN'S UPPER LIMB) AND BEGINNING OF MORNING TWILIGHT ON THE MERIDIAN OF GREENWICH To obtain the standard time at any station, add four minutes for each degree if the station is west of the standard meridian, or deduct four minutes for each degree if the station is east of the standard meridian. In India, to obtain I.S.T., add 4 x ( 82º.5 -  ) mins. or deduct 4 x (  - 82º.5 ) mins. as the station is west or east of 82º.5 E. Longitude. Lat. 0º

10º

30º

20º

35º

40º

45º

50º

52º

54º

56º

58º

60º

Date h m h m h m h m h m h m h m h m h m h m h m h m h m Apr.

2 6 10 14 18 22

6 5 5 5 5 5

00 59 58 57 56 55

5 5 5 5 5 5

57 54 52 50 48 46

5 5 5 5 5 5

53 49 46 43 39 37

5 5 5 5 5 5

48 43 38 34 30 25

5 5 5 5 5 5

45 40 34 29 24 19

5 5 5 5 5 5

42 36 29 23 17 12

5 5 5 5 5 5

38 31 24 17 10 03

5 5 5 5 5 4

34 25 17 08 00 53

5 5 5 5 4 4

32 23 14 05 56 48

5 5 5 5 4 4

30 20 10 01 51 42

5 5 5 4 4 4

27 17 06 56 46 36

5 5 5 4 4 4

24 13 02 51 40 30

5 5 4 4 4 4

21 09 57 45 34 22

26 30 May 4 8 12 16

5 5 5 5 5 5

54 54 53 53 53 53

5 5 5 5 5 5

44 43 42 40 39 39

5 5 5 5 5 5

34 31 29 27 25 23

5 5 5 5 5 5

22 18 14 11 08 06

5 5 5 5 4 4

14 10 06 02 59 56

5 5 4 4 4 4

06 01 56 52 47 44

4 4 4 4 4 4

57 50 45 39 34 30

4 4 4 4 4 4

45 38 31 24 18 12

4 4 4 4 4 4

39 32 24 17 10 04

4 4 4 4 4 3

33 25 17 09 02 55

4 4 4 4 3 3

27 18 09 00 52 45

4 4 3 3 3 3

19 09 59 50 41 33

4 4 3 3 3 3

11 00 49 39 29 19

20 24 28 1 5 9

5 5 5 5 5 5

53 53 54 54 55 56

5 5 5 5 5 5

38 38 38 38 38 39

5 5 5 5 5 5

22 21 20 20 20 20

5 5 5 4 4 4

04 02 00 59 59 58

4 4 4 4 4 4

53 51 49 47 46 46

4 4 4 4 4 4

40 37 35 33 32 31

4 4 4 4 4 4

25 22 19 16 15 13

4 4 3 3 3 3

07 03 59 56 53 51

3 3 3 3 3 3

59 54 49 46 43 41

3 3 3 3 3 3

49 43 39 35 31 29

3 3 3 3 3 3

38 32 26 22 18 15

3 3 3 3 3 2

25 18 12 07 02 59

3 3 2 2 2 2

10 02 55 49 44 40

13 17 21 25 29 3

5 5 5 5 6 6

57 57 58 59 00 01

5 5 5 5 5 5

39 40 41 42 43 44

5 5 5 5 5 5

20 21 22 23 24 25

4 4 5 5 5 5

58 59 00 01 02 04

4 4 4 4 4 4

46 46 47 48 49 51

4 4 4 4 4 4

31 31 31 33 34 36

4 4 4 4 4 4

13 13 13 15 16 19

3 3 3 3 3 3

50 50 51 52 54 57

3 3 3 3 3 3

40 39 40 41 43 46

3 3 3 3 3 3

28 27 28 29 31 34

3 3 3 3 3 3

14 13 13 15 17 21

2 2 2 2 3 3

57 56 56 58 01 05

2 2 2 2 2 2

37 36 36 38 41 45

Jun.

July

BEGINNING OF MORNING TWILIGHT h m h m h m h m h m h m h m h m h m h m h m h m h m Apr.

6 14 22 30 May 8 16

4 4 4 4 4 4

50 47 45 43 41 40

4 4 4 4 4 4

44 39 34 30 26 24

4 4 4 4 4 4

35 27 20 14 08 03

4 4 4 3 3 3

21 11 01 51 42 35

4 4 3 3 3 3

13 00 48 36 26 16

4 3 3 3 3 2

02 47 32 18 05 53

3 3 3 2 2 2

47 30 12 54 36 20

24 1 9 17 25 3 11

4 4 4 4 4 4 4

40 40 41 42 44 46 48

4 4 4 4 4 4 4

22 21 21 22 24 26 29

3 3 3 3 3 4 4

59 57 56 57 59 01 05

3 3 3 3 3 3 3

29 25 22 22 24 28 33

3 3 3 2 3 3 3

09 03 00 59 01 05 11

2 2 2 2 2 2 2

42 34 29 28 29 34 42

2 1 1 1 1 1 2

05 0 56 52 44 40 42 49 01

June

July

3 3 2 2 1 1

29 06 43 19 54 27

3 2 2 2 1 0

19 55 29 00 28 47

3 2 2 1 0

08 41 11 36 48

2 2 1 0

56 2 40 2 21 24 2 03 1 34 48 1 14 58

283

SUNSET, 2020 LOCAL MEAN TIME OF SUNSET (SUN'S UPPER LIMB) AND ENDING OF EVENING TWILIGHT ON THE MERIDIAN OF GREENWICH To obtain the standard time at any station, add four minutes for each degree if the station is west of the standard meridian, or deduct four minutes for each degree if the station is east of the standard meridian. In India, to obtain I.S.T., add 4 x ( 82º.5 - O ) mins. or deduct 4 x ( O - 82º.5 ) mins. as the station is west or east of 82º.5 E. Longitude. Lat. 0º

10º

20º

30º

35º

40º

45º

50º

52º

54º

56º

58º

60º

Date h m h m h m h m h m h m h m h m h m h m h m h m h m Apr.

2 6 10 14 18 22

18 18 18 18 18 18

07 06 04 03 03 02

18 18 18 18 18 18

11 10 10 10 11 11

18 18 18 18 18 18

15 16 17 18 19 21

18 18 18 18 18 18

20 22 24 27 29 32

18 18 18 18 18 18

22 26 29 32 35 38

18 18 18 18 18 18

26 30 34 38 42 46

18 18 18 18 18 18

29 35 40 45 50 55

18 18 18 18 18 19

34 40 47 53 59 05

18 18 18 18 19 19

36 43 50 57 04 10

18 18 18 19 19 19

39 46 53 01 08 16

18 18 18 19 19 19

41 49 57 06 14 22

18 18 19 19 19 19

44 53 02 11 20 29

18 18 19 19 19 19

47 57 07 17 27 37

26 30 May 4 8 12 16

18 18 18 18 18 18

01 01 00 00 00 00

18 18 18 18 18 18

11 12 12 13 13 14

18 18 18 18 18 18

22 23 25 26 28 30

18 18 18 18 18 18

34 37 40 42 45 47

18 18 18 18 18 18

42 45 48 51 55 58

18 18 18 19 19 19

50 54 58 02 06 10

19 19 19 19 19 19

00 05 10 15 19 24

19 19 19 19 19 19

12 18 24 30 36 41

19 19 19 19 19 19

17 24 31 37 43 50

19 19 19 19 19 19

23 31 38 45 52 59

19 19 19 19 20 20

30 38 46 54 02 09

19 19 19 20 20 20

38 47 56 04 13 21

19 19 20 20 20 20

47 56 06 16 26 35

20 24 28 June 1 5 9

18 18 18 18 18 18

00 00 01 02 02 03

18 18 18 18 18 18

15 16 17 18 19 20

18 18 18 18 18 18

31 33 34 36 37 39

18 18 18 18 18 19

50 52 55 57 59 00

19 19 19 19 19 19

01 04 06 09 11 13

19 19 19 19 19 19

13 17 20 23 26 28

19 19 19 19 19 19

28 32 36 40 43 46

19 19 19 20 20 20

47 52 57 01 04 08

19 20 20 20 20 20

56 01 06 11 15 18

20 20 20 20 20 20

05 11 17 22 27 30

20 20 20 20 20 20

16 23 29 35 40 44

20 20 20 20 20 21

29 37 44 50 56 00

20 20 21 21 21 21

44 53 01 08 15 20

13 17 21 25 29 3

18 18 18 18 18 18

04 05 06 06 07 08

18 18 18 18 18 18

21 22 23 24 25 25

18 18 18 18 18 18

40 41 42 43 43 44

19 19 19 19 19 19

02 03 04 05 05 05

19 19 19 19 19 19

15 16 17 18 18 18

19 19 19 19 19 19

30 31 32 33 33 32

19 19 19 19 19 19

48 49 50 51 51 50

20 20 20 20 20 20

10 12 13 13 13 12

20 20 20 20 20 20

21 23 24 24 24 22

20 20 20 20 20 20

33 35 36 36 36 34

20 20 20 20 20 20

47 49 50 51 50 48

21 21 21 21 21 21

04 06 07 07 06 04

21 21 21 21 21 21

24 27 28 28 26 23

July

END OF EVENING TWILIGHT h m h m h m h m h m h m h m h m h m h m h m h m h m Apr.

6 14 22 30 May 8 16

19 19 19 19 19 19

15 13 12 12 12 13

19 19 19 19 19 19

21 22 23 25 27 29

19 19 19 19 19 19

30 34 37 41 46 50

19 19 19 20 20 20

44 50 57 04 11 18

19 20 20 20 20 20

53 01 10 19 28 37

20 20 20 20 20 21

04 15 26 38 50 01

20 20 20 21 21 21

19 32 47 02 18 35

24 1 9 17 25 3 11

19 19 19 19 19 19 19

14 16 18 20 22 23 23

19 19 19 19 19 19 19

32 35 38 40 42 42 42

19 19 20 20 20 20 20

55 59 03 05 07 07 06

20 20 20 20 20 20 20

25 32 37 40 41 41 38

20 20 21 21 21 21 21

46 54 00 03 05 04 00

21 21 21 21 21 21 21

13 22 30 35 36 34 28

21 22 22 22 22 22 22

50 23 03 05 16 23 24 19 09 23 51

June

July

20 20 21 21 22 22

38 56 16 38 02 29

20 21 21 21 22 23

47 08 31 57 28 13

20 21 21 22 23

58 22 49 23 14

21 21 22 23

12 21 27 21 47 39 22 01 22 32 14 22 49 04

284

SUNRISE, 2020 LOCAL MEAN TIME OF SUNRISE (SUN'S UPPER LIMB) AND BEGINNING OF MORNING TWILIGHT ON THE MERIDIAN OF GREENWICH To obtain the standard time at any station, add four minutes for each degree if the station is west of the standard meridian, or deduct four minutes for each degree if the station is east of the standard meridian. In India, to obtain I.S.T., add 4 x ( 82º.5 -  ) mins. or deduct 4 x (  - 82º.5 ) mins. as the station is west or east of 82º.5 E. Longitude. Lat. 0º

10º

20º

30º

35º

40º

45º

50º

52º

54º

56º

58º

60º

Date h m h m h m h m h m h m h m h m h m h m h m h m h m July

3 7 11 15 19 23

6 6 6 6 6 6

01 01 02 02 03 03

5 5 5 5 5 5

44 45 46 47 47 48

5 5 5 5 5 5

25 26 28 29 31 32

5 5 5 5 5 5

04 05 07 09 12 14

4 4 4 4 5 5

51 53 55 58 00 03

4 4 4 4 4 4

36 38 41 44 47 51

4 4 4 4 4 4

19 21 24 28 32 36

3 4 4 4 4 4

57 00 04 08 13 18

3 3 3 3 4 4

46 50 54 58 04 09

3 3 3 3 3 3

34 38 43 48 53 59

3 3 3 3 3 3

21 25 30 36 42 48

3 3 3 3 3 3

05 09 15 21 28 36

2 2 2 3 3 3

45 51 57 04 13 21

27 31 Aug. 4 8 12 16

6 6 6 6 6 6

03 03 03 02 02 01

5 5 5 5 5 5

49 50 50 51 51 51

5 5 5 5 5 5

34 35 37 38 39 40

5 5 5 5 5 5

16 19 21 23 26 28

5 5 5 5 5 5

06 09 12 15 18 21

4 4 5 5 5 5

54 58 02 05 09 13

4 4 4 4 4 5

40 45 49 54 59 03

4 4 4 4 4 4

23 28 34 40 46 52

4 4 4 4 4 4

15 21 27 33 40 46

4 4 4 4 4 4

06 12 19 26 33 40

3 4 4 4 4 4

56 03 10 18 26 34

3 3 4 4 4 4

44 52 00 09 17 26

3 3 3 3 4 4

30 39 49 58 08 18

20 24 28 Sept. 1 5 9

6 5 5 5 5 5

00 59 58 57 55 54

5 5 5 5 5 5

51 51 51 51 51 50

5 5 5 5 5 5

42 43 44 45 45 46

5 5 5 5 5 5

31 33 35 37 39 42

5 5 5 5 5 5

24 27 30 33 36 39

5 5 5 5 5 5

17 21 24 28 32 36

5 5 5 5 5 5

08 13 18 22 27 32

4 5 5 5 5 5

58 04 10 16 21 27

4 4 5 5 5 5

53 59 06 12 19 25

4 4 5 5 5 5

47 55 02 09 16 23

4 4 4 5 5 5

42 49 57 05 13 21

4 4 4 5 5 5

35 44 52 01 09 18

4 4 4 4 5 5

27 37 46 56 05 15

13 17 21 25 29 3

5 5 5 5 5 5

53 51 50 48 47 46

5 5 5 5 5 5

50 50 49 49 49 49

5 5 5 5 5 5

47 48 49 50 50 51

5 5 5 5 5 5

44 46 48 50 52 55

5 5 5 5 5 5

42 45 48 50 53 57

5 5 5 5 5 5

39 43 47 51 55 59

5 5 5 5 5 6

37 41 46 51 56 01

5 5 5 5 5 6

33 39 45 51 57 04

5 5 5 5 5 6

32 38 45 52 58 05

5 5 5 5 5 6

30 37 45 52 59 06

5 5 5 5 6 6

28 36 44 52 00 08

5 5 5 5 6 6

26 35 43 52 01 09

5 5 5 5 6 6

24 33 43 52 02 11

Oct.

BEGINNING OF MORNING TWILIGHT h m h m h m h m h m h m h m h m h m h m h m h m h m July

3 11 19 27 Aug. 4 12

4 4 4 4 4 4

46 48 49 50 51 50

4 4 4 4 4 4

26 29 31 34 36 38

4 4 4 4 4 4

01 05 09 13 18 21

3 3 3 3 3 3

28 33 39 45 52 59

3 3 3 3 3 3

05 11 18 27 36 44

2 2 2 3 3 3

34 42 52 03 14 26

1 2 2 2 2 3

49 01 15 30 46 02

1 1 2 2

06 38 0 57 04 1 38 0 57 27 2 08 1 43 1 05

20 28 Sept. 5 13 21 29 Oct. 7

4 4 4 4 4 4 4

50 48 46 44 41 38 35

4 4 4 4 4 4 4

39 40 40 40 39 39 38

4 4 4 4 4 4 4

25 28 31 33 35 37 39

4 4 4 4 4 4 4

06 12 18 23 28 33 38

3 4 4 4 4 4 4

53 01 09 16 23 29 36

3 3 3 4 4 4 4

37 48 58 07 16 24 33

3 3 3 3 4 4 4

16 30 43 56 07 18 28

2 3 3 3 3 4 4

48 07 24 40 55 09 22

2 2 3 3 3 4 4

33 55 15 33 49 05 19

2 2 3 3 3 4 4

15 41 04 24 43 00 15

1 2 2 3 3 3 4

52 25 51 14 35 54 11

1 2 2 3 3 3 4

18 03 36 02 26 47 07

1 2 2 3 3 4

34 16 48 15 39 01

285

SUNSET, 2020 LOCAL MEAN TIME OF SUNSET (SUN'S UPPER LIMB) AND ENDING OF EVENING TWILIGHT ON THE MERIDIAN OF GREENWICH To obtain the standard time at any station, add four minutes for each degree if the station is west of the standard meridian, or deduct four minutes for each degree if the station is east of the standard meridian. In India, to obtain I.S.T., add 4 x ( 82º.5 - O ) mins. or deduct 4 x ( O - 82º.5 ) mins. as the station is west or east of 82º.5 E. Longitude. Lat. 0º

10º

20º

30º

35º

40º

45º

50º

52º

54º

56º

58º

60º

Date h m h m h m h m h m h m h m h m h m h m h m h m h m July

3 7 11 15 19 23

18 18 18 18 18 18

08 09 09 10 10 10

18 18 18 18 18 18

25 25 26 25 25 25

18 18 18 18 18 18

44 44 43 43 42 41

19 19 19 19 19 18

05 05 04 02 01 59

19 19 19 19 19 19

18 17 16 14 12 10

19 19 19 19 19 19

32 31 30 28 25 22

19 19 19 19 19 19

50 48 46 44 40 37

20 20 20 20 19 19

12 10 07 03 59 55

20 20 20 20 20 20

22 20 17 13 08 03

20 20 20 20 20 20

34 31 28 23 18 13

20 20 20 20 20 20

48 44 40 36 30 23

21 21 20 20 20 20

04 00 55 50 43 36

21 21 21 21 20 20

23 18 13 06 59 50

27 31 Aug. 4 8 12 16

18 18 18 18 18 18

10 10 09 09 08 08

18 18 18 18 18 18

24 23 22 21 19 17

18 18 18 18 18 18

39 37 35 33 30 28

18 18 18 18 18 18

56 54 51 47 44 40

19 19 19 18 18 18

07 03 00 56 51 47

19 19 19 19 19 18

18 14 10 05 00 55

19 19 19 19 19 19

32 27 22 17 11 04

19 19 19 19 19 19

49 43 37 30 23 16

19 19 19 19 19 19

57 51 44 37 29 21

20 19 19 19 19 19

06 59 52 44 36 27

20 20 20 19 19 19

16 09 00 52 43 33

20 20 20 20 19 19

28 19 10 01 51 41

20 20 20 20 20 19

41 32 22 11 00 49

20 24 28 Sept. 1 5 9

18 18 18 18 18 18

07 06 04 03 02 00

18 18 18 18 18 18

15 13 11 09 06 04

18 18 18 18 18 18

25 22 18 15 11 08

18 18 18 18 18 18

36 31 27 22 17 12

18 18 18 18 18 18

42 37 32 26 21 15

18 18 18 18 18 18

49 43 37 31 25 18

18 18 18 18 18 18

58 51 44 36 29 22

19 19 18 18 18 18

08 00 52 43 35 26

19 19 18 18 18 18

13 04 55 46 37 28

19 19 18 18 18 18

18 09 59 50 40 30

19 19 19 18 18 18

24 14 04 53 43 32

19 19 19 18 18 18

30 20 09 58 46 35

19 19 19 19 18 18

38 26 14 02 50 38

13 17 21 25 29 3

17 17 17 17 17 17

59 58 56 55 53 52

18 17 17 17 17 17

01 59 56 54 51 49

18 18 17 17 17 17

04 00 57 53 50 46

18 18 17 17 17 17

07 02 57 52 47 43

18 18 17 17 17 17

09 04 58 52 46 41

18 18 17 17 17 17

11 05 58 52 45 39

18 18 17 17 17 17

14 06 59 51 44 36

18 18 17 17 17 17

17 08 59 51 42 33

18 18 18 17 17 17

19 09 00 51 41 32

18 18 18 17 17 17

20 10 00 50 40 31

18 18 18 17 17 17

22 11 01 50 39 29

18 18 18 17 17 17

24 12 01 50 38 27

18 18 18 17 17 17

26 14 02 50 37 25

Oct.

END OF EVENING TWILIGHT h m h m h m h m h m h m h m h m h m h m h m h m h m July

3 11 19 27 Aug. 4 12

19 19 19 19 19 19

23 23 23 23 21 19

19 19 19 19 19 19

42 42 41 39 36 32

20 20 20 19 19 19

07 06 03 59 54 48

20 20 20 20 20 20

41 38 33 27 19 10

21 21 20 20 20 20

04 00 54 46 36 25

21 21 21 21 20 20

34 28 20 09 57 43

22 22 21 21 21 21

19 09 56 41 24 07

23 23 22 22 21

51 03 33 23 10 06 22 30 23 08 40 21 59 22 23 22 58

20 28 Sept. 5 13 21 29 Oct. 7

19 19 19 19 19 19 19

17 14 11 08 05 02 00

19 19 19 19 19 19 18

27 22 17 11 06 01 57

19 19 19 19 19 19 18

41 34 26 18 10 03 56

20 19 19 19 19 19 18

00 50 39 28 17 07 57

20 20 19 19 19 19 18

13 00 48 35 22 10 59

20 20 19 19 19 19 19

28 13 58 44 29 15 02

20 20 20 19 19 19 19

49 30 12 55 38 21 06

21 20 20 20 19 19 19

16 53 31 10 49 30 12

21 21 20 20 19 19 19

31 05 40 17 55 34 15

21 21 20 20 20 19 19

48 18 51 25 01 39 18

22 21 21 20 20 19 19

10 35 03 35 09 45 22

22 21 21 20 20 19 19

42 55 18 46 18 51 27

22 21 21 20 19 19

23 37 00 28 59 33

286

SUNRISE, 2020 LOCAL MEAN TIME OF SUNRISE (SUN'S UPPER LIMB) AND BEGINNING OF MORNING TWILIGHT ON THE MERIDIAN OF GREENWICH To obtain the standard time at any station, add four minutes for each degree if the station is west of the standard meridian, or deduct four minutes for each degree if the station is east of the standard meridian. In India, to obtain I.S.T., add 4 x ( 82º.5 -  ) mins. or deduct 4 x (  - 82º.5 ) mins. as the station is west or east of 82º.5 E. Longitude. Lat. 0º

10º

20º

30º

35º

40º

45º

50º

52º

54º

56º

58º

60º

Date h m h m h m h m h m h m h m h m h m h m h m h m h m Oct.

3 7 11 15 19 23

5 5 5 5 5 5

46 44 43 42 42 41

5 5 5 5 5 5

49 48 48 48 49 49

5 5 5 5 5 5

51 53 54 55 56 58

5 5 6 6 6 6

55 57 00 02 05 08

5 6 6 6 6 6

57 00 03 06 10 13

5 6 6 6 6 6

59 03 07 11 15 19

6 6 6 6 6 6

01 06 11 16 21 27

6 6 6 6 6 6

04 10 16 22 29 35

6 6 6 6 6 6

05 12 18 25 32 39

6 6 6 6 6 6

06 14 21 29 36 44

6 6 6 6 6 6

08 16 24 32 40 49

6 6 6 6 6 6

09 18 27 36 45 54

6 6 6 6 6 7

11 21 30 40 50 00

27 31 Nov. 4 8 12 16

5 5 5 5 5 5

40 40 40 40 41 41

5 5 5 5 5 5

50 50 51 52 54 55

5 6 6 6 6 6

59 01 03 05 07 10

6 6 6 6 6 6

10 13 16 20 23 26

6 6 6 6 6 6

17 20 24 28 32 36

6 6 6 6 6 6

24 28 33 37 42 47

6 6 6 6 6 6

32 38 43 49 54 59

6 6 6 7 7 7

42 49 55 02 08 15

6 6 7 7 7 7

47 54 01 08 15 22

6 6 7 7 7 7

52 59 07 15 23 30

6 7 7 7 7 7

57 06 14 23 31 39

7 7 7 7 7 7

03 13 22 31 41 50

7 7 7 7 7 8

10 21 31 41 51 01

20 24 28 2 6 10

5 5 5 5 5 5

42 43 44 46 47 49

5 5 6 6 6 6

57 58 00 02 04 06

6 6 6 6 6 6

12 14 17 19 22 24

6 6 6 6 6 6

29 33 36 39 42 45

6 6 6 6 6 6

40 43 47 51 54 57

6 6 7 7 7 7

51 56 00 04 08 11

7 7 7 7 7 7

05 10 15 19 24 28

7 7 7 7 7 7

21 27 33 39 43 48

7 7 7 7 7 7

29 36 42 48 53 57

7 7 7 7 8 8

38 45 51 58 03 08

7 7 8 8 8 8

47 55 02 09 15 20

7 8 8 8 8 8

58 07 15 22 29 35

8 8 8 8 8 8

11 21 30 38 45 51

14 18 22 26 30 34

5 5 5 5 5 6

51 53 55 57 59 01

6 6 6 6 6 6

08 10 13 14 16 18

6 6 6 6 6 6

27 29 31 33 34 36

6 6 6 6 6 6

48 50 52 54 55 56

7 7 7 7 7 7

00 03 05 06 08 08

7 7 7 7 7 7

14 17 19 21 22 22

7 7 7 7 7 7

31 34 36 37 38 38

7 7 7 7 7 7

51 54 57 58 59 58

8 8 8 8 8 8

01 04 06 08 08 08

8 8 8 8 8 8

12 15 18 19 19 18

8 8 8 8 8 8

25 28 30 31 32 30

8 8 8 8 8 8

39 43 45 46 46 44

8 9 9 9 9 9

56 00 03 03 03 01

Dec

BEGINNING OF MORNING TWILIGHT h m h m h m h m h m h m h m h m h m h m h m h m h m Oct.

7 15 23 31 Nov. 8 16

4 4 4 4 4 4

35 33 31 29 28 29

4 4 4 4 4 4

38 38 38 39 40 42

4 4 4 4 4 4

39 41 44 46 50 53

4 4 4 4 4 5

38 42 47 52 58 03

4 4 4 4 5 5

36 42 48 55 01 08

4 4 4 4 5 5

33 41 49 57 05 13

4 4 4 4 5 5

28 38 48 58 08 17

4 4 4 4 5 5

22 35 47 59 11 22

4 4 4 4 5 5

19 33 46 59 12 23

4 4 4 4 5 5

15 31 45 59 12 25

4 4 4 4 5 5

11 28 44 59 13 27

4 4 4 4 5 5

07 25 42 59 14 29

4 4 4 4 5 5

01 21 40 58 15 31

24 2 10 18 26 34 42

4 4 4 4 4 4 4

30 32 34 38 42 46 50

4 4 4 4 4 5 5

44 47 51 55 59 03 06

4 5 5 5 5 5 5

57 02 06 10 14 17 20

5 5 5 5 5 5 5

09 15 20 25 29 31 33

5 5 5 5 5 5 5

15 21 27 32 36 38 39

5 5 5 5 5 5 5

20 27 34 39 43 45 45

5 5 5 5 5 5 5

26 34 41 47 51 52 52

5 5 5 5 5 6 5

32 41 49 55 59 00 58

5 5 5 5 6 6 6

34 44 52 58 02 03 01

5 5 5 6 6 6 6

37 47 56 02 06 06 04

5 5 5 6 6 6 6

39 50 59 06 09 10 07

5 5 6 6 6 6 6

42 54 03 10 13 14 10

5 5 6 6 6 6 6

45 57 07 14 18 18 14

Dec.

287

SUNSET, 2020 LOCAL MEAN TIME OF SUNSET (SUN'S UPPER LIMB) AND ENDING OF EVENING TWILIGHT ON THE MERIDIAN OF GREENWICH To obtain the standard time at any station, add four minutes for each degree if the station is west of the standard meridian, or deduct four minutes for each degree if the station is east of the standard meridian. In India, to obtain I.S.T., add 4 x ( 82º.5 - O ) mins. or deduct 4 x ( O - 82º.5 ) mins. as the station is west or east of 82º.5 E. Longitude. Lat. 0º

10º

20º

30º

35º

40º

45º

50º

52º

54º

56º

58º

60º

Date h m h m h m h m h m h m h m h m h m h m h m h m h m Oct.

3 7 11 15 19 23

17 17 17 17 17 17

52 51 50 49 48 48

17 17 17 17 17 17

49 47 45 43 41 39

17 17 17 17 17 17

46 43 39 36 33 31

17 17 17 17 17 17

43 38 33 29 25 21

17 17 17 17 17 17

41 35 30 25 20 15

17 17 17 17 17 17

39 32 26 20 14 09

17 17 17 17 17 17

36 29 22 15 08 01

17 17 17 17 17 16

33 25 16 08 00 52

17 17 17 17 16 16

32 23 14 05 57 48

17 17 17 17 16 16

31 21 11 02 53 44

17 17 17 16 16 16

29 19 08 58 49 39

17 17 17 16 16 16

27 16 05 54 44 33

17 17 17 16 16 16

25 13 02 50 38 27

27 31 Nov. 4 8 12 16

17 17 17 17 17 17

47 47 47 47 48 48

17 17 17 17 17 17

38 37 36 35 35 35

17 17 17 17 17 17

28 26 24 22 21 20

17 17 17 17 17 17

17 13 10 08 05 03

17 17 17 16 16 16

11 06 03 59 56 54

17 16 16 16 16 16

03 58 54 50 46 43

16 16 16 16 16 16

55 49 44 38 34 30

16 16 16 16 16 16

45 38 31 25 19 14

16 16 16 16 16 16

40 33 26 19 13 07

16 16 16 16 16 15

35 27 19 12 05 59

16 16 16 16 15 15

30 21 12 04 57 50

16 16 16 15 15 15

23 14 04 55 47 39

16 16 15 15 15 15

16 06 55 46 36 28

20 24 28 Dec. 2 6 10

17 17 17 17 17 17

49 50 52 53 55 57

17 17 17 17 17 17

35 35 36 37 38 40

17 17 17 17 17 17

19 19 19 20 20 21

17 17 17 17 17 17

02 01 00 00 00 01

16 16 16 16 16 16

52 50 49 48 48 49

16 16 16 16 16 16

40 38 36 35 35 35

16 16 16 16 16 16

26 23 21 19 19 18

16 16 16 16 15 15

10 06 03 00 59 58

16 15 15 15 15 15

02 58 54 51 49 49

15 15 15 15 15 15

53 48 44 41 39 38

15 15 15 15 15 15

44 38 33 30 27 25

15 15 15 15 15 15

32 26 21 17 13 11

15 15 15 15 14 14

20 12 06 01 57 54

14 18 22 26 30 34

17 18 18 18 18 18

59 01 03 05 06 08

17 17 17 17 17 17

41 43 45 47 49 51

17 17 17 17 17 17

23 25 27 29 31 33

17 17 17 17 17 17

02 03 05 08 10 13

16 16 16 16 16 17

50 51 53 55 58 01

16 16 16 16 16 16

35 37 39 41 44 47

16 16 16 16 16 16

19 20 22 24 27 31

15 15 16 16 16 16

58 59 01 04 07 11

15 15 15 15 15 16

48 49 51 54 57 02

15 15 15 15 15 15

37 38 40 43 47 51

15 15 15 15 15 15

25 26 27 30 34 39

15 15 15 15 15 15

10 11 13 16 20 25

14 14 14 14 15 15

53 53 55 58 03 09

END OF EVENING TWILIGHT h m h m h m h m h m h m h m h m h m h m h m h m h m Oct.

7 15 23 31 Nov. 8 16

19 18 18 18 18 19

00 59 58 58 59 01

18 18 18 18 18 18

57 53 50 48 47 48

18 18 18 18 18 18

56 50 45 41 38 36

18 18 18 18 18 18

57 48 41 34 29 26

18 18 18 18 18 18

59 49 40 32 26 21

19 18 18 18 18 18

02 50 39 30 22 17

19 18 18 18 18 18

06 52 39 28 19 12

19 18 18 18 18 18

12 55 40 27 16 07

19 18 18 18 18 18

15 57 41 27 15 06

19 18 18 18 18 18

18 59 42 27 14 04

19 19 18 18 18 18

22 02 44 27 13 02

19 19 18 18 18 18

27 05 45 27 12 00

19 19 18 18 18 17

33 09 47 28 12 58

24 2 10 18 26 34 42

19 19 19 19 19 19 19

04 08 12 16 20 23 26

18 18 18 18 19 19 19

49 52 55 59 03 07 10

18 18 18 18 18 18 18

36 37 40 43 47 52 56

18 18 18 18 18 18 18

24 24 26 29 33 38 44

18 18 18 18 18 18 18

19 18 19 22 26 31 37

18 18 18 18 18 18 18

13 11 12 14 19 24 31

18 18 18 18 18 18 18

07 05 05 07 11 17 25

18 17 17 17 18 18 18

01 58 57 59 03 10 18

17 17 17 17 18 18 18

59 55 54 55 00 06 15

17 17 17 17 17 18 18

56 52 50 52 56 03 12

17 17 17 17 17 18 18

54 48 47 48 52 00 09

17 17 17 17 17 17 18

51 45 43 44 48 56 06

17 17 17 17 17 17 18

48 41 39 39 44 52 03

Dec.

288

DURATION OF TWILIGHT, 2020 MORNING AND EVENING TWILIGHT: CIVIL (6º ), NAUTICAL (12º ) AND ASTRONOMICAL (18º ) Lat. Date

Jan.

Feb.

Mar.

Apr.

May June

July

Aug.

Sept.

Oct.

Nov.

Dec.

Civ.

0º Nt. Ast. Civ.

10º Nt. Ast. Civ.

20º Nt. Ast. Civ.

30º Nt. Ast. Civ.

40º Nt. Ast.

0 8 16 24 1 9 17 25

m 23 22 22 22 22 21 21 21

m 49 48 48 47 47 46 46 45

m 75 74 74 73 72 71 70 70

m 23 23 22 22 22 22 21 21

m 49 49 48 48 47 47 46 46

m 75 75 74 73 73 72 71 70

m 24 24 24 23 23 23 22 22

m 51 51 51 50 49 49 48 48

m 79 78 77 76 76 75 74 74

m 26 26 26 25 25 25 24 24

m 56 56 55 54 54 53 52 52

m 85 85 84 83 82 81 80 80

m 30 30 30 29 29 28 28 27

m 64 64 63 62 61 60 59 59

m 97 96 95 94 93 92 91 90

5 13 21 29 6 14 22 30

21 21 21 21 21 21 21 21

45 45 45 45 45 45 46 46

69 69 69 69 69 70 70 71

21 21 21 21 21 21 22 22

46 45 45 46 46 46 47 47

70 70 70 70 71 71 72 73

22 22 22 22 22 23 23 23

48 48 48 48 48 49 50 50

73 73 73 74 75 76 77 77

24 24 24 24 24 25 25 25

52 52 52 52 53 54 55 55

79 80 80 81 82 83 85 87

27 27 27 27 28 28 29 29

59 58 59 59 61 62 63 65

90 90 91 92 95 97 100 103

8 16 24 1 9 17 25 3

22 22 22 22 23 23 23 23

47 47 48 48 49 49 49 49

72 73 74 74 75 75 75 75

22 22 23 23 23 23 23 23

48 49 49 50 50 50 50 50

74 75 76 77 77 78 78 77

23 24 24 24 25 25 25 24

51 52 53 53 54 54 54 54

79 81 82 83 84 84 84 84

26 26 27 27 27 28 27 27

57 58 59 60 61 61 61 60

89 91 93 95 96 97 97 96

30 31 32 32 33 33 33 33

67 69 71 73 74 75 75 74

108 112 116 119 122 123 123 122

11 19 27 4 12 20 28 5

22 22 22 22 21 21 21 21

48 48 47 47 46 46 45 45

74 74 73 72 71 70 70 69

23 23 22 22 22 22 21 21

50 49 49 48 47 47 46 46

77 76 75 74 73 72 71 71

24 24 24 23 23 23 22 22

53 53 52 51 50 49 49 48

83 82 80 79 78 76 75 74

27 27 26 26 25 25 25 24

60 59 58 56 55 54 53 53

95 93 91 88 86 85 83 82

32 32 31 30 29 29 28 28

73 71 69 67 65 63 61 60

119 115 111 106 103 99 96 94

13 21 29 7 15 23 31 8

21 21 21 21 21 21 21 22

45 45 45 45 45 46 46 47

69 69 69 69 70 70 71 72

21 21 21 21 21 21 22 22

46 45 45 46 46 46 47 47

70 70 70 70 70 71 72 73

22 22 22 22 22 22 23 23

48 48 48 48 48 48 49 49

74 73 73 73 74 74 75 76

24 24 24 24 24 24 25 25

52 52 52 52 52 52 53 54

81 80 79 79 80 80 81 82

27 27 27 27 27 28 28 29

59 59 58 58 59 59 60 61

92 91 90 90 90 91 92 93

16 24 2 10 18 26 34

22 22 22 23 23 23 23

47 48 48 49 49 49 49

73 74 74 75 75 75 75

22 22 23 23 23 23 23

48 48 49 49 49 49 49

73 74 75 75 75 75 75

23 24 24 24 24 24 24

50 51 51 51 52 52 51

76 77 78 78 79 79 78

25 26 26 26 26 26 26

54 55 56 56 56 56 56

83 84 85 85 86 85 85

29 30 30 30 31 31 30

62 63 64 64 65 65 64

94 95 96 97 98 98 97

289

DURATION OF TWILIGHT, 2020 MORNING AND EVENING TWILIGHT: CIVIL (6º ), NAUTICAL (12º ) AND ASTRONOMICAL (18º ) Lat. Civ.

45º Nt.

Ast.

Civ.

50º Nt.

Ast.

Civ.

55º Nt.

Ast.

Civ.

60º Nt.

Ast.

0 8 16 24 1 9 17 25

m 34 33 33 32 31 31 30 30

m 71 70 69 68 67 65 64 64

m 106 105 104 102 101 100 98 98

m 38 38 37 36 35 34 33 33

m 80 78 77 75 74 72 71 70

m 119 117 116 113 112 110 108 108

m 45 44 43 41 40 39 38 37

m 93 91 88 86 84 82 80 79

m 137 135 132 129 126 124 122 121

m 57 55 52 50 48 45 44 42

m 113 111 106 102 98 95 92 91

m 165 161 156 151 147 143 140 139

5 13 21 29 6 14 22 30

29 29 29 30 30 31 32 32

63 64 64 65 66 68 70 72

98 98 99 101 104 108 112 117

32 32 32 33 33 34 35 36

70 70 71 72 74 77 80 83

108 108 110 113 117 123 130 139

36 36 36 37 38 39 41 43

78 79 80 81 85 89 94 100

121 121 125 130 137 147 161 184

42 42 42 43 44 46 50 53

90 90 92 95 100 107 119 135

140 142 147 155 169 193 ** **

8 16 24 1 9 17 25 3

33 35 36 36 37 37 37 37

76 79 82 84 86 87 87 86

123 130 137 144 150 153 153 150

38 40 42 43 44 45 45 44

88 93 99 104 108 110 110 107

151 167 188 ** ** ** ** **

46 49 52 54 57 58 58 57

110 121 136 156 194 ** ** 187

** ** ** ** ** ** ** **

59 65 74 85 96 106 105 95

169 ** ** ** ** ** ** **

** ** ** ** ** ** ** **

11 19 27 4 12 20 28 5

36 35 34 33 32 31 31 30

84 81 78 75 72 69 67 66

144 137 129 123 116 111 107 104

43 41 40 38 36 35 34 33

103 98 93 87 82 79 76 74

** 186 165 149 138 129 122 117

54 51 48 45 42 41 39 38

154 134 120 109 100 93 88 84

** ** ** ** 182 160 146 136

83 73 64 58 53 49 46 44

** ** ** 165 134 118 107 100

** ** ** ** ** ** 192 168

13 21 29 7 15 23 31 8

30 29 29 29 30 30 31 31

65 64 63 63 64 64 65 66

101 99 98 97 98 98 99 101

33 32 32 32 33 33 34 35

72 71 70 70 70 71 72 74

113 110 108 107 107 108 109 111

37 36 36 36 37 37 38 40

81 79 78 78 78 80 81 84

130 125 122 121 121 121 123 126

43 42 41 42 42 43 45 47

95 92 90 90 90 92 94 98

155 147 142 139 139 140 142 146

16 24 2 10 18 26 34

32 33 33 34 34 34 34

68 69 70 71 71 71 71

102 104 105 106 107 107 106

36 37 38 38 39 38 38

75 77 78 80 80 80 79

113 116 117 119 120 119 119

41 43 44 45 46 46 45

86 88 91 92 93 93 92

129 132 135 137 138 138 136

50 52 55 57 58 58 56

102 106 110 113 115 114 112

151 156 161 164 166 166 163

Date

Jan.

Feb.

Mar.

Apr.

May June

July

Aug.

Sept.

Oct.

Nov.

Dec.

290

SUNRISE, SUNSET AND TWILIGHT, 2020 CORRECTION FOR SOUTHERN LATITUDES For

Use

July Dec. 1 31 July Jan. 2 0 3 1 4 2

Add

For

Use

m Aug. +1 7 8 +1 9 0 10 0 11

Feb. 3 4 5 6 7

Add

For

Use

Add

m Sept. Mar. -8 12 10 8 13 11 9 14 12 9 15 13 9 16 14

m -14 14 14 14 14

For

Use

Oct. Apr. 19 16 20 17 21 18 22 19 23 20

Add

m Nov. May -15 26 25 15 27 26 15 28 27 15 29 28 15 30 29

m -10 9 9 9 9

3 4 5 6 7 8

0 -1 1 1 1 2

12 13 14 15 16 17

8 9 10 11 12 13

9 9 10 10 10 10

17 18 19 20 21 22

15 16 17 18 19 20

15 15 15 15 15 15

11 12 13 14 15 16

9 10 11 12 13 14

2 2 2 3 3 3

18 19 20 21 22 23

14 15 16 17 18 19

10 11 11 11 11 11

23 24 25 26 27 28

21 22 23 24 25 26

15 30 27 15 31 28 15 Nov. Apr. 15 1 29 15 2 30 15 Nov. May

14 14

17 18 19 20 21 22

15 16 16 17 18 19

3 3 4 4 4 4

24 25 26 27 28 29

19 20 21 22 23 24

12 12 12 12 12 12

29 26 30 27 Oct. Mar. 1 28 2 29 3 30

15 15

23 24 25 26 27 28

20 21 22 23 24 25

5 30 5 31 5 Sept. 6 1 6 2 6

25 26 Feb. 27 28

13 13

4 31 Oct. Apr. 5 1 6 2 7 3 8 4

15

29 30 31 Aug. 1 2

26 27 28 Jan. 29 30

6 Sept. Mar. 7 3 1 7 4 2 5 3 7 6 4 7 7 5

3 4 Aug. 5 6

30 31 Feb. 1 2

7 8 8 -8

8 9 10 11 12

6 7 8 9 10

21 22 23 24 25 26

Use

5 6 7 8 9 10

13 13

24 25 26 27 28 29

Add

For

14 Dec. May 14 1 30 14 2 31 14 Dec. June 14 3 1 14 4 2

14 14

8 8 8 8

5 6 7 8 9 10

3 5 6 7 8 9

7 7 7 7 6 6

3 4 5 6 7 8

1 2 3 4 5 6

13 13 13 13 13 13

11 12 13 14 15 16

10 11 12 13 14 15

6 6 5 5 5 5

16 16 16 15

9 10 11 12 13 14

7 8 9 10 11 12

13 12 12 12 12 12

17 18 19 20 21 22

16 17 18 19 21 22

4 4 4 4 3 3

12 12 11 11 11 11

23 24 25 26 27 28

23 24 25 26 27 28

3 3 2 2 2 2

11 29 10 30 10 Dec. 10 31 -10 32

29 30 July 1 2

1 1

15 15 15

13 13 13 14 14

9 10 11 12 13 14

5 6 7 9 10 11

15 15 15 15 15 15

15 16 17 18 19 20

13 14 15 17 18 19

14 14 14 14 -14

15 16 17 18 19

12 13 14 15 16

15 15 15 15 -15

21 22 23 24 25

20 21 22 23 24

-1 0

To obtain the times of sunrise, sunset and twilight for southern latitudes for any date, use the tables for the same northern latitude for the corresponding date given above, and apply to the times so obtained the correction given in the column headed 'Add'. In the case of duration of twilight, however, take only the figures for the corresponding date without correction.

291

SUNRISE, SUNSET AND TWILIGHT, 2020 CORRECTION FOR SOUTHERN LATITUDES For

Use

Add

Jan. 0 1 2

July 1 3 4

m 0 0 0

3 4 5 6 7

5 6 7 8 9

0 +1 1 1 1

9 10 11 12 13

13 14 15 16 17

9 10 10 10 10

17 18 19 20 21

19 20 21 22 23

15 15 15 15 15

8 9 10 11 12

10 11 12 13 14

2 2 2 2 3

14 15 16 17 18

18 19 20 21 22

10 11 11 11 11

22 23 24 25 26

24 25 26 27 29

15 15 15 15 15

13 14 15 16 17

15 16 17 18 19

3 3 3 4 4

19 20 21 22 23

23 25 26 27 28

11 27 12 Mar. 12 28 12 29 12 30

30 Oct. 1 2 3

15

18 19 20 21 22

21 22 23 24 25

4 5 5 5 5

24 25 26

29 30 31

12 13 13

31 Apr. 1 2 3

4 Oct. 5 6 7

16

23 24 25 26 27

26 27 28 29 30

6 27 1 6 28 2 6 Mar. Sept. 6 1 3 7 2 4

13 13 13 13

4 5 6 7 8

7

28 31 Jan. Aug. 29 1 30 2 31 3 Feb. Aug. 1 5 2 6 3 7 4 8

For

Use

Feb. Aug. 5 9 6 10 7 11 8 12

Add

For

Use

m Mar. Sept. +9 13 15 9 14 16 9 15 17 9 16 18

Feb. Sept.

Add

For

Use

Add

Use

Add

m Apr. +14 19 14 20 14 21 15 22

Oct. 22 23 24 25

m May Nov. +15 25 26 15 26 27 14 27 28 14 28 29

m +10 9 9 9

26 27 28 29 30

14 29 30 14 May Dec. 14 30 1 14 31 2 14 June Dec.

9

14

23 24 25 26 27

28 31 Apr. Nov. 29 1 30 2 May Nov.

For

8 8

14 14

1 2 3 4 5

3 4 5 5 6

8 8 7 7 7

1 2 3 4 5

3 4 5 6 7

13 13 13 13 13

6 7 8 9 10

7 8 9 10 11

7 7 6 6 6

16 16 16

6 7 8 9 10

8 9 10 11 12

13 13 12 12 12

11 12 13 14 15

12 13 14 15 16

6 5 5 5 5

7 8 9 10 11

15 15 15 15 15

11 12 13 14 15

13 14 15 16 16

12 12 12 12 11

16 17 18 19 20

17 18 19 20 21

4 4 4 4 3

15 15 15

7 7 7

3 4 5 6 7

5 6 7 8 9

13 14 14 14 14

9 10 11 12 13

12 13 14 15 16

15 15 15 15 15

16 17 18 19 20

17 18 19 20 21

11 11 11 11 11

21 22 23 24 25

21 22 23 24 25

3 3 3 3 2

8 8 8 +9

8 9 10 11 12

10 11 12 13 14

14 14 14 14 +14

14 15 16 17 18

17 18 19 20 21

15 15 15 15 +15

21 22 23 24 25

22 23 24 25 26

10 10 10 10 +10

26 27 28 29 30

26 27 28 29 30

2 2 1 1 +1

To obtain the times of sunrise, sunset and twilight for southern latitudes for any date, use the tables for the same northern latitude for the corresponding date given above, and apply to the times so obtained the correction given in the column headed 'Add'. In the case of duration of twilight, however, take only the figures for the corresponding date without correction.

292

Date

SUNRISE AND SUNSET, 2020 INDIAN STANDARD TIME OF SUNRISE AND SUNSET (SUN'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA Kolkata Varanasi Chennai Delhi Mumbai 22º N 32' 25º N 18' 13º N 00' 28º N 35' 18º N 54' Rise Set Rise Set Rise Set Rise Set Rise Set h

m

h

m

h

1 3 5 7 9 11

6 6 6 6 6 6

16.5 17.1 17.7 18.1 18.5 18.7

17 17 17 17 17 17

03.2 04.5 05.8 07.2 08.5 09.9

6 6 6 6 6 6

43.5 44.1 44.5 44.9 45.2 45.4

17 17 17 17 17 17

18.9 20.3 21.7 23.1 24.6 26.0

13 15 17 19 21 23

6 6 6 6 6 6

18.9 19.0 19.0 18.9 18.7 18.4

17 17 17 17 17 17

11.3 12.8 14.2 15.6 17.0 18.4

6 6 6 6 6 6

45.5 45.5 45.4 45.1 44.8 44.4

17 17 17 17 17 17

25 27 29 31 Feb. 2

6 6 6 6 6

18.0 17.6 17.0 16.4 15.7

17 17 17 17 17

19.8 21.2 22.5 23.9 25.2

6 6 6 6 6

43.9 43.3 42.6 41.8 40.9

4 6 8 10 12 14 16

6 6 6 6 6 6 6

14.8 14.0 13.0 12.0 10.8 09.7 08.4

17 17 17 17 17 17 17

26.5 27.7 29.0 30.2 31.3 32.5 33.6

6 6 6 6 6 6 6

18 20 22 24 26 28

6 6 6 6 6 6

07.1 05.7 04.3 02.8 01.3 00.0

17 17 17 17 17 17

34.6 35.7 36.7 37.7 38.6 39.5

1 3 5 7 9 11

5 5 5 5 5 5

58.1 56.5 54.8 53.0 51.3 49.5

17 17 17 17 17 17

13 15 17 19 21 23

5 5 5 5 5 5

47.7 45.8 43.9 42.1 40.2 38.3

25 27 29 31 Apr. 2

5 5 5 5 5

36.4 34.5 32.5 30.6 28.8

Jan.

Mar.

m h

m h

m

h

m h

m

h

6 6 6 6 6 6

31.1 32.0 32.7 33.3 33.9 34.4

17 17 17 17 17 17

53.4 54.8 56.0 57.1 58.2 59.3

27.5 29.0 30.5 32.1 33.6 35.1

6 6 6 6 6 6

34.9 35.3 35.6 35.8 36.0 36.1

18 18 18 18 18 18

17 17 17 17 17

36.6 38.1 39.6 41.1 42.5

6 6 6 6 6

36.1 36.1 35.9 35.7 35.5

40.0 38.9 37.8 36.6 35.3 33.9 32.5

17 17 17 17 17 17 17

43.9 45.3 46.7 48.0 49.3 50.6 51.9

6 6 6 6 6 6 6

6 6 6 6 6 6

31.0 29.4 27.8 26.1 24.4 22.6

17 17 17 17 17 17

53.1 54.3 55.4 56.6 57.7 58.8

40.4 41.3 42.1 42.9 43.7 44.5

6 6 6 6 6 6

20.8 18.9 17.0 15.1 13.1 11.1

18 18 18 18 18 18

17 17 17 17 17 17

45.3 46.0 46.8 47.5 48.2 48.9

6 6 6 6 6 5

09.1 07.1 05.1 03.0 01.0 59.0

17 17 17 17 17

49.6 50.3 51.0 51.7 52.4

5 5 5 5 5

56.9 54.8 52.8 50.7 48.7

m h

m

h

m

7 7 7 7 7 7

14.2 14.7 15.1 15.4 15.6 15.6

17 17 17 17 17 17

35.0 36.6 38.1 39.6 41.1 42.7

7 7 7 7 7 7

12.0 12.6 13.2 13.7 14.2 14.5

18 18 18 18 18 18

11.9 13.3 14.5 15.8 17.0 18.3

00.4 01.5 02.5 03.6 04.6 05.6

7 7 7 7 7 7

15.6 15.5 15.2 14.9 14.4 13.9

17 17 17 17 17 17

44.3 45.9 47.5 49.1 50.8 52.4

7 7 7 7 7 7

14.8 15.0 15.1 15.2 15.1 15.0

18 18 18 18 18 18

19.6 20.9 22.1 23.4 24.7 25.9

18 18 18 18 18

06.5 07.5 08.4 09.2 10.1

7 7 7 7 7

13.2 12.4 11.5 10.6 09.5

17 17 17 17 18

54.1 55.7 57.4 59.0 00.6

7 7 7 7 7

14.8 14.5 14.1 13.6 13.0

18 18 18 18 18

27.1 28.3 29.5 30.7 31.8

35.1 34.7 34.2 33.7 33.1 32.4 31.7

18 18 18 18 18 18 18

10.9 11.6 12.3 13.0 13.6 14.2 14.8

7 7 7 7 7 7 7

08.3 07.1 05.7 04.3 02.8 01.2 00.0

18 18 18 18 18 18 18

02.2 03.7 05.3 06.8 08.3 09.8 11.3

7 7 7 7 7 7 7

12.4 11.7 10.9 10.0 09.1 08.1 07.1

18 18 18 18 18 18 18

32.9 33.9 35.0 36.0 36.9 37.9 38.8

6 6 6 6 6 6

30.9 30.0 29.1 28.2 27.2 26.1

18 18 18 18 18 18

15.3 15.8 16.3 16.7 17.1 17.4

6 6 6 6 6 6

57.8 56.0 54.2 52.2 50.3 48.2

18 18 18 18 18 18

12.7 14.1 15.5 16.9 18.2 19.5

7 7 7 7 7 6

05.9 04.7 03.5 02.2 00.8 59.4

18 18 18 18 18 18

39.6 40.4 41.2 42.0 42.7 43.5

00.0 00.9 01.9 02.8 03.8 04.8

6 6 6 6 6 6

25.1 23.9 22.8 21.6 20.4 19.2

18 18 18 18 18 18

17.8 18.1 18.3 18.6 18.8 19.0

6 6 6 6 6 6

46.2 44.1 41.9 39.7 37.5 35.3

18 18 18 18 18 18

20.8 22.1 23.4 24.6 25.8 27.0

6 6 6 6 6 6

58.0 56.5 55.0 53.4 51.9 50.3

18 18 18 18 18 18

44.1 44.8 45.4 46.0 46.6 47.2

18 18 18 18 18 18

05.7 06.6 07.5 08.4 09.3 10.2

6 6 6 6 6 6

17.9 16.6 15.3 14.0 12.7 11.4

18 18 18 18 18 18

19.2 19.4 19.5 19.7 19.8 19.9

6 6 6 6 6 6

33.0 30.7 28.4 26.1 23.8 21.5

18 18 18 18 18 18

28.2 29.3 30.5 31.6 32.8 33.9

6 6 6 6 6 6

48.6 47.0 45.3 43.6 41.9 40.2

18 18 18 18 18 18

47.7 48.2 48.7 49.2 49.7 50.2

18 18 18 18 18

11.1 12.0 12.8 13.7 14.6

6 6 6 6 6

10.1 08.8 07.5 06.2 04.9

18 18 18 18 18

20.0 20.2 20.3 20.4 20.5

6 6 6 6 6

19.2 16.9 14.6 12.3 10.0

18 18 18 18 18

35.0 36.1 37.3 38.4 39.5

6 6 6 6 6

38.6 36.9 35.2 33.5 31.8

18 18 18 18 18

50.7 51.2 51.7 52.1 52.6

293

Date

SUNRISE AND SUNSET, 2020 INDIAN STANDARD TIME OF SUNRISE AND SUNSET (SUN'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA Kolkata Varanasi Chennai Delhi Mumbai 22º N 32' 25º N 18' 13º N 00' 28º N 35' 18º N 54' Set Rise Set Rise Set Rise Set Rise Set Rise h

m

h

m

h

2 4 6 8 10 12

5 5 5 5 5 5

28.8 26.9 25.0 23.2 21.4 19.6

17 17 17 17 17 17

52.4 53.1 53.8 54.5 55.2 55.9

5 5 5 5 5 5

48.7 46.7 44.7 42.7 40.7 38.7

18 18 18 18 18 18

14.6 15.5 16.3 17.2 18.1 19.0

14 16 18 20 22 24

5 5 5 5 5 5

17.8 16.1 14.4 12.7 11.1 09.6

17 17 17 17 18 18

56.6 57.4 58.1 58.9 00.0 00.4

5 5 5 5 5 5

36.8 34.9 33.1 31.3 29.5 27.8

18 18 18 18 18 18

26 28 30 May 2 4 6

5 5 5 5 5 5

08.1 06.6 05.2 03.8 02.6 01.3

18 18 18 18 18 18

01.2 02.1 02.9 03.7 04.6 05.5

5 5 5 5 5 5

26.2 24.5 23.0 21.5 20.1 18.7

8 10 12 14 16 18

5 4 4 4 4 4

00.2 59.1 58.1 57.1 56.3 55.4

18 18 18 18 18 18

06.3 07.2 08.1 09.0 09.9 10.8

5 5 5 5 5 5

20 22 24 26 28 30

4 4 4 4 4 4

54.7 54.1 53.5 53.0 52.6 52.2

18 18 18 18 18 18

11.8 12.7 13.6 14.5 15.3 16.2

1 3 5 7 9 11

4 4 4 4 4 4

52.0 51.8 51.7 51.6 51.6 51.7

18 18 18 18 18 18

13 15 17 19 21 23

4 4 4 4 4 4

51.9 52.1 52.4 52.8 53.2 53.7

25 27 29 July 1 3

4 4 4 4 4

54.2 54.8 55.4 56.0 56.7

Apr.

June

m h

m h

m

h

m

h

m

h

m h

m

h

m

6 6 6 6 6 5

04.9 03.6 02.3 01.1 00.0 58.7

18 18 18 18 18 18

20.5 20.7 20.8 21.0 21.1 21.3

6 6 6 6 6 5

10.0 07.8 05.6 03.4 01.2 59.1

18 18 18 18 18 18

39.5 40.6 41.7 42.8 44.0 45.1

6 6 6 6 6 6

31.8 30.2 28.5 26.9 25.3 23.8

18 18 18 18 18 18

52.6 53.1 53.6 54.1 54.6 55.1

19.9 20.9 21.8 22.7 23.7 24.7

5 5 5 5 5 5

57.5 56.4 55.2 54.2 53.1 52.1

18 18 18 18 18 18

21.5 21.7 21.9 22.2 22.5 22.7

5 5 5 5 5 5

57.0 54.9 52.9 50.9 49.0 47.1

18 18 18 18 18 18

46.3 47.4 48.6 49.7 50.9 52.1

6 6 6 6 6 6

22.3 20.8 19.3 17.9 16.5 15.2

18 18 18 18 18 18

55.7 56.2 56.8 57.3 57.9 58.5

18 18 18 18 18 18

25.6 26.6 27.6 28.6 29.7 30.7

5 5 5 5 5 5

51.1 50.2 49.3 48.5 47.7 47.0

18 18 18 18 18 18

23.1 23.4 23.7 24.1 24.5 24.9

5 5 5 5 5 5

45.2 43.5 41.7 40.1 38.4 36.9

18 18 18 18 18 18

53.3 54.5 55.7 56.9 58.2 59.4

6 6 6 6 6 6

13.9 12.7 11.5 10.4 09.3 08.3

18 19 19 19 19 19

59.2 00.0 00.5 01.1 01.8 02.5

17.4 16.2 15.0 13.9 12.9 12.0

18 18 18 18 18 18

31.7 32.8 33.8 34.9 35.9 37.0

5 5 5 5 5 5

46.3 45.6 45.1 44.5 44.1 43.7

18 18 18 18 18 18

25.4 25.9 26.3 26.9 27.4 27.9

5 5 5 5 5 5

35.4 34.1 32.7 31.5 30.3 29.3

19 19 19 19 19 19

00.6 01.8 03.1 04.3 05.5 06.7

6 6 6 6 6 6

07.3 06.5 05.6 04.9 04.2 03.5

19 19 19 19 19 19

03.3 04.0 04.8 05.5 06.3 07.1

5 5 5 5 5 5

11.2 10.4 09.7 09.1 08.6 08.2

18 18 18 18 18 18

38.0 39.1 40.1 41.1 42.1 43.0

5 5 5 5 5 5

43.3 43.0 42.8 42.6 42.5 42.4

18 18 18 18 18 18

28.5 29.1 29.6 30.2 30.8 31.5

5 5 5 5 5 5

28.3 27.4 26.6 25.9 25.2 24.7

19 19 19 19 19 19

07.9 09.1 10.2 11.4 12.5 13.5

6 6 6 6 6 6

03.0 02.5 02.1 01.7 01.4 01.2

19 19 19 19 19 19

07.9 08.6 09.4 10.2 11.0 11.8

17.0 17.9 18.6 19.4 20.1 20.8

5 5 5 5 5 5

07.8 07.6 07.4 07.3 07.3 07.3

18 18 18 18 18 18

44.0 44.9 45.7 46.6 47.3 48.1

5 5 5 5 5 5

42.4 42.4 42.5 42.7 42.8 43.1

18 18 18 18 18 18

32.1 32.7 33.3 33.9 34.4 35.0

5 5 5 5 5 5

24.2 23.9 23.6 23.4 23.4 23.4

19 19 19 19 19 19

14.6 15.6 16.5 17.4 18.3 19.1

6 6 6 6 6 6

01.0 00.9 00.9 00.9 01.0 01.2

19 19 19 19 19 19

12.5 13.3 14.0 14.7 15.4 16.0

18 18 18 18 18 18

21.5 22.1 22.6 23.1 23.6 24.0

5 5 5 5 5 5

07.5 07.7 07.9 08.3 08.7 09.2

18 18 18 18 18 18

48.8 49.4 50.0 50.5 51.0 51.3

5 5 5 5 5 5

43.3 43.7 44.0 44.4 44.8 45.3

18 18 18 18 18 18

35.6 36.1 36.6 37.1 37.5 37.9

5 5 5 5 5 5

23.4 23.6 23.9 24.2 24.6 25.1

19 19 19 19 19 19

19.8 20.5 21.1 21.6 22.0 22.4

6 6 6 6 6 6

01.4 01.6 01.9 02.3 02.7 03.2

19 19 19 19 19 19

16.6 17.2 17.7 18.2 18.7 19.1

18 18 18 18 18

24.3 24.5 24.7 24.9 24.9

5 5 5 5 5

09.7 10.3 10.9 11.6 12.3

18 18 18 18 18

51.7 51.9 52.1 52.1 52.1

5 5 5 5 5

45.7 46.2 46.7 47.3 47.8

18 18 18 18 18

38.3 38.6 38.9 39.1 39.3

5 5 5 5 5

25.6 26.2 26.9 27.6 28.4

19 19 19 19 19

22.7 22.9 23.0 23.1 23.0

6 6 6 6 6

03.7 04.2 04.7 05.3 06.0

19 19 19 19 19

19.4 19.7 19.9 20.1 20.2

294

Date

SUNRISE AND SUNSET, 2020 INDIAN STANDARD TIME OF SUNRISE AND SUNSET (SUN'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA Kolkata Varanasi Chennai Delhi Mumbai 22º N 32' 25º N 18' 13º N 00' 28º N 35' 18º N 54' Rise Set Rise Set Rise Set Rise Set Rise Set h

m

h

m

h

1 3 5 7 9 11

4 4 4 4 4 5

56.0 56.7 57.4 58.2 59.0 00.0

18 18 18 18 18 18

24.9 24.9 24.9 24.8 24.6 24.4

5 5 5 5 5 5

11.6 12.3 13.1 13.9 14.8 15.6

18 18 18 18 18 18

52.1 52.1 52.1 51.9 51.6 51.3

13 15 17 19 21 23

5 5 5 5 5 5

00.6 01.4 02.3 03.1 04.0 04.8

18 18 18 18 18 18

24.0 23.6 23.1 22.6 21.9 21.2

5 5 5 5 5 5

16.5 17.5 18.4 19.3 20.3 21.3

18 18 18 18 18 18

25 27 29 31 Aug. 2 4

5 5 5 5 5 5

05.7 06.5 07.4 08.2 09.1 09.9

18 18 18 18 18 18

20.4 19.5 18.6 17.6 16.5 15.3

5 5 5 5 5 5

22.2 23.2 24.2 25.1 26.1 27.1

6 8 10 12 14 16

5 5 5 5 5 5

10.7 11.5 12.3 13.0 13.8 14.5

18 18 18 18 18 18

14.1 12.8 11.5 10.1 08.6 07.1

5 5 5 5 5 5

18 20 22 24 26 28

5 5 5 5 5 5

15.2 15.9 16.6 17.3 17.9 18.6

18 18 18 18 17 17

05.5 03.9 02.3 00.6 58.9 57.1

30 1 3 5 7 9

5 5 5 5 5 5

19.2 19.8 20.4 21.0 21.6 22.2

17 17 17 17 17 17

11 13 15 17 19 21

5 5 5 5 5 5

22.7 23.3 23.9 24.5 25.0 25.6

23 25 27 29 Oct. 1

5 5 5 5 5

26.2 26.8 27.4 28.0 28.7

July

Sept.

m h

m h

m

h

m

h

m

h

m h

m

h

m

5 5 5 5 5 5

47.3 47.8 48.4 48.9 49.5 50.0

18 18 18 18 18 18

39.1 39.3 39.5 39.6 39.6 39.6

5 5 5 5 5 5

27.6 28.4 29.3 30.1 31.1 32.0

19 19 19 19 19 19

23.1 23.0 22.9 22.6 22.3 21.9

6 6 6 6 6 6

05.3 06.0 06.6 07.3 07.9 08.6

19 19 19 19 19 19

20.1 20.2 20.3 20.2 20.1 20.0

50.9 50.4 49.8 49.1 48.4 47.5

5 5 5 5 5 5

50.6 51.1 51.7 52.2 52.7 53.2

18 18 18 18 18 18

39.5 39.4 39.2 38.9 38.6 38.2

5 5 5 5 5 5

33.0 34.0 35.1 36.1 37.2 38.3

19 19 19 19 19 19

21.3 20.7 20.0 19.2 18.3 17.3

6 6 6 6 6 6

09.3 10.0 10.7 11.5 12.2 12.9

19 19 19 19 19 19

19.7 19.4 19.1 18.6 18.1 17.5

18 18 18 18 18 18

46.6 45.6 44.5 43.3 42.1 40.8

5 5 5 5 5 5

53.7 54.1 54.6 55.0 55.4 55.8

18 18 18 18 18 18

37.8 37.3 36.7 36.1 35.4 34.7

5 5 5 5 5 5

39.4 40.5 41.7 42.8 43.9 45.0

19 19 19 19 19 19

16.2 15.1 13.8 12.5 11.1 09.6

6 6 6 6 6 6

13.6 14.3 14.9 15.6 16.2 16.9

19 19 19 19 19 19

16.8 16.1 15.3 14.4 13.5 12.5

28.0 28.9 29.9 30.8 31.7 32.6

18 18 18 18 18 18

39.4 37.9 36.4 34.8 33.2 31.5

5 5 5 5 5 5

56.1 56.4 56.7 57.0 57.3 57.5

18 18 18 18 18 18

33.9 33.1 32.2 31.3 30.3 29.2

5 5 5 5 5 5

46.1 47.2 48.3 49.4 50.5 51.6

19 19 19 19 19 18

08.0 06.4 04.6 02.9 01.0 59.1

6 6 6 6 6 6

17.5 18.1 18.7 19.2 19.8 20.3

19 19 19 19 19 19

11.4 10.3 09.1 07.9 06.6 05.2

5 5 5 5 5 5

33.4 34.3 35.1 35.9 36.8 37.6

18 18 18 18 18 18

29.8 28.0 26.1 24.2 22.3 20.3

5 5 5 5 5 5

57.7 57.8 58.0 58.1 58.2 58.3

18 18 18 18 18 18

28.1 27.0 25.9 24.7 23.4 22.2

5 5 5 5 5 5

52.6 53.7 54.7 55.7 56.7 57.7

18 18 18 18 18 18

57.1 55.1 53.0 50.9 48.7 46.5

6 6 6 6 6 6

20.8 21.3 21.8 22.2 22.7 23.1

19 19 19 18 18 18

03.8 02.4 00.9 59.4 57.8 56.2

55.3 53.5 51.6 49.7 47.8 45.8

5 5 5 5 5 5

38.3 39.1 39.9 40.7 41.4 42.2

18 18 18 18 18 18

18.3 16.3 14.2 12.2 10.1 08.0

5 5 5 5 5 5

58.4 58.5 58.5 58.6 58.6 58.6

18 18 18 18 18 18

20.9 19.6 18.2 16.9 15.5 14.1

5 6 6 6 6 6

58.7 00.0 00.6 01.6 02.6 03.5

18 18 18 18 18 18

44.3 42.0 39.7 37.4 35.0 32.7

6 6 6 6 6 6

23.5 23.9 24.3 24.6 25.0 25.3

18 18 18 18 18 18

54.5 52.9 51.2 49.5 47.7 46.0

17 17 17 17 17 17

43.9 41.9 39.9 37.9 35.9 33.9

5 5 5 5 5 5

42.9 43.6 44.4 45.1 45.9 46.6

18 18 18 17 17 17

05.8 03.7 01.6 59.4 57.3 55.2

5 5 5 5 5 5

58.6 58.6 58.6 58.6 58.6 58.6

18 18 18 18 18 18

12.7 11.3 09.9 08.5 07.1 05.7

6 6 6 6 6 6

04.5 05.4 06.4 07.3 08.3 09.3

18 18 18 18 18 18

30.3 27.9 25.5 23.1 20.7 18.3

6 6 6 6 6 6

25.7 26.0 26.4 26.7 27.1 27.4

18 18 18 18 18 18

44.2 42.4 40.6 38.8 37.0 35.3

17 17 17 17 17

31.9 29.9 28.0 26.0 24.0

5 5 5 5 5

47.4 48.2 48.9 49.7 50.5

17 17 17 17 17

53.0 50.9 48.8 46.7 44.6

5 5 5 5 5

58.6 58.7 58.7 58.7 58.8

18 18 18 18 17

04.3 02.9 01.5 00.1 58.8

6 6 6 6 6

10.2 11.2 12.2 13.3 14.3

18 18 18 18 18

15.9 13.5 11.2 08.9 06.6

6 6 6 6 6

27.8 28.2 28.6 29.0 29.4

18 18 18 18 18

33.5 31.7 30.0 28.2 26.5

295

Date

SUNRISE AND SUNSET, 2020 INDIAN STANDARD TIME OF SUNRISE AND SUNSET (SUN'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA Kolkata Varanasi Chennai Delhi Mumbai 22º N 32' 25º N 18' 13º N 00' 28º N 35' 18º N 54' Rise Set Rise Set Rise Set Rise Set Rise Set h

m

h

1 3 5 7 9 11

5 5 5 5 5 5

28.7 29.2 29.8 30.5 31.2 32.0

17 17 17 17 17 17

24.0 22.6 20.7 18.8 17.0 15.2

13 15 17 19 21 23

5 5 5 5 5 5

32.7 33.5 34.3 35.2 36.0 36.9

17 17 17 17 17 17

25 27 29 31 Nov. 2 4

5 5 5 5 5 5

37.9 38.8 39.8 40.9 41.9 43.0

6 8 10 12 14 16

5 5 5 5 5 5

18 20 22 24 26 28

Oct.

Dec.

m h

m

h

m h

m

h

m

h

m

h

5 5 5 5 5 5

50.5 51.2 52.0 52.8 53.7 54.6

17 17 17 17 17 17

44.6 43.0 40.9 38.9 36.9 34.9

13.4 11.7 10.0 08.3 06.7 05.2

5 5 5 5 5 6

55.5 56.5 57.5 58.5 59.5 00.5

17 17 17 17 17 17

17 17 17 16 16 16

03.8 02.4 01.0 59.8 58.6 57.5

6 6 6 6 6 6

01.6 02.7 03.9 05.1 06.3 07.5

44.1 45.3 46.5 47.7 48.9 50.2

16 16 16 16 16 16

56.4 55.5 54.6 53.8 53.1 52.5

6 6 6 6 6 6

5 5 5 5 5 5

51.4 52.7 54.0 55.4 56.7 58.0

16 16 16 16 16 16

52.0 51.6 51.3 51.1 50.9 50.9

30 2 4 6 8 10

5 6 6 6 6 6

59.3 00.6 01.9 03.2 04.5 05.8

16 16 16 16 16 16

12 14 16 18 20 22

6 6 6 6 6 6

07.0 08.2 09.3 10.4 11.5 12.5

24 26 28 30 32

6 6 6 6 6

13.5 14.4 15.2 15.9 16.6

m h

m

h

m

5 5 5 5 5 5

58.8 58.6 58.7 58.8 59.0 59.1

17 17 17 17 17 17

58.8 57.6 56.3 55.0 53.7 52.5

6 6 6 6 6 6

14.3 15.0 16.1 17.2 18.3 19.4

18 18 18 18 17 17

06.6 04.8 02.5 00.3 58.1 55.9

6 6 6 6 6 6

29.4 29.6 30.1 30.5 31.0 31.6

18 18 18 18 18 18

26.5 25.2 23.5 21.9 20.2 18.7

33.0 31.1 29.2 27.4 25.7 24.0

5 5 5 6 6 6

59.3 59.6 59.8 00.1 00.4 00.8

17 17 17 17 17 17

51.3 50.2 49.1 48.0 47.0 46.0

6 6 6 6 6 6

20.6 21.8 23.0 24.2 25.5 26.8

17 17 17 17 17 17

53.8 51.7 49.7 47.7 45.8 43.9

6 6 6 6 6 6

32.1 32.7 33.3 33.9 34.6 35.3

18 18 18 18 18 18

17.1 15.7 14.2 12.8 11.5 10.2

17 17 17 17 17 17

22.4 20.8 19.3 17.9 16.6 15.3

6 6 6 6 6 6

01.2 01.6 02.1 02.6 03.2 03.7

17 17 17 17 17 17

45.1 44.3 43.5 42.8 42.1 41.5

6 6 6 6 6 6

28.1 29.4 30.8 32.2 33.7 35.1

17 17 17 17 17 17

42.1 40.3 38.6 37.0 35.5 34.0

6 6 6 6 6 6

36.0 36.8 37.6 38.4 39.3 40.2

18 18 18 18 18 18

09.0 07.8 06.7 05.7 04.7 03.8

08.8 10.1 11.4 12.8 14.1 15.5

17 17 17 17 17 17

14.1 13.0 12.0 11.0 10.2 09.5

6 6 6 6 6 6

04.4 05.1 05.8 06.5 07.3 08.2

17 17 17 17 17 17

40.9 40.5 40.1 39.8 39.5 39.3

6 6 6 6 6 6

36.6 38.2 39.7 41.3 42.8 44.4

17 17 17 17 17 17

32.6 31.3 30.1 29.0 28.0 27.1

6 6 6 6 6 6

41.1 42.1 43.2 44.2 45.3 46.4

18 18 18 18 18 18

03.0 02.3 01.6 01.0 00.5 00.1

6 6 6 6 6 6

16.9 18.4 19.8 21.2 22.7 24.1

17 17 17 17 17 17

08.8 08.3 07.9 07.5 07.3 07.1

6 6 6 6 6 6

09.0 09.9 10.9 11.9 12.9 13.9

17 17 17 17 17 17

39.2 39.2 39.3 39.4 39.6 39.9

6 6 6 6 6 6

46.0 47.6 49.3 50.9 52.5 54.1

17 17 17 17 17 17

26.3 25.6 25.0 24.6 24.2 23.9

6 6 6 6 6 6

47.5 48.7 49.9 51.1 52.3 53.6

17 17 17 17 17 17

59.8 59.5 59.3 59.3 59.3 59.4

51.0 51.1 51.4 51.7 52.1 52.7

6 6 6 6 6 6

25.6 27.0 28.4 29.8 31.2 32.5

17 17 17 17 17 17

07.1 07.2 07.4 07.6 08.0 08.5

6 6 6 6 6 6

14.9 16.0 17.1 18.1 19.2 20.3

17 17 17 17 17 17

40.2 40.6 41.1 41.7 42.3 43.0

6 6 6 7 7 7

55.7 57.2 58.8 00.3 01.7 03.1

17 17 17 17 17 17

23.8 23.7 23.8 24.0 24.3 24.7

6 6 6 6 6 7

54.8 56.1 57.3 58.6 59.8 01.0

17 17 18 18 18 18

59.5 59.8 00.1 00.5 01.0 01.6

16 16 16 16 16 16

53.3 54.0 54.7 55.6 56.5 57.5

6 6 6 6 6 6

33.8 35.1 36.3 37.4 38.5 39.6

17 17 17 17 17 17

09.0 09.7 10.4 11.3 12.2 13.2

6 6 6 6 6 6

21.4 22.5 23.6 24.6 25.7 26.7

17 17 17 17 17 17

43.7 44.5 45.4 46.3 47.2 48.2

7 7 7 7 7 7

04.5 05.8 07.1 08.3 09.4 10.4

17 17 17 17 17 17

25.2 25.8 26.5 27.3 28.2 29.2

7 7 7 7 7 7

02.2 03.4 04.5 05.7 06.7 07.8

18 18 18 18 18 18

02.3 03.0 03.8 04.6 05.5 06.5

16 16 17 17 17

58.6 59.7 00.9 02.1 03.3

6 6 6 6 6

40.5 41.4 42.2 43.0 43.6

17 17 17 17 17

14.2 15.4 16.5 17.8 19.1

6 6 6 6 6

27.7 28.6 29.5 30.4 31.2

17 17 17 17 17

49.2 50.3 51.3 52.4 53.5

7 7 7 7 7

11.4 12.3 13.0 13.7 14.3

17 17 17 17 17

30.2 31.4 32.6 33.9 35.2

7 7 7 7 7

08.7 09.7 10.5 11.3 12.1

18 18 18 18 18

07.5 08.6 09.7 10.9 12.0

296

MOONRISE, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONRISE (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º

10º

20º

30º

40º

50º

Kolkata Chennai

Delhi

Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

0 1 2 3 4 5 6 7 8 9

10 10 11 12 12 13 14 15 15 16

03 46 27 08 49 31 17 05 57 53

10 10 11 12 12 13 14 14 15 16

13 52 30 07 45 24 06 51 41 36

10 10 11 12 12 13 13 14 15 16

23 59 33 07 41 17 55 37 24 17

10 11 11 12 12 13 13 14 15 15

35 07 37 07 37 08 42 21 05 55

10 11 11 12 12 12 13 14 14 15

50 17 42 07 31 58 27 00 40 28

11 11 11 12 12 12 13 13 14 14

09 30 49 06 24 43 06 32 06 49

10 10 11 11 12 12 13 14 14 15

02 37 11 43 16 51 28 09 55 47

10 11 11 12 12 13 14 14 15 16

25 04 41 17 53 32 12 57 46 40

10 11 11 12 12 13 14 14 15 16

55 28 59 29 59 31 06 45 30 21

11 11 12 12 13 13 14 15 16 16

02 38 13 47 21 57 36 18 06 59

10 11 12 13 14 15 16 17 18 19

17 18 19 20 21 22 23 ** 0 1

52 52 51 48 42 33 24 ** 13 03

17 18 19 20 21 22 23 ** 0 1

34 35 36 36 34 30 25 ** 19 13

17 18 19 20 21 22 23 ** 0 1

15 17 20 24 26 27 26 ** 24 22

16 17 19 20 21 22 23 ** 0 1

53 56 02 10 17 23 27 ** 30 33

16 17 18 19 21 22 23 ** 0 1

25 29 40 53 06 18 29 ** 38 47

15 16 18 19 20 22 23 ** 0 2

45 52 08 29 50 11 31 ** 49 07

16 17 18 19 21 22 23 ** 0 1

45 47 52 56 00 01 02 ** 01 01

17 18 19 20 21 22 23 ** 0 1

38 39 41 42 42 39 35 ** 30 25

17 18 19 20 21 22 23 ** 0 1

18 21 28 35 41 46 49 ** 52 54

17 18 20 21 22 23 ** 0 1 2

57 59 02 05 07 07 ** 06 04 01

20 21 22 23 24 25 26 27 28 29

1 2 3 4 5 6 7 7 8 9

55 48 42 36 30 21 10 57 41 22

2 3 3 4 5 6 7 8 8 9

07 03 59 54 47 37 24 08 48 27

2 3 4 5 6 6 7 8 8 9

21 19 17 13 06 55 39 20 57 32

2 3 4 5 6 7 7 8 9 9

36 38 39 36 28 15 56 33 06 37

2 4 5 6 6 7 8 8 9 9

56 02 06 04 55 39 17 50 18 44

3 4 5 6 7 8 8 9 9 9

23 36 44 44 34 14 46 12 34 53

2 3 3 4 5 6 7 7 8 9

00 00 58 54 47 35 19 59 35 09

2 3 4 5 6 6 7 8 9 9

21 17 14 09 02 52 38 21 00 38

2 3 4 5 6 7 8 8 9 9

56 3 58 3 58 4 54 5 47 6 34 7 16 8 53 8 27 9 59 10

00 58 56 51 44 33 17 58 36 11

30 31 Feb. 1 2 3 4 5 6 7 8

10 10 11 12 12 13 14 15 16 17

03 44 25 08 54 44 37 34 33 33

10 10 11 11 12 13 14 15 16 17

04 42 20 59 42 29 20 16 15 17

10 10 11 11 12 13 14 14 15 17

06 39 13 50 29 13 02 56 56 00

10 10 11 11 12 12 13 14 15 16

07 36 06 39 14 54 41 34 34 40

10 10 10 11 11 12 13 14 15 16

09 33 58 25 56 32 15 06 07 15

10 10 10 11 11 12 12 13 14 15

11 28 47 07 31 00 38 26 27 40

9 10 10 11 12 12 13 14 15 16

42 15 48 23 01 44 32 27 27 31

10 10 11 12 12 13 14 15 16 17

14 50 27 06 48 34 24 20 19 22

10 10 11 12 12 13 14 15 16 17

29 59 30 02 39 19 06 00 00 06

10 11 11 12 13 13 14 15 16 17

45 19 53 30 10 54 43 38 38 42

9 10 11 12 13 14 15

18 19 20 21 22 23 23

32 29 24 17 08 00 52

18 19 20 21 22 23 **

19 20 19 16 12 08 **

18 19 20 21 22 23 **

05 10 14 16 16 16 **

17 18 20 21 22 23 **

49 59 08 15 21 26 **

17 18 20 21 22 23 **

29 45 00 14 27 38 **

17 18 19 21 22 23 **

01 26 50 13 35 55 **

17 18 19 20 21 22 23

37 43 48 51 53 54 55

18 19 20 21 22 23 **

25 27 27 26 23 20 **

18 19 20 21 22 23 **

14 23 31 38 43 47 **

18 19 20 21 22 23 **

47 52 55 56 56 56 **

Jan.

The symbol (**) indicates that the phenomenon will occur on the next day

297

MOONSET, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONSET (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º h

Jan.

Feb.

10º m

h

20º

30º

40º

50º

Kolkata Chennai Delhi Mumbai

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h m

0 22 24 22 15 1 23 06 23 01 2 23 47 23 45 3 ** ** ** ** 4 0 27 0 29 5 1 09 1 15 6 1 53 2 02 7 2 39 2 52 8 3 30 3 45 9 4 24 4 41

22 22 23 ** 0 1 2 3 4 4

06 55 43 ** 31 20 11 04 01 59

21 22 23 ** 0 1 2 3 4 5

56 49 42 ** 34 27 22 19 19 20

21 22 23 ** 0 1 2 3 4 5

44 42 39 ** 37 35 36 38 42 46

21 22 23 ** 0 1 2 4 5 6

26 31 36 ** 41 47 54 04 15 24

21 22 23 ** 0 0 1 2 3 4

40 29 19 ** 08 58 50 44 41 40

22 23 23 ** 0 1 2 3 3 4

22 08 54 ** 40 26 14 05 59 56

22 23 ** 0 0 1 2 3 4 5

20 22 47 12 23 36 ** ** ** 04 0 23 56 1 11 48 2 00 43 2 50 40 3 43 39 4 39 39 5 37

10 11 12 13 14 15 16 17 18 19

5 6 7 8 9 10 10 11 12 13

21 21 20 18 14 07 57 47 37 28

5 6 7 8 9 10 10 11 12 13

39 38 36 31 23 12 59 44 30 17

5 6 7 8 9 10 11 11 12 13

58 57 53 45 33 17 00 41 22 06

6 7 8 9 9 10 11 11 12 12

21 19 12 01 44 24 01 37 14 52

6 7 8 9 9 10 11 11 12 12

49 46 37 20 58 32 03 33 03 36

7 8 9 9 10 10 11 11 11 12

29 24 10 47 17 42 05 27 49 14

5 6 7 8 9 9 10 11 11 12

39 38 33 25 12 55 36 16 56 38

5 6 7 8 9 10 11 11 12 13

54 53 51 45 36 23 08 53 37 23

6 7 8 9 10 10 11 12 12 13

40 38 32 21 05 45 23 00 37 17

6 7 8 9 10 10 11 12 13 13

37 35 31 24 12 57 39 21 03 46

20 21 22 23 24 25 26 27 28 29

14 15 16 17 17 18 19 20 21 21

20 13 08 02 55 45 33 18 01 42

14 14 15 16 17 18 19 20 20 21

06 57 50 44 38 30 20 09 55 39

13 14 15 16 17 18 19 19 20 21

51 40 31 25 19 14 07 58 48 36

13 14 15 16 16 17 18 19 20 21

34 19 09 02 58 55 51 47 40 33

13 13 14 15 16 17 18 19 20 21

13 54 42 34 32 31 32 32 31 29

12 13 14 14 15 16 18 19 20 21

44 19 02 54 54 58 05 12 18 23

13 14 15 15 16 17 18 19 20 21

23 11 02 55 50 45 39 31 22 11

14 15 15 16 17 18 19 20 21 21

11 02 54 48 42 35 26 15 02 48

13 14 15 16 17 18 19 20 21 21

59 45 35 28 24 20 16 11 04 56

14 15 16 17 18 18 19 20 21 22

32 21 13 07 01 55 48 39 28 16

30 22 23 22 24 22 24 22 25 22 26 22 27 22 00 22 33 22 47 23 04 31 23 04 23 08 23 12 23 17 23 23 23 32 22 49 23 19 23 39 23 52 1 23 46 23 53 ** ** ** ** ** ** ** ** 23 39 ** ** ** ** ** ** 2 ** ** ** ** 0 01 0 11 0 22 0 38 ** ** 0 05 0 32 0 40 3 0 30 0 41 0 52 1 06 1 22 1 45 0 31 0 54 1 26 1 31 4 1 17 1 31 1 46 2 03 2 24 2 54 1 26 1 45 2 23 2 25 5 2 09 2 25 2 42 3 02 3 27 4 03 2 22 2 39 3 21 3 20 6 3 04 3 21 3 40 4 02 4 30 5 09 3 21 3 36 4 21 4 18 7 4 02 4 20 4 39 5 01 5 29 6 09 4 20 4 35 5 20 5 17 8 5 02 5 19 5 37 5 57 6 23 7 00 5 17 5 34 6 17 6 15 9 6 02 6 16 6 32 6 49 7 11 7 10 7 00 7 11 7 23 7 36 7 53 8 11 7 56 8 03 8 10 8 19 8 29 8 12 8 49 8 52 8 55 8 58 9 02 9 13 9 41 9 40 9 38 9 36 9 34 9 14 10 33 10 27 10 21 10 14 10 05 9 15 11 24 11 15 11 04 10 52 10 38 10

41 6 15 7 43 7 07 8 30 9 53 9 18 10

12 6 30 7 09 7 10 02 7 24 7 56 8 01 48 8 15 8 40 8 49 32 9 03 9 20 9 34 14 9 49 9 58 10 18 55 10 35 10 37 11 01 37 11 21 11 16 11 45

The symbol (**) indicates that the phenomenon will occur on the next day

298

MOONRISE, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONRISE (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º h

10º m

h

20º m

h

30º m

h

40º m

h

50º m

h

Kolkata Chennai m

h

m

h

Delhi

m

h

m

Mumbai h

m

Feb. 15 23 52 ** ** ** ** ** ** ** ** ** ** 23 55 ** ** ** ** ** ** 16 ** ** 0 03 0 16 0 30 0 48 1 13 ** ** 0 17 0 50 0 55 17 0 44 0 59 1 15 1 33 1 56 2 28 0 55 1 13 1 53 1 53 18 1 38 1 55 2 13 2 34 3 00 3 38 1 53 2 10 2 53 2 51 19 2 32 2 50 3 09 3 31 3 59 4 40 2 50 3 05 3 50 3 47 20 3 25 3 43 4 02 4 24 4 52 5 32 3 43 3 58 4 43 4 40 21 4 16 4 33 4 51 5 12 5 38 6 14 4 32 4 48 5 31 5 29 22 5 06 5 21 5 36 5 54 6 17 6 48 5 17 5 35 6 14 6 15 23 5 53 6 05 6 18 6 32 6 51 7 15 5 57 6 18 6 52 6 56 24 6 37 6 46 6 56 7 07 7 20 7 38 6 34 6 59 7 27 7 34 25 26 27 28 29 Mar. 1 2 3 4 5

7 8 8 9 10 10 11 12 13 14

20 01 41 22 04 48 35 25 18 15

7 8 8 9 9 10 11 12 13 13

25 03 40 17 56 37 21 08 01 57

7 8 8 9 9 10 11 11 12 13

31 05 39 12 47 25 06 51 42 37

7 8 8 9 9 10 10 11 12 13

38 08 37 07 38 11 49 31 20 15

7 8 8 9 9 9 10 11 11 12

47 7 58 7 11 8 16 7 36 8 33 8 00 8 51 8 26 9 10 9 55 9 32 9 27 9 58 10 06 10 31 11 52 11 13 12 47 12 06 13

09 42 15 47 21 58 38 22 12 08

7 8 8 9 10 10 11 12 13 14

37 13 49 26 03 43 26 13 05 01

7 8 9 9 10 10 11 11 12 13

59 30 00 30 01 35 13 56 45 41

8 8 9 9 10 11 11 12 13 14

10 45 18 52 28 06 47 32 23 19

6 7 8 9 10 11 12 13 14 15

15 16 17 18 19 19 20 21 22 23

14 13 11 07 02 56 49 43 37 32

14 15 16 18 18 19 20 21 22 23

56 58 59 00 59 58 56 54 51 49

14 15 16 17 18 20 21 22 23 **

38 42 47 52 57 00 03 05 06 **

14 15 16 17 18 20 21 22 23 **

17 24 33 43 53 02 10 18 23 **

13 15 16 17 18 20 21 22 23 **

50 01 16 32 49 05 20 34 45 **

13 14 15 17 18 20 21 22 ** 0

12 29 52 17 44 09 34 56 ** 16

14 15 16 17 18 19 20 21 22 23

09 13 19 26 31 36 40 43 46 47

15 16 17 18 19 20 21 22 23 **

01 03 05 07 08 08 07 06 05 **

14 15 16 18 19 20 21 22 23 **

43 49 58 07 16 24 32 38 43 **

15 16 17 18 19 20 21 22 23 **

20 24 29 33 37 40 42 44 45 **

16 17 18 19 20 21 22 23 24 25

** 0 1 2 3 3 4 5 6 6

** ** ** 27 0 45 21 1 40 14 2 31 04 3 19 51 4 04 36 4 46 18 5 25 00 6 03 40 6 40

0 1 1 2 3 4 4 5 6 6

07 04 59 50 36 18 56 32 07 40

0 1 2 3 3 4 5 5 6 6

27 27 22 11 55 34 09 41 11 40

0 1 2 3 4 4 5 5 6 6

53 55 50 38 19 53 24 51 16 40

1 2 3 4 4 5 5 6 6 6

30 35 31 16 52 21 44 04 22 40

** 0 1 2 3 3 4 5 5 6

** 46 40 31 16 58 35 10 44 16

0 1 1 2 3 4 4 5 6 6

04 00 55 46 34 18 58 37 14 50

0 1 2 3 4 4 5 6 6 7

46 46 41 30 14 53 29 01 32 02

0 1 2 3 4 4 5 6 6 7

45 43 37 28 14 56 35 11 46 19

17 7 13 7 09 7 55 7 48 7 39 7 35 8 24 8 12 7 18 9 03 8 47 8 03 9 46 9 27 9 53 10 34 10 12 9 46 11 26 11 04 10

04 29 56 27 03 45 35

6 7 7 7 8 9 9

57 6 48 7 26 7 15 7 22 8 03 8 35 7 57 8 41 8 59 8 35 9 23 9 29 9 18 10 08 9 06 10 05 10 57 10 54 10 57 11 50 11

26 7 21 7 27 8 02 7 28 8 45 8 29 9 31 9 30 10 19 10 31 11 10 10 Apr. 1 12 04 11

The symbol (**) indicates that the phenomenon will occur on the next day

32 7 53 03 8 28 36 9 05 12 9 44 52 10 28 38 11 16 29 12 08

299

MOONSET, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONSET (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º

10º

20º

30º

40º

50º

Kolkata Chennai Delhi Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

15 16 17 18 19 20 21 22 23 24

11 12 13 14 14 15 16 17 18 18

24 17 10 04 57 50 41 29 14 58

11 12 12 13 14 15 16 17 18 18

15 03 54 46 39 32 25 15 04 50

11 11 12 13 14 15 16 17 17 18

04 49 37 27 20 14 08 01 52 42

10 11 12 13 13 14 15 16 17 18

52 33 18 06 57 52 48 44 39 33

10 11 11 12 13 14 15 16 17 18

38 13 53 39 29 24 23 23 23 22

10 10 11 12 12 13 14 15 17 18

18 46 19 00 49 45 48 53 00 06

10 11 12 12 13 14 15 16 17 18

37 21 08 58 50 44 39 33 25 16

11 12 12 13 14 15 16 17 18 18

21 09 59 50 43 37 29 21 10 58

11 11 12 13 14 15 16 17 18 18

16 58 43 31 23 18 13 09 04 57

11 12 13 14 15 15 16 17 18 19

45 30 18 09 02 55 49 42 33 23

25 26 27 28 29 Mar. 1 2 3 4 5

19 20 21 21 22 23 23 ** 0 1

40 20 01 42 25 10 58 ** 50 45

19 20 21 21 22 23 ** 0 1 2

36 20 04 49 35 23 ** 14 07 03

19 20 21 21 22 23 ** 0 1 2

31 19 07 55 45 37 ** 30 26 23

19 20 21 22 22 23 ** 0 1 2

26 19 11 03 57 52 ** 49 47 45

19 20 21 22 23 ** 0 1 2 3

20 18 15 13 12 ** 12 13 14 14

19 20 21 22 23 ** 0 1 2 3

12 17 21 26 32 ** 39 47 53 54

19 19 20 21 22 23 ** 0 1 2

06 55 44 33 24 16 ** 11 07 04

19 20 21 22 22 23 ** 0 1 2

44 29 14 00 47 36 ** 28 22 19

19 20 21 22 23 ** 0 1 2 3

49 41 32 24 17 ** 12 09 06 04

20 20 21 22 23 ** 0 1 2 3

11 59 47 35 24 ** 15 09 04 01

Feb.

Apr.

6 2 43 3 7 3 42 3 8 4 40 4 9 5 38 5 10 6 33 6 11 7 28 7 12 8 21 8 13 9 15 9 14 10 09 9 15 11 04 10

01 3 58 4 53 5 47 5 38 6 28 7 17 8 06 8 57 9 48 10

20 3 15 4 07 5 57 6 44 6 28 7 13 8 57 8 44 9 32 10

42 35 23 08 49 29 08 47 29 13

4 4 5 6 6 7 8 8 9 9

09 59 43 22 57 29 02 35 11 50

4 5 6 6 7 7 7 8 8 9

16 17 18 19 20 21 22 23 24 25

11 12 13 14 15 16 16 17 18 19

59 53 47 38 27 13 56 38 19 00

11 12 13 14 15 16 16 17 18 19

41 35 29 21 12 01 48 33 18 02

11 12 13 14 14 15 16 17 18 19

23 16 09 04 57 49 39 28 16 04

11 11 12 13 14 15 16 17 18 19

01 53 47 43 39 34 28 21 14 06

10 11 12 13 14 15 16 17 18 19

35 24 19 17 16 16 15 14 11 09

26 27 28 29 30 31 1

19 20 21 21 22 23 **

41 23 07 54 43 36 **

19 20 21 22 23 23 **

46 32 19 09 00 54 **

19 20 21 22 23 ** 0

52 41 32 24 18 ** 14

19 20 21 22 23 ** 0

59 52 47 43 39 ** 36

20 21 22 23 ** 0 1

07 05 05 05 ** 06 05

h m

48 3 33 3 10 4 40 5 06 6 30 7 53 7 18 8 46 9 18 10

01 3 16 4 55 4 12 4 47 5 07 5 35 5 59 6 21 6 49 7 05 7 38 7 48 8 25 8 31 9 13 9 16 10 03 9 03 10 53 10

01 3 58 54 4 53 43 5 46 29 6 36 11 7 23 51 8 08 31 8 53 11 9 38 53 10 25 39 11 13

9 10 11 12 13 14 15 17 18 19

57 44 39 40 45 51 57 03 08 13

10 11 12 13 14 15 16 17 17 18

54 46 40 34 28 21 12 02 51 40

11 12 13 14 15 16 16 17 18 19

46 39 33 26 17 07 55 41 27 12

11 12 13 14 15 15 16 17 18 19

27 19 13 08 04 59 52 45 36 28

12 12 13 14 15 16 17 18 18 19

04 57 51 45 38 30 20 08 56 43

20 21 22 23 ** 0 1

18 24 30 38 ** 43 45

19 20 21 22 22 23 **

29 20 11 04 59 55 **

19 20 21 22 23 ** 0

57 44 32 23 15 ** 09

20 21 22 23 23 ** 0

20 13 07 02 59 ** 55

20 21 22 23 23 ** 0

31 20 11 03 57 ** 52

The symbol (**) indicates that the phenomenon will occur on the next day

300

MOONRISE, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONRISE (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

Apr.

May

0º

10º

20º

30º

40º

50º

Kolkata Chennai

Delhi

Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

12 13 13 14 15 16 17 18 19 20

04 00 57 54 50 44 39 33 27 23

11 12 13 14 15 16 17 18 19 20

46 42 41 41 40 39 38 37 36 36

11 12 13 14 15 16 17 18 19 20

26 23 24 26 30 34 37 41 45 49

11 12 13 14 15 16 17 18 19 21

04 01 04 10 18 27 37 46 56 05

10 11 12 13 15 16 17 18 20 21

35 33 38 49 04 19 36 53 09 24

9 10 12 13 14 16 17 19 20 21

54 53 03 21 44 09 35 01 27 52

10 11 12 13 15 16 17 18 19 20

57 54 55 58 03 08 13 18 23 29

11 12 13 14 15 16 17 18 19 20

50 47 46 46 47 47 47 48 48 49

11 12 13 14 15 16 17 19 20 21

29 27 29 35 43 51 59 08 17 25

12 13 14 15 16 17 18 19 20 21

08 05 05 08 11 14 18 21 25 28

11 21 20 21 36 12 22 17 22 35 13 23 14 23 32 14 ** ** ** ** 15 0 08 0 26 16 1 00 1 17 17 1 49 2 03 18 2 34 2 46 19 3 18 3 26 20 3 59 4 04

21 22 23 ** 0 1 2 2 3 4

53 22 12 22 37 23 12 54 23 16 23 44 ** ** 52 ** ** ** ** 0 24 ** 0 15 0 44 1 26 46 1 08 1 36 2 16 34 1 54 2 20 2 55 18 2 35 2 56 3 26 57 3 11 3 28 3 51 34 3 44 3 56 4 12 08 4 14 4 21 4 30

21 22 23 ** 0 1 1 2 3 3

33 35 33 ** 27 15 58 37 12 46

21 22 23 ** 0 1 2 2 3 4

50 22 32 22 31 50 23 35 23 33 48 ** ** ** ** ** 0 34 0 30 42 1 27 1 24 31 2 13 2 12 17 2 55 2 56 59 3 31 3 36 38 4 04 4 13 15 4 35 4 47

1 2 3 4 5 6 7 8 9 10

21 4 40 4 22 5 20 5 23 6 01 5 24 6 44 6 25 7 29 7 26 8 16 8 27 9 07 8 28 10 00 9 29 10 54 10 30 11 49 11

41 4 42 4 18 5 15 5 55 5 49 5 35 6 25 6 16 7 03 6 01 7 45 7 49 8 31 8 41 9 21 8 36 10 16 9 32 11 14 10

43 4 12 5 42 5 13 5 48 6 26 7 09 7 58 8 53 9 53 10

45 08 33 59 29 03 43 30 24 26

4 5 5 5 6 6 7 7 8 9

1 2 3 4 5 6 7 8 9 10

30 27 24 21 18 16 16 17 18 18

56 01 07 14 22 31 40 50 58 01

33 44 56 10 25 40 57 12 24 30

11 12 13 15 16 17 19 20 22 23

12 13 14 15 16 17 18 19 20 21

44 39 32 24 17 10 05 02 01 00

12 13 14 15 16 17 18 19 20 21

12 13 14 15 16 17 18 19 20 21

14 15 16 18 20 23 27 32 36 38

11 13 14 15 16 17 18 19 20 22

11 12 13 15 16 17 18 20 21 22

47 4 04 4 21 5 41 5 03 6 31 7 05 8 49 8 43 9 48 10

18 4 51 5 05 5 21 50 5 26 5 34 5 55 23 6 03 6 05 6 29 58 6 41 6 37 7 05 35 7 22 7 12 7 44 16 8 06 7 51 8 26 02 8 54 8 35 9 12 52 9 45 9 24 10 03 46 10 40 10 19 10 58 45 11 37 11 18 11 56

01 20 41 04 28 54 19 44 03 12

45 47 50 53 56 01 06 12 17 19

11 12 13 14 15 17 18 19 20 21

12 13 14 15 16 17 18 19 20 21

35 33 32 30 29 28 29 31 33 34

12 13 14 15 16 17 19 20 21 22

21 26 31 38 44 52 01 10 17 20

12 13 14 15 17 18 19 20 21 22

56 56 57 59 00 03 06 11 15 16

11 21 57 22 16 22 36 22 59 23 28 ** ** 22 17 22 31 23 18 23 14 12 22 52 23 09 23 28 23 49 ** ** 0 10 23 09 23 24 ** ** ** ** 13 23 43 23 58 ** ** ** ** 0 16 0 54 23 55 ** ** 0 08 0 06 14 ** ** ** ** 0 15 0 33 0 57 1 29 ** ** 0 13 0 53 0 53 15 0 31 0 43 0 56 1 12 1 30 1 56 0 36 0 57 1 31 1 35 16 1 15 1 24 1 34 1 46 1 59 2 18 1 13 1 37 2 06 2 13 17 1 57 2 03 2 10 2 17 2 25 2 37 1 47 2 15 2 38 2 48 The symbol (**) indicates that the phenomenon will occur on the next day

301

MOONSET, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONSET (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º h

Apr.

May

10º m

h

20º

30º

40º

50º

Kolkata Chennai Delhi Mumbai

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h m

0 1 2 2 3 4 5 6 6 7

14 09 03 55 44 31 16 00 45 32

0 1 2 3 3 4 5 5 6 7

36 32 24 13 58 40 19 58 38 19

1 2 2 3 4 4 5 5 6 7

05 00 50 35 15 50 24 56 29 04

1 2 3 4 4 5 5 5 6 6

45 ** ** 41 0 50 27 1 44 06 2 35 38 3 23 05 4 09 29 4 53 52 5 36 16 6 20 42 7 05

0 1 2 2 3 4 5 6 7 7

09 05 00 53 45 35 23 11 00 50

0 1 2 3 4 5 5 6 7 7

55 50 43 32 18 01 41 21 01 43

0 1 2 3 4 5 5 6 7 8

52 47 41 33 23 10 55 40 26 13

1 2 3 4 5 6 7 8 9 10

** 0 1 2 3 4 5 6 6 7

** ** ** 31 0 49 28 1 45 24 2 39 21 3 32 16 4 23 10 5 13 04 6 02 58 6 52 54 7 43

11 12 13 14 15 16 17 18 19 20

8 9 10 11 12 13 14 14 15 16

50 48 45 40 34 24 11 55 38 19

8 9 10 11 12 13 13 14 15 16

36 31 26 22 16 08 58 46 31 16

8 9 10 11 11 12 13 14 15 16

21 13 07 02 57 52 45 35 25 13

8 8 9 10 11 12 13 14 15 16

04 52 44 39 36 33 29 23 17 09

7 8 9 10 11 12 13 14 15 16

42 26 16 10 08 09 09 09 07 05

7 7 8 9 10 11 12 13 14 15

13 50 35 29 29 35 41 48 54 59

7 8 9 10 11 12 13 14 14 15

53 44 37 32 28 23 17 08 59 48

8 9 10 11 12 13 14 14 15 16

41 35 30 26 20 13 04 52 39 25

8 9 10 11 12 12 13 14 15 16

29 18 10 05 02 58 54 48 40 32

9 9 10 11 12 13 14 15 16 16

02 54 49 44 39 33 26 16 05 53

21 22 23 24 25 26 27 28 29 30

16 17 18 19 19 20 21 22 23 **

59 40 22 05 51 40 32 26 21 **

17 17 18 19 20 20 21 22 23 **

00 44 29 16 06 57 50 44 39 **

17 17 18 19 20 21 22 23 23 **

01 49 38 28 21 14 09 04 58 **

17 17 18 19 20 21 22 23 ** 0

01 54 47 42 38 35 32 27 ** 20

17 18 18 19 21 22 23 23 ** 0

03 00 59 59 00 01 00 56 ** 47

17 18 19 20 21 22 23 ** 0 1

04 09 15 22 30 37 41 ** 38 26

16 17 18 19 20 20 21 22 23 **

37 26 16 07 01 55 50 45 39 **

17 17 18 19 20 21 22 23 23 **

10 55 41 29 19 12 05 00 54 **

17 18 19 20 20 21 22 23 ** 0

24 15 08 02 58 54 51 46 ** 39

17 18 19 20 20 21 22 23 ** 0

40 28 17 07 59 53 48 42 ** 36

1 2 3 4 5 6 7 8 9 10

0 1 2 2 3 4 5 6 7 8

16 10 04 57 49 42 36 32 30 29

0 1 2 3 3 4 5 6 7 8

32 23 13 02 50 38 28 20 14 11

0 1 2 3 3 4 5 6 6 7

49 37 23 07 50 34 19 07 58 52

1 1 2 3 3 4 5 5 6 7

08 53 34 13 51 29 09 51 38 30

1 2 2 3 3 4 4 5 6 7

33 13 48 21 52 23 56 33 14 02

2 2 3 3 3 4 4 5 5 6

07 39 07 31 53 15 40 07 41 23

0 1 2 2 3 4 4 5 6 7

29 17 02 45 26 09 52 39 29 23

0 1 2 3 3 4 5 6 7 8

46 37 26 13 59 46 35 26 19 15

1 2 2 3 4 4 5 6 7 7

28 13 55 34 13 52 32 16 04 56

1 2 3 3 4 5 5 6 7 8

27 16 02 46 30 14 59 48 39 34

11 12 13 14 15 16 17

9 10 11 12 12 13 14

28 24 17 06 52 36 17

9 10 11 11 12 13 14

09 06 00 52 41 28 13

8 9 10 11 12 13 14

49 46 43 37 30 20 09

8 9 10 11 12 13 14

25 23 22 20 16 10 03

7 8 9 10 11 12 13

56 55 56 58 59 59 57

7 8 9 10 11 12 13

14 14 19 28 36 43 48

8 9 10 11 12 12 13

19 16 14 09 02 53 43

9 10 11 11 12 13 14

13 10 05 58 48 35 21

8 9 10 11 12 13 14

51 49 48 45 41 34 27

9 10 11 12 13 14 14

31 28 24 19 11 00 49

The symbol (**) indicates that the phenomenon will occur on the next day

302

MOONRISE, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONRISE (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º

10º

20º

30º

40º

50º

Kolkata Chennai

Delhi

Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

May 17 18 19 20 21 22 23 24 25 26

1 2 3 3 4 5 6 7 7 8

57 38 19 59 42 26 13 03 56 50

2 2 3 3 4 5 5 6 7 8

03 41 17 55 33 14 58 46 37 32

2 2 3 3 4 5 5 6 7 8

10 43 16 50 25 02 43 28 18 11

2 2 3 3 4 4 5 6 6 7

17 46 15 44 15 48 25 07 55 48

2 2 3 3 4 4 5 5 6 7

25 49 13 37 03 31 03 42 27 19

2 2 3 3 3 4 4 5 5 6

37 54 11 28 46 07 33 05 46 37

1 2 2 3 3 4 5 5 6 7

47 20 52 24 58 35 15 59 48 42

2 2 3 4 4 5 6 6 7 8

15 51 27 03 40 20 03 50 41 35

2 3 3 4 4 5 5 6 7 8

38 08 37 07 38 12 50 33 21 14

2 3 3 4 5 5 6 7 7 8

48 22 56 30 05 43 24 09 59 53

27 28 29 30 31 June 1 2 3 4 5

9 10 11 12 13 14 14 15 16 17

46 40 34 26 17 07 59 51 46 44

9 10 11 12 13 14 15 16 16 17

28 25 21 17 12 07 03 00 59 59

9 10 11 12 13 14 15 16 17 18

09 08 08 08 07 07 07 09 12 16

8 9 10 11 13 14 15 16 17 18

47 49 52 57 01 06 12 19 28 36

8 9 10 11 12 14 15 16 17 19

19 24 33 43 54 06 19 33 47 01

7 8 10 11 12 14 15 16 18 19

39 50 06 25 45 06 28 51 14 36

8 9 10 11 12 13 14 15 16 17

39 39 40 41 41 42 44 47 52 57

9 10 11 12 13 14 15 16 17 18

32 30 27 24 20 17 14 12 12 14

9 10 11 12 13 14 15 16 17 18

13 14 17 21 25 29 34 40 48 56

9 10 11 12 13 14 15 16 17 18

51 50 49 49 48 47 47 48 51 55

6 7 8 9 10 11 12 13 14 15

18 19 20 21 22 23 23 ** 0 1

42 41 39 33 23 10 53 ** 35 16

19 20 20 21 22 23 ** 0 0 1

00 00 57 49 37 20 ** 01 39 16

19 20 21 22 22 23 ** 0 0 1

20 20 16 07 52 32 ** 09 43 16

19 20 21 22 23 23 ** 0 0 1

42 44 39 27 08 45 ** 17 47 16

20 21 22 22 23 ** 0 0 0 1

11 13 07 52 29 ** 01 28 53 17

20 21 22 23 23 ** 0 0 1 1

51 56 48 27 58 ** 23 43 01 17

19 20 20 21 22 23 23 ** 0 0

01 02 58 47 32 11 47 ** 20 52

19 20 21 22 22 23 ** 0 0 1

16 16 12 04 51 33 ** 13 50 25

20 21 21 22 23 ** 0 0 1 1

01 03 58 46 28 ** 05 38 09 38

19 20 21 22 23 ** 0 0 1 1

58 59 55 45 30 ** 10 47 22 55

16 17 18 19 20 21 22 23 24 25

1 2 3 4 4 5 6 7 8 9

56 38 21 07 56 48 43 40 36 31

1 2 3 3 4 5 6 7 8 9

53 31 11 53 40 31 25 22 19 17

1 2 3 3 4 5 6 7 8 9

49 23 00 39 23 11 05 02 02 02

1 2 2 3 4 4 5 6 7 8

45 15 47 23 03 49 42 39 41 45

1 2 2 3 3 4 5 6 7 8

40 05 32 03 39 22 12 11 16 24

1 1 2 2 3 3 4 5 6 7

34 51 11 35 05 42 30 30 39 55

1 1 2 3 3 4 5 6 7 8

24 57 33 11 54 42 35 32 33 34

2 2 3 3 4 5 6 7 8 9

01 38 17 59 45 35 29 26 24 22

2 2 3 3 4 5 6 7 8 9

08 38 11 48 29 15 07 05 07 11

2 3 3 4 5 5 6 7 8 9

29 04 40 20 04 53 47 44 44 44

26 27 28 29 30 July 1 2

10 11 12 12 13 14 15

23 14 04 54 44 37 31

10 11 12 12 13 14 15

13 08 02 56 51 48 46

10 11 12 12 13 14 16

02 02 00 59 59 59 02

9 10 11 13 14 15 16

50 54 58 02 07 13 20

9 10 11 13 14 15 16

35 45 56 06 18 30 42

9 10 11 13 14 15 17

13 33 52 12 33 54 14

9 10 11 12 13 14 15

35 36 36 36 36 38 41

10 11 12 13 14 15 16

20 16 11 07 03 01 00

10 11 12 13 14 15 16

14 18 21 24 28 33 39

10 11 12 13 14 15 16

44 42 41 39 38 38 40

The symbol (**) indicates that the phenomenon will occur on the next day

303

MOONSET, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONSET (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

May

June

July

0º

10º

20º

30º

40º

50º

Kolkata Chennai Delhi Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

14 14 15 16 17 17 18 19 20 21

17 58 38 20 03 48 37 28 22 17

14 14 15 16 17 18 18 19 20 21

13 57 41 26 13 01 52 46 40 35

14 14 15 16 17 18 19 20 21 21

09 56 44 33 23 15 09 05 00 55

14 14 15 16 17 18 19 20 21 22

03 56 48 41 36 32 29 27 23 17

13 14 15 16 17 18 19 20 21 22

57 55 52 51 51 52 54 55 53 46

13 14 15 17 18 19 20 21 22 23

48 53 59 04 12 20 28 34 35 26

13 14 15 16 17 17 18 19 20 21

43 32 21 11 02 55 50 46 42 36

14 15 15 16 17 18 19 20 20 21

21 06 52 38 25 15 07 01 56 50

14 15 16 17 17 18 19 20 21 22

27 18 10 02 56 51 48 46 42 36

27 22 12 22 29 22 47 23 07 23 33 ** ** 22 27 22 44 28 23 06 23 20 23 35 23 53 ** ** 0 09 23 15 23 34 29 23 59 ** ** ** ** ** ** 0 14 0 43 ** ** ** ** 30 ** ** 0 10 0 21 0 34 0 50 1 12 0 00 0 23 31 0 50 0 57 1 04 1 12 1 22 1 36 0 42 1 09 1 1 41 1 43 1 46 1 49 1 53 1 57 1 23 1 54 2 2 32 2 30 2 28 2 25 2 22 2 18 2 03 2 39 3 3 23 3 17 3 10 3 03 2 53 2 41 2 44 3 25 4 4 17 4 06 3 55 3 43 3 27 3 06 3 28 4 13 5 5 13 4 59 4 44 4 27 4 05 3 35 4 16 5 04

23 ** 0 0 1 2 2 3 4 4

26 23 25 ** ** ** 12 0 14 54 1 00 33 1 43 11 2 25 48 3 07 26 3 51 07 4 36 51 5 25

6 7 8 9 10 11 12 13 14 15

6 7 8 9 9 10 11 12 12 13

12 11 09 05 57 46 31 14 55 35

5 6 7 8 9 10 11 12 12 13

54 52 51 48 42 34 22 08 53 37

5 6 7 8 9 10 11 12 12 13

36 32 30 29 26 20 12 02 50 38

5 6 7 8 9 10 11 11 12 13

15 09 07 07 07 05 01 55 48 40

4 5 6 7 8 9 10 11 12 13

49 40 38 40 43 46 47 47 45 43

4 4 5 7 8 9 10 11 12 13

12 59 55 00 09 19 28 35 41 46

5 6 7 7 8 9 10 11 12 13

07 03 01 59 57 52 45 36 26 15

5 6 7 8 9 10 11 12 13 13

59 56 54 52 47 39 29 16 02 47

5 6 7 8 9 10 11 12 13 14

41 35 33 33 32 30 25 19 11 02

6 7 8 9 10 11 11 12 13 14

18 14 12 11 07 02 53 42 30 18

16 17 18 19 20 21 22 23 24 25

14 14 15 16 17 18 19 20 21 21

16 58 43 30 21 15 10 07 02 56

14 15 15 16 17 18 19 20 21 22

21 07 55 45 38 33 29 24 17 08

14 15 16 17 17 18 19 20 21 22

27 16 07 01 56 53 49 43 33 20

14 15 16 17 18 19 20 21 21 22

33 27 22 19 18 16 12 04 52 35

14 15 16 17 18 19 20 21 22 22

41 40 40 42 45 45 41 31 15 52

14 15 17 18 19 20 21 22 22 23

51 58 06 15 23 26 22 09 46 16

14 14 15 16 17 18 19 20 21 22

04 54 47 41 37 34 30 24 14 00

14 15 16 16 17 18 19 20 21 22

32 19 08 59 53 49 44 39 32 21

14 15 16 17 18 19 20 21 22 22

54 47 42 39 37 35 31 23 11 55

15 15 16 17 18 19 20 21 22 22

06 55 46 39 35 31 27 21 12 59

26 22 48 22 56 23 04 23 14 23 26 23 42 27 23 38 23 42 23 46 23 51 23 56 ** ** 28 ** ** ** ** ** ** ** ** ** ** 0 04 29 0 28 0 27 0 27 0 26 0 25 0 24 30 1 17 1 13 1 08 1 02 0 55 0 45 1 2 09 2 00 1 50 1 39 1 26 1 08 2 3 02 2 50 2 36 2 20 2 01 1 35

22 23 ** 0 0 1 2

43 23 08 23 23 53 ** ** ** 02 0 37 42 1 21 24 2 07 08 2 55

23 ** 0 0 1 2 2

35 23 43 ** ** ** 12 0 25 48 1 06 25 1 48 03 2 31 45 3 17

17 18 19 20 21 22 23 24 25 26

The symbol (**) indicates that the phenomenon will occur on the next day

h m 14 15 16 17 18 18 19 20 21 22

49 36 24 12 02 54 48 43 38 33

304

MOONRISE, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONRISE (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

July

Aug.

0º

10º

20º

30º

40º

50º

Kolkata Chennai

Delhi

Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

14 15 16 17 18 19 20 21 21 22

37 31 28 27 25 20 13 02 47 30

14 15 16 17 18 19 20 21 21 22

48 46 46 45 43 38 28 14 56 35

14 16 17 18 19 19 20 21 22 22

59 02 04 05 03 56 44 27 05 41

15 16 17 18 19 20 21 21 22 22

13 20 25 28 26 18 03 42 16 47

15 16 17 18 19 20 21 22 22 22

30 42 52 58 55 45 25 00 29 55

15 17 18 19 20 21 21 22 22 23

54 14 31 40 37 22 57 25 47 05

14 15 16 17 18 19 20 21 21 22

38 41 45 46 45 37 24 06 44 19

15 16 17 18 18 19 20 21 22 22

01 00 01 01 59 53 42 27 08 47

15 16 17 18 19 20 21 22 22 23

33 39 45 47 45 37 22 01 36 08

15 16 17 18 19 20 21 22 22 23

38 40 42 44 41 35 22 05 44 20

11 23 11 23 13 23 15 23 17 23 19 23 23 12 23 52 23 50 23 48 23 46 23 43 23 39 13 ** ** ** ** ** ** ** ** ** ** 23 56 14 0 33 0 27 0 21 0 15 0 07 ** ** 15 1 15 1 06 0 56 0 46 0 33 0 15 16 1 59 1 47 1 34 1 20 1 01 0 37 17 2 47 2 32 2 16 1 58 1 35 1 03 18 3 38 3 21 3 02 2 41 2 15 1 37 19 4 32 4 14 3 54 3 31 3 02 2 21 20 5 29 5 10 4 50 4 27 3 58 3 16

22 23 23 ** 0 1 1 2 3 4

51 23 23 23 38 23 54 23 23 59 ** ** ** ** 56 ** ** 0 08 0 27 ** 0 35 0 38 1 01 30 1 13 1 09 1 37 07 1 53 1 44 2 15 48 2 37 2 23 2 57 33 3 25 3 07 3 44 24 4 18 3 57 4 36 21 5 14 4 53 5 32

21 22 23 24 25 26 27 28 29 30

6 7 8 9 10 10 11 12 13 14

26 23 18 10 01 51 41 33 26 21

6 7 8 9 9 10 11 12 13 14

09 08 06 03 58 53 47 42 39 37

5 6 7 8 9 10 11 12 13 14

50 52 54 55 55 54 53 53 54 55

5 6 7 8 9 10 12 13 14 15

29 34 40 46 51 56 00 05 10 15

5 6 7 8 9 10 12 13 14 15

02 11 23 35 47 58 09 20 31 41

4 5 6 8 9 11 12 13 15 16

23 39 59 20 41 01 21 41 01 18

5 6 7 8 9 10 11 12 13 14

21 24 27 29 30 30 31 32 33 35

6 7 8 9 10 11 11 12 13 14

13 13 13 10 07 03 59 55 53 52

5 6 8 9 10 11 12 13 14 15

55 59 05 10 14 18 22 26 30 34

6 7 8 9 10 11 12 13 14 15

32 34 36 36 35 34 33 32 32 33

31 1 2 3 4 5 6 7 8 9

15 16 17 18 18 19 20 21 21 22

17 14 10 04 54 41 25 07 48 28

15 16 17 18 19 19 20 21 21 22

36 33 28 20 07 51 31 10 47 24

15 16 17 18 19 20 20 21 21 22

55 53 48 37 21 2 38 13 46 20

16 17 18 18 19 20 20 21 21 22

18 17 10 57 38 14 47 17 46 15

16 17 18 19 19 20 20 21 21 22

47 46 38 21 58 29 56 21 45 08

17 18 19 19 20 20 21 21 21 22

28 29 18 56 26 50 9 27 44 00

15 16 17 18 19 19 20 20 21 21

36 35 29 18 01 41 17 50 22 54

15 16 17 18 19 20 20 21 21 22

51 49 44 34 21 04 43 20 56 32

16 17 18 19 19 20 21 21 22 22

37 35 29 16 57 34 07 38 08 37

16 17 18 19 20 20 21 21 22 22

33 31 26 15 00 40 17 52 26 59

10 23 09 23 02 22 54 22 44 11 23 52 23 42 23 30 23 17 12 ** ** ** ** ** ** 23 52 13 0 38 0 24 0 09 ** ** 14 1 27 1 10 0 53 0 33 15 2 19 2 01 1 41 1 19 16 3 14 2 56 2 35 2 12

22 23 23 ** 0 0 1

33 00 31 ** 08 51 43

22 22 23 23 ** 0 1

18 38 02 32 ** 11 01

22 23 23 ** 0 1 2

28 23 09 23 08 23 34 03 23 48 23 41 ** ** 41 ** ** ** ** 0 11 ** 0 29 0 17 0 50 24 1 15 0 58 1 34 12 2 05 1 45 2 23 06 2 59 2 38 3 17

1 2 3 4 5 6 7 8 9 10

The symbol (**) indicates that the phenomenon will occur on the next day

305

MOONSET, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONSET (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º h

July

Aug.

10º m

20º

30º

40º

50º

Kolkata Chennai Delhi Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

1 2 2 3 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10

09 2 02 2 58 3 56 4 55 5 52 6 46 7 37 8 24 9 08 10

00 50 42 38 36 34 30 23 14 01

1 2 3 4 5 6 7 8 9 9

50 36 25 19 16 14 12 08 02 54

1 2 3 3 4 5 6 7 8 9

39 20 06 57 52 51 52 51 49 45

1 2 2 3 4 5 6 7 8 9

26 01 42 29 23 23 26 30 33 34

1 1 2 2 3 4 5 7 8 9

08 35 08 49 40 42 50 00 11 19

1 2 2 3 4 5 6 7 8 9

24 2 08 2 57 3 49 4 46 5 44 6 43 7 40 8 35 9 27 10

07 2 55 2 47 3 42 4 40 5 38 6 34 7 29 8 20 9 09 10

03 2 45 3 31 4 22 5 18 5 17 6 17 7 17 8 14 9 09 10

31 17 07 01 58 56 54 50 43 34

11 12 13 14 15 16 17 18 19 20

10 11 12 12 13 14 15 16 16 17

50 31 11 53 36 22 11 04 59 56

10 11 12 13 13 14 15 16 17 18

47 31 15 00 47 36 27 22 18 14

10 11 12 13 13 14 15 16 17 18

43 31 19 08 58 50 45 41 38 34

10 11 12 13 14 15 16 17 18 18

39 31 24 17 11 07 05 04 01 56

10 11 12 13 14 15 16 17 18 19

33 31 29 28 27 28 30 32 30 24

10 11 12 13 14 15 17 18 19 20

26 32 37 43 50 58 06 12 12 04

10 11 11 12 13 14 15 16 17 18

18 07 56 46 37 30 25 22 19 15

10 11 12 13 13 14 15 16 17 18

55 41 26 12 59 49 42 37 33 30

11 11 12 13 14 15 16 17 18 19

02 54 45 38 31 27 24 22 20 15

11 12 12 13 14 15 16 17 18 19

23 11 59 47 37 29 23 19 16 12

21 22 23 24 25 26 27 28 29 30

18 19 20 21 22 23 ** 0 0 1

54 49 43 35 25 15 ** 06 58 52

19 20 20 21 22 23 23 ** 0 1

10 02 52 40 26 11 58 ** 46 37

19 20 21 21 22 23 23 ** 0 1

27 16 02 45 27 08 49 ** 33 21

19 20 21 21 22 23 23 ** 0 1

46 32 13 51 28 03 40 ** 19 02

20 20 21 21 22 22 23 ** 0 0

11 52 27 59 29 58 29 ** 02 39

20 21 21 22 22 22 23 23 ** 0

45 18 46 09 30 51 13 38 ** 08

19 19 20 21 22 22 23 ** 0 0

07 56 41 23 03 43 23 ** 06 52

19 20 21 21 22 23 ** 0 0 1

24 16 05 51 36 20 ** 05 52 42

20 20 21 22 22 23 ** 0 0 1

06 52 34 13 50 26 ** 04 44 27

20 20 21 22 23 23 ** 0 1 2

05 55 41 24 06 48 ** 30 14 02

31 2 1 3 2 4 3 5 4 6 5 7 6 8 7 8 8 9 9 10

48 2 45 3 41 4 36 5 28 6 17 7 02 7 45 8 26 9 07 10

30 2 26 3 23 4 19 5 13 5 05 6 54 7 40 8 25 9 09 10

12 1 06 2 03 3 01 4 57 5 52 6 45 7 35 8 24 9 12 10

50 1 43 2 40 3 39 4 39 5 38 6 34 7 29 8 22 9 15 10

23 0 14 1 11 2 12 3 16 4 19 5 21 7 22 8 20 9 18 10

45 32 28 33 43 54 04 11 18 23

1 2 3 4 5 6 7 8 8 9

10 11 12 13 14 15 16

48 30 14 01 52 45 42

54 39 27 17 09 04 00

00 49 40 33 28 24 20

07 01 56 52 50 47 43

16 15 15 16 17 16 12

29 35 42 50 56 58 53

10 11 12 13 14 15 16

10 11 12 13 13 14 15

10 11 12 13 14 15 16

11 11 12 13 14 15 16

11 12 12 13 14 15 16

11 12 13 14 15 16 17

11 12 13 14 15 16 17

h

m

h

m

h m

42 2 36 3 33 4 31 5 29 6 25 7 18 8 09 8 59 9 49 10

34 2 30 3 27 4 23 5 18 6 11 7 01 7 48 8 34 9 20 10

16 2 53 09 3 48 06 4 45 05 5 42 04 6 39 02 7 33 58 8 25 52 9 15 45 10 04 37 10 52

38 28 20 13 09 05 01

05 52 40 31 24 19 16

29 21 16 11 09 06 02

11 11 12 13 14 15 16

11 12 13 14 15 16 17

The symbol (**) indicates that the phenomenon will occur on the next day

11 12 13 14 15 16 16

39 28 19 11 06 02 58

306

MOONRISE, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONRISE (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º h

10º m

h

20º

26 27 28 29 30 31 Sept. 1 2 3 4

12 13 14 15 15 16 17 18 19 19

17 12 09 04 58 49 36 21 3 44

12 13 14 15 16 17 17 18 19 19

32 31 28 23 15 03 47 29 8 45

12 13 14 15 16 17 17 18 19 19

49 50 48 43 33 18 59 37 12 46

13 14 15 16 16 17 18 18 19 19

09 12 12 06 54 36 13 47 17 47

13 14 15 16 17 17 18 18 19 19

34 40 41 34 20 58 30 58 24 48

14 15 16 17 17 18 18 19 19 19

09 21 24 16 56 28 53 14 32 49

12 13 14 15 16 16 17 18 18 19

30 31 29 24 14 59 39 15 50 22

12 13 14 15 16 17 18 18 19 19

47 46 43 38 30 17 00 41 18 55

13 14 15 16 17 17 18 19 19 20

28 31 30 24 13 55 33 07 39 08

13 14 15 16 17 17 18 19 19 20

28 28 26 21 11 57 38 16 51 25

5 6 7 8 9 10 11 12 13 14

20 21 21 22 23 ** 0 1 1 2

25 06 48 32 19 ** 08 01 56 53

20 20 21 22 23 23 ** 0 1 2

22 59 38 19 03 51 ** 42 38 36

20 20 21 22 22 23 ** 0 1 2

19 52 27 05 46 32 ** 22 18 17

20 20 21 21 22 23 23 ** 0 1

15 45 15 49 27 10 59 ** 54 55

20 20 21 21 22 22 23 ** 0 1

11 35 01 30 03 42 29 ** 25 28

20 20 20 21 21 22 22 23 ** 0

5 22 41 03 30 04 47 43 ** 50

19 20 21 21 22 23 23 ** 0 1

54 27 01 37 18 02 52 ** 48 48

20 21 21 22 23 23 ** 0 1 2

31 07 44 24 08 55 ** 46 41 40

20 21 21 22 22 23 ** 0 1 2

38 08 39 14 52 35 ** 25 20 21

20 21 22 22 23 ** 0 1 2 2

59 32 08 46 27 ** 13 04 00 59

35 3 19 3 34 4 22 4 33 5 26 5 31 6 29 6 29 7 31 7 27 8 34 8 25 9 38 9 25 10 41 11 25 11 44 12 23 12 44 13

01 09 17 26 35 43 52 00 06 07

2 3 5 6 7 8 10 11 12 13

38 52 07 23 39 54 10 23 33 37

2 3 4 6 7 9 10 11 13 14

06 2 50 3 28 3 55 4 53 4 59 5 18 6 04 6 44 7 08 7 10 8 12 8 34 9 17 9 57 10 21 10 13 11 24 11 20 12 25 12

40 40 40 40 39 39 39 39 40 39

3 4 5 6 7 9 10 11 12 13

26 33 41 49 57 04 12 19 25 26

4 5 6 7 8 9 10 11 12 13

01 04 06 09 11 14 17 20 22 22

20 12 01 46 28 07 45

03 53 37 15 49 20 49

14 15 16 16 17 17 17

33 20 00 33 02 28 52

15 15 16 16 17 17 17

16 59 33 59 21 39 56

35 28 16 00 40 18 55

14 15 15 16 17 17 18

22 12 56 34 09 41 11

14 15 15 16 17 17 18

18 09 56 38 16 52 26

13 14 15 16 16 17 17

40 31 18 00 38 13 47

14 14 15 16 16 17 17

h

m

h

m

h

13 14 14 15 16 16 17

m

21 12 58 39 16 51 23

h

13 14 15 16 16 17 17

m

h

The symbol (**) indicates that the phenomenon will occur on the next day

m

Mumbai

17 16 18 20 23 25 26 26 26 27

13 14 15 15 16 17 17

m

Delhi

06 2 59 2 38 3 04 3 57 3 38 4 07 4 58 4 41 5 11 5 58 5 48 6 15 6 59 6 55 7 18 7 57 8 02 8 21 8 55 9 08 9 23 9 52 10 13 10 25 10 50 11 19 11 27 11 48 12 24 12

01 55 46 34 19 01 43

h

Kolkata Chennai

Aug. 16 3 14 2 56 2 35 2 12 1 43 1 01 2 17 4 12 3 53 3 34 3 12 2 43 2 03 3 18 5 09 4 53 4 36 4 16 3 51 3 15 4 19 6 06 5 53 5 39 5 23 5 03 4 35 5 20 7 01 6 52 6 42 6 31 6 17 5 58 6 21 7 54 7 49 7 44 7 38 7 31 7 22 7 22 8 45 8 45 8 45 8 45 8 45 8 45 8 23 9 37 9 41 9 46 9 52 9 58 10 08 9 24 10 29 10 38 10 47 10 58 11 11 11 30 10 25 11 22 11 35 11 48 12 04 12 23 12 51 11

13 13 14 15 16 17 17

m

50º

m

25 26 27 28 29 30 Oct. 1

h

40º

h

15 3 49 3 16 4 45 4 17 5 40 5 18 6 33 6 19 7 26 7 20 8 19 8 21 9 14 9 22 10 10 10 23 11 07 11 24 12 04 12

m

30º

307

MOONSET, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONSET (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º

10º

20º

30º

40º

50º

Kolkata Chennai Delhi Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

Aug. 16 17 18 19 20 21 22 23 24 25

15 16 17 18 19 20 21 22 22 23

42 39 36 32 26 18 10 01 54 48

16 16 17 18 19 20 21 21 22 23

00 56 51 43 33 21 08 55 43 33

16 17 18 18 19 20 21 21 22 23

20 15 06 55 40 23 05 48 32 18

16 17 18 19 19 20 21 21 22 23

43 36 24 08 48 26 03 40 19 01

17 18 18 19 19 20 20 21 22 22

12 02 46 24 58 29 59 30 03 39

17 18 19 19 20 20 20 21 21 22

53 39 16 46 11 34 55 17 41 10

16 16 17 18 19 20 20 21 22 22

01 56 46 34 18 00 41 22 05 50

16 17 18 18 19 20 21 22 22 23

16 11 05 56 45 31 17 02 49 39

17 17 18 19 20 20 21 22 22 23

02 55 44 28 09 48 25 03 43 26

26 27 28 29 30 31 Sept. 1 2 3 4

** 0 1 2 3 4 5 5 6 7

** ** ** ** ** 23 47 23 21 22 44 43 0 26 0 08 ** ** ** ** 23 28 40 1 21 1 01 0 38 0 09 ** ** 36 2 17 1 57 1 33 1 04 0 21 31 3 13 2 53 2 31 2 03 1 23 23 4 07 3 50 3 30 3 05 2 30 12 4 59 4 45 4 29 4 08 3 40 58 5 48 5 38 5 26 5 11 4 50 41 6 35 6 29 6 21 6 12 5 59 23 7 21 7 18 7 15 7 11 7 06

23 ** 0 1 2 3 4 5 6 6

39 ** ** ** 0 31 31 1 25 27 2 21 24 3 17 21 4 12 17 5 04 11 5 55 03 6 43 53 7 29

** 0 1 1 2 3 4 5 6 7

** ** ** 13 0 50 04 1 43 59 2 39 57 3 35 56 4 31 54 5 26 50 6 19 45 7 09 38 7 58

5 6 7 8 9 10 11 12 13 14

8 8 9 10 10 11 12 13 14 15

04 44 26 09 54 42 33 27 23 20

8 8 9 10 11 11 12 13 14 15

05 49 34 20 09 59 52 46 42 36

8 8 9 10 11 12 13 14 15 15

06 54 43 33 24 17 12 07 01 53

8 9 9 10 11 12 13 14 15 16

08 00 53 47 42 38 35 30 23 13

8 9 10 11 12 13 14 15 15 16

09 07 06 05 04 05 04 00 51 37

8 9 10 11 12 13 14 15 16 17

12 17 23 29 36 42 45 42 31 11

7 8 9 10 11 11 12 13 14 15

42 32 21 12 04 58 53 48 42 34

8 9 9 10 11 12 13 14 14 15

15 00 46 33 23 14 07 02 57 51

8 9 10 11 12 12 13 14 15 16

30 22 14 07 02 57 54 49 42 32

8 9 10 11 12 12 13 14 15 16

46 34 22 11 03 55 50 45 39 32

15 16 17 18 19 20 21 22 23 24

16 17 18 18 19 20 21 22 23 **

16 11 05 58 51 45 40 37 34 **

16 17 18 18 19 20 21 22 23 **

29 20 10 58 46 36 27 21 16 **

16 17 18 18 19 20 21 22 22 23

43 30 14 58 41 26 13 03 56 52

16 17 18 18 19 20 20 21 22 23

58 40 20 57 35 15 57 43 33 28

17 17 18 18 19 20 20 21 22 22

18 54 26 57 28 01 37 18 05 58

17 18 18 18 19 19 20 20 21 22

44 11 35 57 19 42 09 43 24 15

16 17 17 18 19 19 20 21 22 23

22 08 52 34 16 59 45 34 27 22

16 17 18 19 19 20 21 22 23 **

43 33 21 07 54 43 33 25 20 **

17 18 18 19 19 20 21 22 22 23

18 01 41 20 58 39 22 08 59 54

17 18 18 19 20 21 21 22 23 **

21 09 54 37 21 07 54 45 38 **

25 26 27 28 29 30 1

0 1 2 3 3 4 5

32 27 20 09 56 40 22

0 1 2 2 3 4 5

12 08 03 55 45 32 18

** 0 1 2 3 4 5

** ** ** 23 57 23 14 49 0 26 ** ** ** ** 45 1 24 0 58 0 21 40 2 23 2 01 1 30 33 3 20 3 03 2 40 24 4 15 4 04 3 48 14 5 09 5 03 4 55

** 0 1 2 3 3 4

** 19 16 12 06 58 48

0 1 2 3 3 4 5

16 ** ** 12 0 52 08 1 50 01 2 48 51 3 44 40 4 39 26 5 32

0 1 2 3 4 5 5

34 31 27 22 14 05 54

Oct.

The symbol (**) indicates that the phenomenon will occur on the next day

h m 16 17 18 19 20 21 21 22 23 24

58 53 45 33 19 03 45 28 13 00

308

MOONRISE, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONRISE (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

Oct.

Nov.

0º

10º

20º

30º

40º

50º

Kolkata Chennai

Delhi

Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

1 2 3 4 5 6 7 8 9 10

17 18 19 19 20 21 22 22 23 **

43 23 04 45 29 14 02 53 46 **

17 18 18 19 20 20 21 22 23 **

45 21 58 36 16 59 45 34 27 **

17 18 18 19 20 20 21 22 23 **

47 20 53 27 04 43 26 14 06 **

17 18 18 19 19 20 21 21 22 23

49 17 46 16 49 25 05 51 42 40

17 18 18 19 19 20 20 21 22 23

52 15 38 03 31 02 38 22 12 11

17 18 18 18 19 19 20 20 21 22

56 12 28 46 06 30 01 40 29 30

17 17 18 19 19 20 20 21 22 23

23 55 27 01 36 15 57 44 36 33

17 18 19 19 20 21 21 22 23 **

55 30 06 43 22 04 49 38 30 **

18 18 19 19 20 20 21 22 23 **

11 40 09 40 13 50 31 17 09 **

18 18 19 20 20 21 22 22 23 **

26 59 33 07 44 24 08 56 48 **

11 12 13 14 15 16 17 18 19 20

0 1 2 3 4 5 6 6 7 8

40 35 30 24 17 10 03 59 56 55

0 1 2 3 4 5 6 7 8 9

22 19 17 14 12 10 08 08 10 12

0 1 2 3 4 5 6 7 8 9

02 02 03 05 07 10 14 18 24 30

** 0 1 2 4 5 6 7 8 9

** ** ** 23 41 0 16 ** 46 1 26 0 53 2 39 2 01 3 54 3 10 5 10 5 20 6 27 6 30 7 45 8 41 9 02 9 51 10 17 10

40 ** ** ** 0 33 58 1 34 20 2 38 44 3 41 10 4 45 37 5 51 05 6 57 32 8 04 56 9 10

0 1 2 3 4 5 6 7 8 9

26 0 24 1 22 2 21 3 20 4 19 5 20 6 21 7 23 9 27 10

06 0 07 1 11 2 18 3 25 4 32 5 41 6 51 7 01 9 10 10

44 43 44 46 48 50 53 58 03 08

21 22 23 24 25 26 27 28 29 30

9 10 11 12 13 14 15 15 16 17

54 53 50 43 32 18 01 42 23 03

10 11 12 12 13 14 15 15 16 16

13 13 08 59 46 28 08 45 22 59

10 11 12 13 14 14 15 15 16 16

34 33 28 17 00 39 15 49 22 54

10 11 12 13 14 14 15 15 16 16

57 57 51 37 17 52 23 53 21 49

11 12 13 14 14 15 15 15 16 16

27 28 19 02 37 07 33 57 20 43

12 13 14 14 15 15 15 16 16 16

10 12 00 37 05 28 47 03 19 35

10 11 12 12 13 14 14 15 15 16

15 15 09 57 40 18 53 26 58 29

10 11 12 13 13 14 15 15 16 17

29 28 24 14 59 41 19 56 31 07

11 12 13 13 14 15 15 16 16 17

16 16 09 56 36 12 44 14 43 12

11 12 13 13 14 15 15 16 17 17

12 11 06 55 38 18 54 28 01 34

31 1 2 3 4 5 6 7 8 9

17 18 19 19 20 21 22 23 ** 0

44 27 12 59 49 41 34 27 ** 20

17 18 18 19 20 21 22 23 ** 0

36 16 57 42 30 21 15 10 ** 06

17 18 18 19 20 21 21 22 23 **

28 4 42 24 10 01 55 51 50 **

17 17 18 19 19 20 21 22 23 **

19 50 25 04 47 37 31 30 32 **

17 17 18 18 19 20 21 22 23 **

07 34 03 38 19 06 01 03 09 **

16 17 17 18 18 19 20 21 22 23

52 11 34 02 38 23 19 24 37 55

17 17 18 18 19 20 21 22 23 **

02 37 14 55 41 31 25 22 21 **

17 18 19 19 20 21 22 23 ** 0

43 22 03 47 34 25 19 14 ** 11

17 18 18 19 20 21 21 22 23 **

42 14 50 29 13 03 57 56 57 **

18 18 19 20 20 21 22 23 ** 0

08 44 23 06 52 43 37 33 ** 32

10 11 12 13 14 15 16

1 2 2 3 4 5 6

12 04 55 46 40 36 35

1 1 2 3 4 5 6

01 57 52 49 47 48 51

0 1 2 3 4 6 7

49 49 50 51 55 00 07

0 1 2 3 5 6 7

36 41 47 54 03 14 26

0 1 2 3 5 6 7

19 30 43 58 14 32 50

** 1 2 4 5 6 8

** 15 38 02 29 57 25

0 1 2 3 4 5 6

22 23 24 27 32 39 47

1 2 3 3 4 6 7

07 04 01 59 59 01 05

1 2 3 4 5 6 7

00 04 10 16 25 35 46

1 2 3 4 5 6 7

31 30 30 31 34 39 46

The symbol (**) indicates that the phenomenon will occur on the next day

309

MOONSET, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONSET (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º h

Oct.

Nov.

10º

30º

40º

50º

h

m

h

m

h

m

h

m

h

1 5 22 5 2 6 02 6 3 6 43 6 4 7 24 7 5 8 06 8 6 8 50 9 7 9 37 9 8 10 26 10 9 11 18 11 10 12 12 12

18 02 46 31 17 04 53 45 37 31

5 6 6 7 8 9 10 11 11 12

14 02 50 39 28 19 11 04 58 51

5 6 6 7 8 9 10 11 12 13

09 02 55 47 41 35 31 27 22 14

5 6 7 7 8 9 10 11 12 13

03 02 00 58 57 57 56 55 52 44

11 12 13 14 15 16 17 18 19 20

24 16 07 56 44 33 22 14 08 05

13 14 15 16 16 17 18 19 19 20

43 32 18 03 47 30 15 02 52 46

14 14 15 16 16 17 18 18 19 20

04 50 32 11 49 27 06 48 33 24

14 15 15 16 16 17 17 18 19 19

21 22 23 22 03 22 23 21 23 02 23 ** ** 23 58 24 0 16 ** ** 25 1 07 0 52 26 1 54 1 42 27 2 39 2 30 28 3 21 3 16 29 4 02 4 00 30 4 42 4 44

21 22 23 ** 0 1 2 3 3 4

43 41 39 ** 35 29 21 11 59 47

21 22 23 ** 0 1 2 3 3 4

19 17 17 ** 17 14 10 04 57 50

31 1 2 3 4 5 6 7 8 9

5 6 6 7 8 9 10 11 11 12

23 04 48 34 23 14 06 00 53 45

5 6 7 7 8 9 10 11 12 12

29 14 01 50 41 33 26 18 09 58

5 6 7 8 9 9 10 11 12 13

35 24 15 07 00 53 46 37 26 12

5 6 7 8 9 10 11 12 12 13

10 11 12 13 14 15 16

13 14 15 16 17 18 19

37 28 19 12 06 04 04

13 14 15 16 16 17 18

46 32 19 07 57 50 47

13 14 15 16 16 17 18

55 37 19 02 47 36 29

14 14 15 15 16 17 18

13 14 14 15 16 17 18 19 20 21

m

20º

07 01 55 49 42 35 29 26 24 23

13 14 15 15 16 17 18 19 20 21

Kolkata Chennai Delhi Mumbai m

h

m

h

m

h

m

4 6 7 8 9 10 11 12 13 14

55 4 48 5 02 5 38 6 07 6 27 6 13 7 17 7 19 8 07 8 26 8 58 9 33 9 51 10 36 10 45 11 35 11 39 11 26 12 32 12

26 12 57 43 29 18 08 00 53 46

5 6 7 8 9 9 10 11 12 13

32 24 16 08 01 55 50 46 40 33

5 6 7 8 9 9 10 11 12 13

54 42 30 18 07 57 49 42 36 29

31 12 48 21 53 23 55 30 10 56

15 15 16 16 16 17 17 18 18 19

08 42 11 35 57 18 41 07 38 16

13 14 14 15 16 17 17 18 19 20

24 12 58 41 23 05 48 34 23 16

39 30 20 07 54 41 30 20 13 09

14 15 15 16 17 17 18 19 19 20

23 09 52 32 11 50 29 12 58 50

14 15 15 16 17 18 18 19 20 21

21 10 57 42 26 10 55 43 34 28

20 21 22 23 ** 0 1 2 3 4

49 47 50 53 ** 56 57 57 55 53

20 21 22 23 ** 0 1 2 3 4

05 04 10 19 ** 30 39 46 53 58

21 22 23 ** 0 1 1 2 3 4

13 22 07 21 45 22 25 11 23 05 22 44 23 23 10 ** ** 23 43 ** ** ** 0 02 ** ** 0 21 07 0 57 0 42 1 17 02 1 48 1 39 2 11 54 2 37 2 34 3 02 45 3 24 3 28 3 51 34 4 10 4 20 4 39 23 4 55 5 12 5 26

42 36 30 26 22 17 10 00 45 27

5 6 7 8 9 10 11 12 13 13

52 51 50 50 50 47 40 28 10 47

6 7 8 9 10 11 12 13 13 14

04 11 18 25 30 30 23 08 44 13

5 6 6 7 8 9 10 11 12 12

13 03 54 47 41 35 28 18 06 51

5 6 7 8 8 9 10 11 12 13

40 27 15 04 56 48 41 33 23 12

6 6 7 8 9 10 11 12 13 13

04 56 50 45 41 36 29 18 05 47

6 7 7 8 9 10 11 12 13 13

14 03 53 45 38 31 24 15 04 50

06 43 19 57 36 20 08

14 14 15 15 16 16 17

19 50 19 50 22 59 43

14 14 15 15 16 16 17

37 59 20 41 04 31 06

13 14 14 15 16 17 18

34 15 55 37 20 08 00

13 14 15 16 17 17 18

58 44 29 15 04 56 52

14 15 15 16 17 17 18

27 04 41 19 00 44 34

14 15 15 16 17 18 19

34 17 59 42 28 17 11

13 14 15 16 16 17 18 19 20 21

The symbol (**) indicates that the phenomenon will occur on the next day

h m

310

MOONRISE, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONRISE (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º

10º

20º

30º

40º

50º

Kolkata Chennai

Delhi

Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

Nov. 16 17 18 19 20 21 22 23 24 25

6 7 8 9 10 11 12 12 13 14

35 36 38 38 34 27 15 59 41 22

6 7 8 9 10 11 12 13 13 14

51 54 57 57 52 41 26 07 46 22

7 8 9 10 11 11 12 13 13 14

07 14 18 18 11 57 39 16 50 23

7 8 9 10 11 12 12 13 13 14

26 37 42 41 32 15 53 26 56 24

7 9 10 11 11 12 13 13 14 14

50 05 13 11 59 38 10 38 02 25

8 9 10 11 12 13 13 13 14 14

25 47 58 54 37 09 34 54 11 27

6 7 9 9 10 11 12 12 13 14

47 55 00 59 52 38 18 54 28 00

7 8 9 10 11 11 12 13 13 14

05 10 13 13 07 56 39 19 57 32

7 8 10 11 11 12 13 13 14 14

46 56 01 00 51 35 13 46 17 46

7 8 9 10 11 12 13 13 14 15

46 52 56 56 49 35 17 55 29 03

26 27 28 29 30 Dec. 1 2 3 4 5

15 15 16 17 17 18 19 20 21 22

02 42 24 09 56 45 37 30 24 16

14 15 16 16 17 18 19 20 21 22

59 36 14 55 39 27 18 11 06 01

14 15 16 16 17 18 18 19 20 21

56 29 04 41 22 08 57 50 46 44

14 15 15 16 17 17 18 19 20 21

52 21 52 25 3 45 33 26 24 25

14 15 15 16 16 17 18 18 19 21

48 12 37 05 38 17 03 56 56 00

14 14 15 15 16 16 17 18 19 20

43 59 17 38 4 37 20 12 15 26

14 15 15 16 16 17 18 19 20 21

31 03 37 14 54 38 27 20 17 15

15 15 16 17 17 18 19 20 21 22

08 43 21 01 44 31 21 15 10 05

15 15 16 16 17 18 18 19 20 21

15 44 16 50 28 11 59 52 50 50

15 16 16 17 18 18 19 20 21 22

36 09 44 22 04 49 39 32 28 26

6 23 08 22 55 22 42 22 27 22 07 21 41 22 14 23 01 22 51 23 23 7 23 58 23 49 23 40 23 29 23 16 22 58 23 13 23 56 23 53 ** ** 8 ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** 0 21 9 0 47 0 42 0 38 0 33 0 26 0 17 0 12 0 51 0 56 1 18 10 1 36 1 36 1 36 1 37 1 37 1 37 1 12 1 46 1 59 2 16 11 2 27 2 31 2 36 2 42 2 50 3 00 2 13 2 42 3 04 3 16 12 3 19 3 29 3 39 3 50 4 04 4 24 3 17 3 41 4 11 4 18 13 4 16 4 29 4 43 5 00 5 21 5 51 4 23 4 43 5 20 5 22 14 5 15 5 32 5 50 6 11 6 37 7 15 5 30 5 47 6 30 6 29 15 6 17 6 36 6 56 7 20 7 50 8 33 6 37 6 51 7 39 7 34 16 17 18 19 20 21 22 23 24 25

7 8 9 10 10 11 12 12 13 14

19 19 15 06 53 37 19 59 39 21

7 8 9 10 11 11 12 12 13 14

38 37 31 19 03 43 21 58 34 12

7 8 9 10 11 11 12 12 13 14

59 57 48 33 13 49 23 56 29 03

8 9 10 10 11 11 12 12 13 13

24 20 08 49 25 57 26 54 23 52

8 9 10 11 11 12 12 12 13 13

54 49 33 09 39 05 29 52 15 40

9 10 11 11 11 12 12 12 13 13

39 30 08 36 59 17 34 49 05 22

7 8 9 10 10 11 12 12 13 13

41 38 29 13 52 27 00 32 03 36

7 8 9 10 11 11 12 13 13 14

54 53 46 33 15 54 31 07 42 19

8 9 10 11 11 12 12 13 13 14

42 39 27 09 45 17 47 16 46 16

8 9 10 11 11 12 13 13 14 14

37 35 26 12 52 28 02 36 09 43

26 27 28 29 30 31 32

15 15 16 17 18 19 20

04 50 39 30 24 18 12

14 15 16 17 18 19 19

52 35 21 11 05 00 56

14 15 16 16 17 18 19

39 19 03 51 44 40 38

14 15 15 16 17 18 19

25 00 41 28 20 17 18

14 14 15 15 16 17 18

07 38 14 58 49 48 52

13 14 14 15 16 17 18

42 06 37 16 05 06 15

14 14 15 16 17 18 19

12 50 33 21 14 10 09

14 15 16 17 18 19 20

58 40 25 15 08 04 00

14 15 16 16 17 18 19

49 25 07 54 46 43 43

15 16 16 17 18 19 20

20 00 44 33 26 22 20

The symbol (**) indicates that the phenomenon will occur on the next day

311

MOONSET, 2020 LOCAL MEAN TIME AND INDIAN STANDARD TIME OF MOONSET (MOON'S UPPER LIMB) FOR CERTAIN STATIONS IN INDIA IN I.S.T

FOR THE CENTRAL MERIDIAN OF INDIA ( 82º.5 E ) IN L. M. T.

Lat. Date

0º

10º

20º

30º

40º

50º

Kolkata Chennai Delhi Mumbai

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

h

m

Nov. 16 17 18 19 20 21 22 23 24 25

19 20 21 22 23 23 ** 0 1 2

04 06 07 05 00 50 ** 36 20 01

18 19 20 21 22 23 ** 0 1 1

47 47 47 47 44 37 ** 26 13 58

18 19 20 21 22 23 ** 0 1 1

29 26 26 27 26 22 ** 16 06 55

18 19 20 21 22 23 ** 0 0 1

08 03 02 04 06 06 ** 03 59 52

17 18 19 20 21 22 23 ** 0 1

43 33 31 35 40 45 48 ** 49 48

17 17 18 19 21 22 23 ** 0 1

06 51 47 52 03 16 27 ** 36 42

18 18 19 20 21 22 23 ** 0 1

00 57 56 57 57 54 49 ** 40 30

18 19 20 21 22 23 ** 0 1 2

52 50 51 51 48 42 ** 33 21 07

18 19 20 21 22 23 ** 0 1 2

34 29 28 30 31 31 ** 28 22 15

26 27 28 29 30 1 2 3 4 5

2 3 4 4 5 6 7 8 8 9

6 7 8 9 10 11 12 13 14 15

Dec.

h m 19 20 21 22 23 ** 0 0 1 2

11 08 08 09 08 ** 04 57 47 35

41 2 21 3 03 4 46 4 31 5 19 6 10 7 03 8 56 9 49 10

42 2 26 3 11 4 57 5 46 6 36 6 29 7 22 8 15 9 06 10

43 2 31 3 20 4 10 5 02 6 55 7 49 8 43 9 35 9 24 10

44 2 46 2 48 2 37 3 44 3 54 3 30 4 43 5 00 3 24 5 42 6 07 4 20 6 43 7 15 5 16 7 43 8 22 6 12 8 42 9 25 7 07 9 37 10 21 8 58 10 27 11 08 9 45 11 10 11 47 10

19 2 08 3 58 4 49 5 42 6 36 6 30 7 24 8 16 9 05 10

52 3 07 3 23 37 3 58 4 10 23 4 51 4 59 11 5 44 5 49 00 6 39 6 40 51 7 35 7 33 44 8 31 8 27 38 9 25 9 21 30 10 17 10 13 21 11 04 11 02

10 11 12 13 14 14 15 16 17 18

41 32 21 10 00 51 46 43 44 46

10 11 12 13 13 14 15 16 17 18

55 42 27 12 57 44 34 28 26 27

11 11 12 13 13 14 15 16 17 18

10 53 34 14 55 37 22 12 07 06

11 12 12 13 13 14 15 15 16 17

27 06 42 17 52 29 09 54 45 42

11 12 12 13 13 14 14 15 16 17

48 21 51 20 48 18 52 30 17 11

12 12 13 13 13 14 14 14 15 16

17 42 04 24 43 04 29 58 37 27

10 11 12 12 13 14 14 15 16 17

50 32 12 51 30 11 55 43 37 36

11 11 12 13 14 14 15 16 17 18

09 55 39 22 06 52 40 33 30 31

11 12 13 13 14 14 15 16 17 18

47 26 03 39 14 52 33 19 10 08

11 12 13 13 14 15 16 16 17 18

48 32 13 54 35 17 03 54 49 48

16 17 18 19 20 21 22 23 24 25

19 20 21 22 23 23 ** 0 1 1

48 46 40 29 15 57 ** 38 18 59

19 20 21 22 23 23 ** 0 1 2

29 28 25 18 07 53 ** 38 22 06

19 20 21 22 22 23 ** 0 1 2

08 10 09 05 58 49 ** 37 25 14

18 19 20 21 22 23 ** 0 1 2

44 48 51 51 49 44 ** 37 30 22

18 19 20 21 22 23 ** 0 1 2

13 20 27 33 37 37 ** 36 35 33

17 18 19 21 22 23 ** 0 1 2

29 40 55 09 20 29 ** 36 41 47

18 19 20 21 22 23 ** 0 1 1

38 40 40 38 32 23 ** 13 02 52

19 20 21 22 23 ** 0 0 1 2

32 33 30 24 14 ** 01 47 32 18

19 20 21 22 23 ** 0 0 1 2

10 14 16 16 13 ** 07 59 51 43

19 20 21 22 23 ** 0 1 2 2

50 52 51 47 39 ** 29 17 05 53

26 27 28 29 30 31 32

2 3 4 5 5 6 7

41 26 13 03 56 50 45

2 3 4 5 6 7 8

52 40 30 22 15 09 02

3 3 4 5 6 7 8

03 54 47 41 36 30 21

3 4 5 6 7 7 8

16 11 07 04 00 53 42

3 4 5 6 7 8 9

32 32 33 33 31 23 09

3 5 6 7 8 9 9

54 02 09 15 14 06 48

2 3 4 5 6 7 8

42 34 28 23 18 11 02

3 3 4 5 6 7 8

05 53 44 37 31 25 17

3 4 5 6 7 8 9

36 31 27 23 19 12 01

3 4 5 6 7 8 8

42 33 25 20 14 08 59

The symbol (**) indicates that the phenomenon will occur on the next day

312

MOONRISE AND MOONSET REDUCTION OF THE L.M.T. OF RISING OR SETTING FOR THE MERIDIAN OF 82°.5 E. LONGITUDE TO THE L.M.T. OF OTHER MERIDIANS LONGITUDE EAST OF GREENWICH Daily Variation in Rising or Setting m 28 29 30 31 32 33 34 35 36 37 38 39

m m m m m m m m m m m + 6.4 + 4.1 + 1.8 + 1.1 + 0.8 + 0.5 + 0.2 - 0.1 - 0.4 - 0.7 - 1.1 0.5 0.1 0.8 6.6 1.8 0.8 0.2 0.4 1.1 1.2 4.2 0.5 0.1 0.8 6.9 1.9 0.9 0.2 0.5 1.1 1.2 4.4 0.6 0.1 0.8 7.1 1.9 0.9 0.2 0.5 1.2 1.2 4.5 0.6 0.1 0.8 7.3 2.0 0.9 0.2 0.5 1.2 1.3 4.7 0.6 0.1 0.9 7.6 2.1 1.0 0.2 0.5 1.2 1.3 4.8 0.1 0.9 7.8 2.1 1.0 0.2 0.5 1.3 1.4 5.0 0.6 0.1 0.9 8.0 2.2 1.0 0.2 0.5 1.3 1.4 5.1 0.6 0.1 0.9 8.2 2.3 1.0 0.2 0.5 1.4 1.4 5.2 0.6 0.2 1.0 8.5 2.3 1.1 0.3 0.6 1.4 1.5 5.4 0.7 0.2 1.0 8.7 2.4 1.1 0.3 0.6 1.4 1.5 5.5 0.7 0.2 1.0 8.9 2.4 1.1 0.3 0.6 1.5 1.6 5.7 0.7

m - 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.9 4.0 4.1

m - 5.3 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 6.9 7.1 7.3

40 41 42 43 44 45 46 47 48 49

+ 9.2 + 5.8 + 2.5 + 1.6 + 1.2 + 0.7 + 0.3 - 0.2 - 0.6 - 1.1 - 1.5 0.2 1.1 9.4 2.6 1.2 0.3 0.6 1.5 6.0 1.7 0.7 1.1 9.6 2.6 1.2 0.3 0.6 1.6 6.1 1.7 0.8 0.2 1.1 9.9 2.7 1.3 0.3 0.7 1.6 6.3 1.7 0.8 0.2 1.2 10.1 2.8 1.3 0.3 0.7 1.7 6.4 1.8 0.8 0.2 1.2 10.3 2.8 1.3 0.3 0.7 1.7 6.6 1.8 0.8 0.2 1.2 10.5 2.9 1.3 0.3 0.7 1.7 6.7 1.9 0.8 0.2 1.2 10.8 2.9 1.4 0.3 0.7 1.8 6.9 1.9 0.8 0.2 1.3 11.0 3.0 1.4 0.3 0.7 1.8 7.0 1.9 0.9 0.2 1.3 11.2 3.1 1.4 0.3 0.7 1.8 7.1 2.0 0.9 0.2

- 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1

- 7.5 7.7 7.9 8.1 8.3 8.4 8.6 8.8 9.0 9.2

50 51 52 53 54 55 56 57 58 59

+ 11.5 + 7.3 + 3.1 + 2.0 + 1.5 + 0.9 + 0.3 - 0.2 - 0.8 - 1.3 - 1.9 11.7 3.2 1.5 0.4 0.8 1.9 7.4 2.1 0.9 0.2 1.3 11.9 3.3 1.5 0.4 0.8 2.0 7.6 2.1 0.9 0.2 1.4 12.1 3.3 1.5 0.4 0.8 2.0 7.7 2.1 1.0 0.2 1.4 12.4 3.4 1.6 0.4 0.8 2.0 7.9 2.2 1.0 0.2 1.4 12.6 3.4 1.6 0.4 0.8 2.1 8.0 2.2 1.0 0.2 1.5 12.8 3.5 1.6 0.4 0.9 2.1 8.2 2.3 1.0 0.2 1.5 13.1 3.6 1.7 0.4 0.9 2.1 8.3 2.3 1.0 0.2 1.5 13.3 3.6 1.7 0.4 0.9 2.2 8.5 2.3 1.0 0.2 1.5 13.5 3.7 1.7 0.4 0.9 2.2 8.6 2.4 1.1 0.2 1.6

- 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1

- 9.4 9.6 9.8 9.9 10.1 10.3 10.5 10.7 10.9 11.1

60 61 62 63 64 65 66 67 68 69

+ 13.7 + 8.7 + 3.8 + 2.4 + 1.7 + 1.1 + 0.4 - 0.2 - 0.9 - 1.6 - 2.3 14.0 3.8 1.8 0.4 2.3 0.9 8.9 2.5 1.1 0.3 1.6 14.2 3.9 1.8 0.4 2.3 0.9 9.0 2.5 1.1 0.3 1.6 14.4 3.9 1.8 0.4 2.4 1.0 9.2 2.5 1.1 0.3 1.7 14.7 4.0 1.9 0.4 2.4 1.0 9.3 2.6 1.2 0.3 1.7 14.9 4.1 1.9 0.5 2.4 1.0 9.5 2.6 1.2 0.3 1.7 15.1 4.1 1.9 0.5 2.5 1.0 9.6 2.7 1.2 0.3 1.7 15.4 4.2 2.0 0.5 2.5 1.0 9.8 2.7 1.2 0.3 1.8 15.6 4.3 2.0 0.5 2.6 1.0 9.9 2.7 1.2 0.3 1.8 15.8 10.1 4.3 2.0 0.5 2.6 1.1 2.8 1.2 0.3 1.8

- 6.2 - 11.3 6.4 11.4 6.5 11.6 6.6 11.8 6.7 12.0 6.8 12.2 6.9 12.4 7.0 12.6 7.1 12.8 7.2 12.9

70 71 72 73 74

+ 16.0 + 10.2 + 4.4 + 2.8 + 2.0 + 1.3 + 0.5 - 0.3 - 1.1 - 1.8 - 2.6 16.3 10.4 4.4 2.1 0.5 2.7 1.1 2.9 1.3 0.3 1.9 16.5 10.5 4.5 2.1 0.5 2.7 1.1 2.9 1.3 0.3 1.9 16.7 10.6 4.6 2.1 0.5 2.7 1.1 2.9 1.3 0.3 1.9 + 17.0 + 10.8 + 4.6 + 3.0 + 2.2 + 1.3 + 0.5 - 0.3 - 1.1 - 2.0 - 2.8

- 7.3 - 13.1 7.4 13.3 7.5 13.5 7.6 13.7 - 7.7 - 13.9

0°

30°

60°

68°

72°

76°

80°

84°

88°

92°

96°

120°

150°

313

SUNRISE, SUNSET AND MOONRISE, MOONSET CORRECTION FOR LATITUDE VARIATION PER 10° OF LATITUDE OF THE TIMES OF SUNRISE, SUNSET AND MOONRISE, MOONSET DISTRIBUTED OVER EACH DEGREE OF LATITUDE Var. per 10° 1° 2° 3° 4° 5° 6° 7° 8° 9° 10° 15' 30' 45' of Lat. m m m m m m m m m m m m m m 5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.1 0.3 0.4 6 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 0.2 0.3 0.5 7 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 7.0 0.2 0.4 0.5 8 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 0.2 0.4 0.6 9 0.9 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 9.0 0.2 0.5 0.7 10 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0.3 0.5 0.8 11 1.1 2.2 3.3 4.4 5.5 6.6 7.7 8.8 9.9 11.0 0.3 0.6 0.8 12 1.2 2.4 3.6 4.8 6.0 7.2 8.4 9.6 10.8 12.0 0.3 0.6 0.9 13 1.3 2.6 3.9 5.2 6.5 7.8 9.1 10.4 11.7 13.0 0.3 0.7 1.0 14 1.4 2.8 4.2 5.6 7.0 8.4 9.8 11.2 12.6 14.0 0.4 0.7 1.1 15 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0 0.4 0.8 1.1 16 1.6 3.2 4.8 6.4 8.0 9.6 11.2 12.8 14.4 16.0 0.4 0.8 1.2 17 1.7 3.4 5.1 6.8 8.5 10.2 11.9 13.6 15.3 17.0 0.4 0.9 1.3 18 1.8 3.6 5.4 7.2 9.0 10.8 12.6 14.4 16.2 18.0 0.5 0.9 1.4 19 1.9 3.8 5.7 7.6 9.5 11.4 13.3 15.2 17.1 19.0 0.5 1.0 1.4 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8

6.0 6.3 6.6 6.9 7.2 7.5 7.8 8.1 8.4 8.7 9.0 9.3 9.6 9.9 10.2

8.0 8.4 8.8 9.2 9.6 10.0 10.4 10.8 11.2 11.6 12.0 12.4 12.8 13.2 13.6

10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0

12.0 12.6 13.2 13.8 14.4 15.0 15.6 16.2 16.8 17.4 18.0 18.6 19.2 19.8 20.4

14.0 14.7 15.4 16.1 16.8 17.5 18.2 18.9 19.6 20.3 21.0 21.7 22.4 23.1 23.8

16.0 16.8 17.6 18.4 19.2 20.0 20.8 21.6 22.4 23.2 24.0 24.8 25.6 26.4 27.2

18.0 18.9 19.8 20.7 21.6 22.5 23.4 24.3 25.2 26.1 27.0 27.9 28.8 29.7 30.6

20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 31.0 32.0 33.0 34.0

0.5 0.5 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9

1.0 1.1 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.5 1.5 1.6 1.6 1.7 1.7

1.5 1.6 1.7 1.7 1.8 1.9 2.0 2.0 2.1 2.2 2.3 2.3 2.4 2.5 2.6

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0

10.5 10.8 11.1 11.4 11.7 12.0 12.3 12.6 12.9 13.2 13.5 13.8 14.1 14.4 14.7 15.0

14.0 14.4 14.8 15.2 15.6 16.0 16.4 16.8 17.2 17.6 18.0 18.4 18.8 19.2 19.6 20.0

17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0

21.0 21.6 22.2 22.8 23.4 24.0 24.6 25.2 25.8 26.4 27.0 27.6 28.2 28.8 29.4 30.0

24.5 25.2 25.9 26.6 27.3 28.0 28.7 29.4 30.1 30.8 31.5 32.2 32.9 33.6 34.3 35.0

28.0 28.8 29.6 30.4 31.2 32.0 32.8 33.6 34.4 35.2 36.0 36.8 37.6 38.4 39.2 40.0

31.5 32.4 33.3 34.2 35.1 36.0 36.9 37.8 38.7 39.6 40.5 41.4 42.3 43.2 44.1 45.0

35.0 36.0 37.0 38.0 39.0 40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0 50.0

0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.3

1.8 1.8 1.9 1.9 2.0 2.0 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5

2.6 2.7 2.8 2.9 2.9 3.0 3.1 3.2 3.2 3.3 3.4 3.5 3.5 3.6 3.7 3.8

314

REDUCTION OF TIME REDUCTION OF LOCAL MEAN TIME OF A PLACE INTO THE INDIAN STANDARD TIME

0 3 6 9 12 15 18 21 24 27 30

67° m 62.0 61.8 61.6 61.4 61.2 61.0 60.8 60.6 60.4 60.2 60.0

68° m 58.0 57.8 57.6 57.4 57.2 57.0 56.8 56.6 56.4 56.2 56.0

A-CORRECTION TO BE ADDED TO L.M.T. TO OBTAIN I.S.T. LONGITUDE OF PLACE (EAST OF GREENWICH) 69° 70° 71° 72° 73° 74° 75° 76° 77° 78° 79° 80° m m m m m m m m m m m m 54.0 50.0 46.0 42.0 38.0 34.0 30.0 26.0 22.0 18.0 14.0 10.0 53.8 49.8 45.8 41.8 37.8 33.8 29.8 25.8 21.8 17.8 13.8 9.8 53.6 49.6 45.6 41.6 37.6 33.6 29.6 25.6 21.6 17.6 13.6 9.6 53.4 49.4 45.4 41.4 37.4 33.4 29.4 25.4 21.4 17.4 13.4 9.4 53.2 49.2 45.2 41.2 37.2 33.2 29.2 25.2 21.2 17.2 13.2 9.2 53.0 49.0 45.0 41.0 37.0 33.0 29.0 25.0 21.0 17.0 13.0 9.0 52.8 48.8 44.8 40.8 36.8 32.8 28.8 24.8 20.8 16.8 12.8 8.8 52.6 48.6 44.6 40.6 36.6 32.6 28.6 24.6 20.6 16.6 12.6 8.6 52.4 48.4 44.4 40.4 36.4 32.4 28.4 24.4 20.4 16.4 12.4 8.4 52.2 48.2 44.2 40.2 36.2 32.2 28.2 24.2 20.2 16.2 12.2 8.2 52.0 48.0 44.0 40.0 36.0 32.0 28.0 24.0 20.0 16.0 12.0 8.0

33 36 39 42 45 48 51 54 57 60

59.8 59.6 59.4 59.2 59.0 58.8 58.6 58.4 58.2 58.0

55.8 55.6 55.4 55.2 55.0 54.8 54.6 54.4 54.2 54.0

51.8 51.6 51.4 51.2 51.0 50.8 50.6 50.4 50.2 50.0

82° m 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

47.8 47.6 47.4 47.2 47.0 46.8 46.6 46.4 46.2 46.0

43.8 43.6 43.4 43.2 43.0 42.8 42.6 42.4 42.2 42.0

39.8 39.6 39.4 39.2 39.0 38.8 38.6 38.4 38.2 38.0

35.8 35.6 35.4 35.2 35.0 34.8 34.6 34.4 34.2 34.0

31.8 31.6 31.4 31.2 31.0 30.8 30.6 30.4 30.2 30.0

27.8 27.6 27.4 27.2 27.0 26.8 26.6 26.4 26.2 26.0

23.8 23.6 23.4 23.2 23.0 22.8 22.6 22.4 22.2 22.0

19.8 19.6 19.4 19.2 19.0 18.8 18.6 18.4 18.2 18.0

81° m 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6 4.4 4.2 4.0

82° m 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

7.8 7.6 7.4 7.2 7.0 6.8 6.6 6.4 6.2 6.0

3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0

B- CORRECTION TO BE SUBTRACTED FROM L.M.T. TO OBTAIN I.S.T. LONGITUDE OF PLACE (EAST OF GREENWICH) 83° 84° 85° 86° 87° 88° 89° 90° 91° 92° 93° 94° 95° m m m m m m m m m m m m m 2.0 6.0 10.0 14.0 18.0 22.0 26.0 30.0 34.0 38.0 42.0 46.0 50.0 2.2 6.2 10.2 14.2 18.2 22.2 26.2 30.2 34.2 38.2 42.2 46.2 50.2 2.4 6.4 10.4 14.4 18.4 22.4 26.4 30.4 34.4 38.4 42.4 46.4 50.4 2.6 6.6 10.6 14.6 18.6 22.6 26.6 30.6 34.6 38.6 42.6 46.6 50.6 2.8 6.8 10.8 14.8 18.8 22.8 26.8 30.8 34.8 38.8 42.8 46.8 50.8 3.0 7.0 11.0 15.0 19.0 23.0 27.0 31.0 35.0 39.0 43.0 47.0 51.0 3.2 7.2 11.2 15.2 19.2 23.2 27.2 31.2 35.2 39.2 43.2 47.2 51.2 3.4 7.4 11.4 15.4 19.4 23.4 27.4 31.4 35.4 39.4 43.4 47.4 51.4 3.6 7.6 11.6 15.6 19.6 23.6 27.6 31.6 35.6 39.6 43.6 47.6 51.6 3.8 7.8 11.8 15.8 19.8 23.8 27.8 31.8 35.8 39.8 43.8 47.8 51.8

96° m 54.0 54.2 54.4 54.6 54.8 55.0 55.2 55.4 55.6 55.8

97° m 58.0 58.2 58.4 58.6 58.8 59.0 59.2 59.4 59.6 59.8

56.0 56.2 56.4 56.6 56.8 57.0 57.2 57.4 57.6 57.8 58.0

60.0 60.2 60.4 60.6 60.8 61.0 61.2 61.4 61.6 61.8 62.0

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0

8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0

12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 14.0

16.0 16.2 16.4 16.6 16.8 17.0 17.2 17.4 17.6 17.8 18.0

20.0 20.2 20.4 20.6 20.8 21.0 21.2 21.4 21.6 21.8 22.0

24.0 24.2 24.4 24.6 24.8 25.0 25.2 25.4 25.6 25.8 26.0

28.0 28.2 28.4 28.6 28.8 29.0 29.2 29.4 29.6 29.8 30.0

32.0 32.2 32.4 32.6 32.8 33.0 33.2 33.4 33.6 33.8 34.0

36.0 36.2 36.4 36.6 36.8 37.0 37.2 37.4 37.6 37.8 38.0

40.0 40.2 40.4 40.6 40.8 41.0 41.2 41.4 41.6 41.8 42.0

15.8 15.6 15.4 15.2 15.0 14.8 14.6 14.4 14.2 14.0

44.0 44.2 44.4 44.6 44.8 45.0 45.2 45.4 45.6 45.8 46.0

11.8 11.6 11.4 11.2 11.0 10.8 10.6 10.4 10.2 10.0

48.0 48.2 48.4 48.6 48.8 49.0 49.2 49.4 49.6 49.8 50.0

52.0 52.2 52.4 52.6 52.8 53.0 53.2 53.4 53.6 53.8 54.0

315

METHOD OF CALCULATION Sunrise and Sunset The local mean times of Sunrise and Sunset for latitudes 0° to 60° North at intervals of 4 days during the year have been given on pages 280 to 287. The timings relate to the visibility of the upper limb of the Sun on the horizon. From these tables the L.M.T. of rise or set for any day of the year and for any latitude of place can be obtained by simple interpolation. If the place is in the southern hemisphere, the corrections given on pages 290 to 291 will then have to be applied to the timings for the corresponding northern latitude. For a station in India, the timings of Sunrise and Sunset so obtained which are in L.M.T. can be reduced to I.S.T. by applying the correction given on page 314 according to the longitude of the station. In addition to the above details given in the publication, the timings of Sunrise and Sunset of five important cities of India, viz., Kolkata, Varanasi, Chennai, Delhi and Mumbai have been specially calculated and given in I.S.T. on pages 292 to 295. Sunrise and Sunset for Southern Latitudes The timings of Sunrise and Sunset for southern latitudes, which have not been tabulated separately, can be deduced from those for the corresponding northern latitudes by applying the corrections given on pages 290 and 291. Twilight The timings of the beginning of morning twilight and ending of evening twilight have been given for latitudes 0° to 60° North on pages 280 to 287. The timings relate to the instant when the center of the Sun is 18° below the horizon. This is now known as astronomical twilight. The period of twilight has been divided into three parts - Civil when the Sun is 6° below the horizon, Nautical when 12° and Astronomical when 18° - and their durations have been given separately on pages 288 and 289 at an interval of 8 days. The figures for any intermediate date can be worked out from the tables by simple interpolation. Moonrise and Moonset The local mean times of Moonrise and Moonset for latitudes 0° to 50° North at 10- degrees interval together with the timings of these events in I.S.T. for four important stations in India, Viz., Kolkata, Chennai, Delhi and Mumbai for each day of the year have been given on pages 296 to 311 along with some supplementary tables on pages 312 to 313. A detailed method of calculation for any station is given below. To find the time of Moonrise and Moonset for any station the figure for the phenomena concerned given against the date is to be taken from the table (pages 296 to 311) for the latitude just lower than the latitude of the station, to which the following corrections will have to be applied : (a) (b) (c)

Correction for difference in latitude; Correction for longitude, if the place is not on the Central Meridian of India (i.e., 82°.5 E. Long); Correction for converting L.M.T. into I.S.T., when and where necessary.

These corrections are detailed below : (a) Correction for difference in latitude - The timings of Moonrise and Moonset have been given for latitudes 0°, 10°, 20°, 30°, 40° and 50° North, and in local mean time. The timing for any particular latitude of place falling within the above limits can be obtained by simple interpolation between figures for the two latitudes, one below and the other above the latitude of the given place. For this purpose the table on page 313 can be conveniently used wherein corrections for latitude are shown according to the variation per 10° of latitude of the timings of Moonrise or Moonset distributed over each degree of latitude. The correction can also be calculated directly by multiplying one-tenth of the time difference between the figures for two consecutive given latitudes by the excess of the latitude of the station over the given lower latitude.

316

METHOD OF CALCULATION (b) Correction for difference in longitude - The timings thus obtained are exact for the Central Meridian of India, i.e, for longitude 82°.5 East of Greenwich. For other longitudes the correction given on page 312 should be applied according to : (i) (ii)

the longitude of the station, and the daily variation of the timings of rising or setting, as the case may be, between two consecutive dates.

If greater accuracy is not required, the daily variation may be assumed to be a constant (i.e., 50 minutes) for all dates and corrections from the following table may be applied instead of taking the corrections from the table on page 312. Longitude of Station

Correction

Longitude of Station

Correction

m

(East)

m

0°

+ 11.5

84°

- 0.2

30°

+ 7.3

88°

- 0.8

60°

+ 3.1

92°

- 1.3

68°

+ 2.0

96°

- 1.9

72°

+ 1.5

120°

- 5.2

76°

+ 0.9

150°

- 9.4

80°

+ 0.3

180°

- 13.5

(East)

The timing thus obtained by the above two operations is in L.M.T. of the station (c) Correction for converting L.M.T. into I.S.T. - The figures obtained by the operations (a) and (b) above would give the local mean time of Moonrise or Moonset for the given station. The local mean time can be reduced to the Indian Standard Time by the help of the reduction table on page 314. In other way to obtain the I.S.T., the L.M.T. may be increased at the rate of 4 minutes per degree of longitude if the station is to the west of 82°.5 East and decreased at the same rate if the station is to the east of 82°.5 East Longitude. In practice, however, when dealing with the same station, it will be convenient to combine corrections (b) and (c) above, as these are constant day after day, and add this constant to the daily times corrected for latitude only. Moonrise and Moonset for southern Latitudes The times of Moonrise and Moonset for southern latitudes have not been given separately. The timings for a station in southern latitude can, however, be deduced from those for the corresponding northern latitude by the following formula : Timings for a southern latitude = 2 × Timing for 0° latitude - Timing for the same northern latitude. In this case the local mean time for the same latitude north will have to be calculated first by applying the latitude correction (a) above, and the corresponding time for the southern latitude will have to be deduced by the above formula by utilising the published figure for 0° latitude. The exact L.M.T. of rising or setting for the place in question will, however, be obtained by applying the correction (b) above to the time so deduced. If necessary, the timings thus obtained may be reduced to I.S.T. by the usual method.

317

PHASES OF THE MOON, 2020 ( Time in I.S.T. )

Full Moon Last Quarter New Moon First Quarter

Dec,19 Dec,19 Dec,19 Jan, 20

d 12 19 26 03

h 10 10 10 10

m 42 27 43 15

Full Moon Last Quarter New Moon First Quarter

Jul Jul Jul Jul

d 05 13 20 27

h 10 04 23 18

m 14 59 03 03

Full Moon Last Quarter New Moon First Quarter

Jan Jan Jan Feb

11 17 25 02

00 18 03 07

51 28 12 12

Full Moon Last Quarter New Moon First Quarter

Aug Aug Aug Aug

03 11 19 25

21 22 08 23

29 15 12 28

Full Moon Last Quarter New Moon First Quarter

Feb Feb Feb Mar

09 16 23 03

13 03 21 01

03 47 02 27

Full Moon Last Quarter New Moon First Quarter

Sep Sep Sep Sep

02 10 17 24

10 14 16 07

52 56 30 25

Full Moon Last Quarter New Moon First Quarter

Mar Mar Mar Apr

09 16 24 01

23 15 14 15

18 04 58 51

Full Moon Last Quarter New Moon First Quarter

Oct Oct Oct Oct

02 10 17 23

02 06 01 18

35 10 01 53

Full Moon Last Quarter New Moon First Quarter

Apr Apr Apr May

08 15 23 01

08 04 07 02

05 26 56 08

Full Moon Last Quarter New Moon First Quarter

Oct Nov Nov Nov

31 08 15 22

20 19 10 10

19 16 37 15

Full Moon Last Quarter New Moon First Quarter

May May May May

07 14 22 30

16 19 23 09

15 33 09 00

Full Moon Last Quarter New Moon First Quarter

Nov Dec Dec Dec

30 08 14 22

15 06 21 05

00 07 47 11

Full Moon Last Quarter New Moon First Quarter

Jun Jun Jun Jun

06 13 21 28

00 11 12 13

42 54 11 46

Full Moon Last Quarter New Moon First Quarter

Dec Jan,21 Jan,21 Jan,21

30 06 13 21

08 15 10 02

58 07 30 32

PART - IV ECLIPSES AND OCCULTATIONS

320

ECLIPSES, 2020 In the year 2020, there are two eclipses of the Sun. I II

June December

21 14

Annular eclipse of the Sun Total eclipse of the Sun

In addition, there are four penumbral eclipses of the Moon

320–329 330–333

January 10 June 5 July 5 November 30

334 335 336 337

I- Annular eclipse of the Sun, June 21, 2020, Sunday. Visible in India. Area of Visibility The eclipse is visible in the region covering Africa (except W. and S. parts), S. E. Europe, Middle East, Asia (except N and E. Russia), Indonesia, Micronesia. ELEMENTS OF THE ECLIPSE Universal Time of Conjunction in Right Ascension : January 21d 6h 41m 24s.21

h 6

Right Ascension Hourly Motion

 Declination Hourly Motion Equatorial Horizontal Parallax True Semi-diameter

23

MOON m 01 ' 32 2 56 15

s 33.22 141.00

h 6

SUN m 01

"



'

23

26

59.68 55.55 31.12 23.70

15

s 33.22 10.40 " 09.7 -0.37 08.65 44.23

CIRCUMSTANCES OF THE ECLIPSE

Eclipse begins Central eclipse begins Greatest eclipse* Central eclipse ends Eclipse ends

Universal Time d h m 21 03 46.1 21 04 48.5 21 06 40.1 21 08 31.7 21 09 34.0

Indian Standard Time d h m 21 09 16.1 21 10 18.5 21 12 10.1 21 14 01.7 21 15 04.0

Latitude  -1 +1 +30 +11 +9

' 01.9 16.1 31.1 28.0 10.5

Longitude  +34 +17 +79 +147 +130

*Magnitude of the eclipse = 0.9936, Maximum duration of annular phase = 1 min 17 s

' 23.0 47.9 40.1 35.3 59.6

321

ANNULAR SOLAR ECLIPSE OF JUNE 21, 2020 Longitude West of Greenwich 60o

70o

150o

90o

180o

170o

180o

50o

40o

NORTH ATLANTIC OCEAN

PACIFIC OCEAN

180o

30o

EUROPE 170o

at

20o

Sunrise

50o

ASIA Sunset

10o

0600

at

at

40o 30o

160o

20o 10o 0o

10o

AFRICA INDIAN OCEAN

20o

AUSTRALIA 30o

0o

10o

20o

30o

40o

50o

60o

70o

80o

90o

100o

110o

Longitude East of Greenwich

120o

130o

140o

150o

Longitude East of Greenwich The timings of beginning and ending are expressed in UT

322

ECLIPSES, 2020 BESSELIAN ELEMENTS OF THE ANNULAR ECLIPSE OF THE SUN JUNE 21 Terrestrial Co-ordinates of the Centre Time of Shadow on the (TT) Fundamental Plane h m x y 3 4

5

6

7

8

9

40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40

-1.615715 -1.527255 -1.438790 -1.350320 -1.261845 -1.173365 -1.084881 -0.996392 -0.907900 -0.819404 -0.730904 -0.642401 -0.553894 -0.465384 -0.376872 -0.288356 -0.199838 -0.111318 -0.022796 +0.065729 +0.154255 +0.242783 +0.331312 +0.419843 +0.508374 +0.596907 +0.685440 +0.773973 +0.862507 +0.951042 +1.039576 +1.128109 +1.216643 +1.305175 +1.393707 +1.482238 +1.570768

-0.036646 -0.027912 -0.019186 -0.010469 -0.001761 +0.006939 +0.015630 +0.024312 +0.032985 +0.041650 +0.050305 +0.058952 +0.067590 +0.076219 +0.084840 +0.093451 +0.102053 +0.110646 +0.119231 +0.127806 +0.136372 +0.144929 +0.153477 +0.162016 +0.170546 +0.179066 +0.187578 +0.196080 +0.204573 +0.213056 +0.221530 +0.229995 +0.238451 +0.246897 +0.255334 +0.263761 +0.272179

Radius of Penumbra and Umbra on the Fundamental Plane l1 l2

Direction of the Axis of Shadow * sin d

cos d

+0.397731 +0.397730 +0.397730 +0.397729 +0.397728 +0.397728 +0.397727 +0.397727 +0.397726 +0.397726 +0.397725 +0.397725 +0.397724 +0.397723 +0.397723 +0.397722 +0.397722 +0.397721 +0.397721 +0.397720 +0.397719 +0.397719 +0.397718 +0.397717 +0.397717 +0.397716 +0.397716 +0.397715 +0.397714 +0.397714 +0.397713 +0.397712 +0.397712 +0.397711 +0.397710 +0.397710 +0.397709

+0.917502 +0.917502 +0.917503 +0.917503 +0.917503 +0.917503 +0.917504 +0.917504 +0.917504 +0.917504 +0.917505 +0.917505 +0.917505 +0.917505 +0.917506 +0.917506 +0.917506 +0.917506 +0.917507 +0.917507 +0.917507 +0.917507 +0.917508 +0.917508 +0.917508 +0.917508 +0.917509 +0.917509 +0.917509 +0.917509 +0.917510 +0.917510 +0.917510 +0.917511 +0.917511 +0.917511 +0.917511

 234 237 239 242 244 247 249 252 254 257 259 262 264 267 269 272 274 277 279 282 284 287 289 292 294 297 299 302 304 307 309 312 314 317 319 322 324

μ ' 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 02 32 01 31

" 18.5 18.0 17.5 16.9 16.4 15.8 15.3 14.8 14.2 13.7 13.2 12.6 12.1 11.5 11.0 10.5 09.9 09.4 08.9 08.3 07.8 07.3 06.7 06.2 05.6 05.1 04.6 04.0 03.5 03.0 02.4 01.9 01.3 00.8 00.3 59.7 59.2

+0.551682 +0.551673 +0.551664 +0.551654 +0.551643 +0.551632 +0.551620 +0.551608 +0.551595 +0.551581 +0.551567 +0.551553 +0.551537 +0.551521 +0.551505 +0.551488 +0.551470 +0.551452 +0.551433 +0.551413 +0.551393 +0.551373 +0.551351 +0.551330 +0.551307 +0.551284 +0.551260 +0.551236 +0.551211 +0.551186 +0.551160 +0.551133 +0.551106 +0.551078 +0.551049 +0.551020 +0.550991

tanf1= 0.00460834

tanf2= 0.00458542

TT

hr

+0.006661 +0.006652 +0.006643 +0.006633 +0.006622 +0.006611 +0.006599 +0.006587 +0.006574 +0.006560 +0.006546 +0.006532 +0.006516 +0.006500 +0.006484 +0.006467 +0.006449 +0.006431 +0.006412 +0.006393 +0.006372 +0.006352 +0.006330 +0.006309 +0.006286 +0.006263 +0.006239 +0.006215 +0.006190 +0.006165 +0.006139 +0.006112 +0.006085 +0.006057 +0.006028 +0.005999 +0.005970

Variations per minute d

 ' 4 23 26 5 23 26 6 23 26 7 23 26 8 23 26 9 23 26 ξ = 0.004364 ρcos φ'cos (μ+λ)

x' " 11 10 09 08 07 06

y'

μ' ' "

+0.008 847 0.000 872 15 +0.008 850 0.000 866 15 +0.008 852 0.000 861 15 +0.008 853 0.000 856 15 +0.008 853 0.000 850 15 +0.008 853 0.000 845 15  = 0.004364 ξsin d

*d stands for declination and μ stands for hour angle

00 00 00 00 00 00

323

ECLIPSES, 2020 PATH OF CENTRAL PHASE DURING THE ANNULAR ECLIPSE OF THE SUN JUNE 21

Terrestrial Time (TT)

Northern Limit Latitude

Central Line

Longitude

Latitude

Southern Limit

Longitude

Latitude

Central Line

Longitude

Duration of Annularity m s º ' -----+34 24.7

Limit h m 4 50

º ' +1 35.4

º ' +17 36.4

º ' +1 16.1

º ' +17 47.9

º ' -1 02.1

+05 08.9

+25 20.1

+05 06.9

+26 04.8

+05 03.8

+26 46.0

1 21

5 00 10 20 30 40 50

+12 16 19 21 23 +25

07.1 03.0 02.9 30.3 34.5 20.2

+38 45 50 55 59 +62

38.0 30.7 43.2 07.0 03.1 42.3

+11 15 18 21 23 +25

57.6 53.7 54.1 22.0 26.7 12.8

+38 45 50 55 59 +62

55.2 42.9 52.6 14.6 09.2 47.2

+11 15 18 21 23 +25

48.1 44.3 45.3 13.8 18.9 05.5

+39 45 51 55 59 +62

12.1 54.9 02.0 22.1 15.3 52.1

1 1 1 0 0 0

12 07 02 58 54 51

6 00 10 20 30 40 50

+26 28 29 29 30 +31

50.3 06.2 09.1 59.4 37.2 02.5

+66 69 72 76 79 +83

11.2 34.4 54.9 15.1 37.0 02.3

+26 27 29 29 30 +30

43.3 59.5 02.6 52.9 30.8 56.1

+66 69 72 76 79 +83

15.2 37.6 57.3 16.9 38.2 02.9

+26 27 28 29 30 +30

36.3 52.8 56.0 46.5 24.4 49.6

+66 69 72 76 79 +83

19.2 40.7 59.8 18.7 39.4 03.4

0 0 0 0 0 0

49 47 45 44 43 43

7 00 10 20 30 40 50

+31 31 30 30 29 +28

15.1 14.2 59.2 28.5 40.4 31.8

+86 90 93 97 102 +106

32.6 09.6 55.5 52.8 05.5 39.6

+31 31 30 30 29 +28

08.5 07.4 52.0 21.0 32.4 23.2

+86 90 93 97 102 +106

32.5 08.8 53.9 50.2 01.8 34.4

+31 31 30 30 29 +28

01.9 00.6 44.9 13.4 24.3 14.6

+86 90 93 97 101 +106

32.4 08.1 52.3 47.7 58.1 29.2

0 0 0 0 0 0

44 45 46 48 51 54

8 00 10 20 30

+26 24 21 +15

57.6 48.2 40.0 29.8

+111 117 125 +139

45.4 43.1 23.4 21.4

+26 24 21 +15

48.4 38.4 30.1 27.0

+111 117 125 +138

38.2 33.0 08.1 39.6

+26 24 21 +15

39.2 28.7 20.1 23.2

+111 117 124 +138

31.1 23.1 53.1 0.8

0 1 1 1

57 02 07 15

Limit

+11 46.1

+147 46.4

+11 28.2

+147 35.2

+11 10.4

+147 24.3

-------

324

ECLIPSES, 2020 THE ANNULAR ECLIPSE OF THE SUN, JUNE 21 LOCAL CIRCUMSTANCES RELATING TO INDIA BEGINNING OF ECLIPSE FOR STATIONS IN INDIA TIME IN I.S.T. Longitude East of Greenwich Beginning 80˚ 84˚ 88˚ 92˚ h m h m h m h m 10 37.1 10 45.4 10 54.5 11 04.2

Lat (North) 36˚

68˚ h m 10 18.0

72˚ h m 10 23.4

76˚ h m 10 29.8

96˚ h m 11 14.3

100˚ h m 11 24.6

32˚

10 09.8

10 15.7

10 22.7

10 30.8

10 39.9

10 50.0

11 00.7

11 11.9

11 23.2

28˚

10 02.7

10 09.1

10 16.8

10 25.7

10 35.8

10 46.9

10 58.7

11 11.0

11 23.2

24˚

9 56.8

10 03.8

10 12.2

10 22.0

10 33.1

10 45.4

10 58.4

11 11.8

11 25.0

20˚

9 52.2

9 59.9

10 09.1

10 19.9

10 32.2

10 45.8

11 00.2

11 14.7

11 28.8

16˚

9 49.1

9 57.6

10 07.8

10 19.8

10 33.6

10 48.7

11 04.4

11 20.0

11 34.8

12˚

9 47.7

9 57.2

10 08.6

10 22.2

10 37.7

10 54.6

11 11.8

11 28.4

11 43.5

8˚

9 48.3

9 59.1

10 12.2

10 27.9

10 45.7

11 04.7

11 23.5

11 40.6

11 55.5

96˚ h m 14 20.6

100˚ h m 14 25.5

ENDING OF ECLIPSE FOR STATIONS IN INDIA TIME IN I.S.T.

Lat (North) 36˚

68˚ h m 13 21.8

72˚ h m 13 32.3

Longitude East of Greenwich Beginning 76˚ 80˚ 84˚ 88˚ 92˚ h m h m h m h m h m 13 42.3 13 51.6 14 00.2 14 08.0 14 14.8

32˚

13 22.5

13 33.7

13 44.5

13 54.7

14 04.0

14 12.5

14 19.8

14 26.2

14 31.5

28˚

13 21.4

13 33.4

13 45.0

13 56.0

14 06.2

14 15.3

14 23.4

14 30.3

14 36.1

24˚

13 18.5

13 31.0

13 43.4

13 55.3

14 16.4

14 25.2

14 32.8

14 32.8

14 39.2

20˚

13 13.4

13 26.5

13 39.6

13 52.3

14 04.3

14 15.3

14 25.0

14 33.5

14 40.5

16˚

13 06.0

13 19.3

13 33.0

13 46.6

13 59.6

14 11.8

14 22.6

14 32.0

14 40.0

12˚

12 56.2

13 09.3

13 23.2

13 37.5

13 51.6

14 05.1

14 17.3

14 28.1

14 37.2

8˚

12 43.8

12 56.1

13 09.6

13 24.1

13 39.2

13 54.2

14 08.3

14 20.8

14 31.5

325

64o

3 36o

3 32o

2 28o

24o

2 20o

1 16o

1 12o

8o

4o

72o

76o

76o

80o

80o

84o

84o

88o

92o

Ann nularity

Annulaarity

at 88o

92o

96o

ANNUL LAR SOLAR R ECLIPSE E OF JUNE 21, 2020 68o

72o

The timings of begin nning and ending aree expressed in IST

100 0o

96o

36o

32o

28o

24o

20o

16o

12o

8o

4o

326

ECLIPSES, 2020 THE ANNULAR ECLIPSE OF THE SUN, JUNE 21 PHASES OF ECLIPSE VISIBLE FROM CERTAIN PLACES OF INDIA AND ITS NEIGHBOURHOOD Places

Partial Eclipse Begins (IST) h

Agartala Ahmadabad Aijwal Ajmer Allahabad Amritsar Bangalore Bhagalpur Bhopal Bhubaneswar Cannanore *Chamoli Chandigarh Chennai Cochin Cooch Behar Cuttack Darjeeling *Dehradun Delhi Dibrugarh Dwarka Gandhinagar Gangtok Gaya Guwahati Haridwar Hazaribagh Hubli Hyderabad Imphal Itanagar Jaipur Jalandhar Jammu *Joshimath

m

10 56.0 10 04.0 11 00.9 10 11.9 10 27.6 10 20.0 10 13.2 10 42.4 10 14.7 10 38.3 10 06.7 10 27.1 10 24.4 10 22.0 10 11.0 10 50.5 10 38.6 10 47.2 10 24.2 10 20.1 11 07.9 9 56.6 10 04.3 10 48.3 10 36.2 10 57.0 10 24.9 10 37.2 10 06.0 10 15.0 11 04.6 11 03.5 10 14.8 10 22.7 10 21.7 10 27.8

Position Angles at Eclipse Begins P V 275 263 276 260 267 252 285 270 267 279 285 257 254 288 290 270 278 268 256 258 270 262 263 268 270 271 256 272 277 278 275 270 260 252 250 257

1 346 3 337 347 319 29 350 351 17 28 325 322 35 37 342 16 339 325 332 282 344 346 336 352 338 324 356 13 14 342 311 337 318 316 325

Annular phase Begins (IST) h 12 12 12

Greatest Eclipse (IST)

m

h

m

08.7 05.0 09.5

12 11 12 11 12 11 11 12 11 12 11 12 12 11 11 12 12 12 12 12 12 11 11 12 12 12 12 12 11 11 12 12 11 12 11 12

45.1 42.2 49.8 51.9 13.6 57.7 47.6 30.9 57.4 26.1 37.5 09.1 04.5 58.5 38.9 39.0 26.6 35.2 05.3 01.6 54.7 31.1 42.6 36.2 24.2 45.5 06.0 25.4 42.6 55.8 53.0 51.1 55.8 01.0 58.5 09.8

Magnitude

0.771 0.823 0.770 0.906 0.831 0.935 0.473 0.811 0.789 0.655 0.461 0.997 0.965 0.453 0.396 0.846 0.661 0.868 0.996 0.952 0.896 0.840 0.827 0.877 0.799 0.842 0.990 0.774 0.586 0.602 0.804 0.879 0.908 0.931 0.904 0.997

Maximum Obscuration

71.1% 77.4% 70.9% 87.9% 78.4% 91.5% 36.5% 76.0% 73.2% 57.0% 35.2% 98.6% 95.4% 34.4% 28.4% 80.3% 57.8% 83.1% 98.6% 93.7% 86.5% 79.5% 77.9% 84.2% 74.4% 79.8% 98.6% 71.4% 49.1% 50.8% 75.0% 84.4% 88.1% 91.0% 87.5% 98.6%

Annular phase Ends (IST) h

m

-

09.4 05.6 10.2

12 12 12

Partial Eclipse Ends (IST) h m 14 13 14 13 14 13 13 14 13 14 13 13 13 13 13 14 14 14 13 13 14 13 13 14 14 14 13 14 13 13 14 14 13 13 13 13

23.6 32.2 26.7 40.6 00.6 41.6 31.5 13.8 47.0 09.7 20.4 53.7 48.7 40.8 17.7 19.2 10.1 16.3 50.4 48.4 29.1 20.1 32.6 17.0 08.9 23.6 50.8 09.9 30.8 43.9 28.7 26.9 44.2 44.5 41.2 54.3

Position Angles at Eclipse Ends P

V

77 70 77 76 75 85 50 77 70 67 47 84 85 50 43 80 68 81 83 80 85 69 70 81 75 81 84 74 56 59 80 84 77 86 87 84

356 340 357 0 356 27 290 358 344 338 274 16 21 298 267 3 339 5 17 9 11 328 341 6 355 4 18 352 301 316 1 9 1 27 32 17

Duration of Eclipse h m 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

‘ - - ‘ indicates annular phase of eclipse is not visible corresponding to the places where only partial eclipse occurs ‘*’ Places where annular phase of eclipse occurs

28 28 26 29 33 22 18 31 32 31 14 27 24 19 07 29 31 29 26 28 21 24 28 28 33 27 26 33 25 29 24 23 29 22 20 27

327

ECLIPSES, 2020 THE ANNULAR ECLIPSE OF THE SUN, JUNE 21 PHASES OF ECLIPSE VISIBLE FROM CERTAIN PLACES OF INDIA AND ITS NEIGHBOURHOOD Places

Partial Eclipse Begins (IST) h

Kanyakumari Kavalur Kavaratti Kohima Kolhapur Kolkata Koraput Kozikode Kurnool *Kurukshetra Lucknow Madurai Mangalore Midnapore Mount Abu Mumbai Murshidabad Muzaffarpur Mysore Nagpur Nalgonda Nasik Nellore Nowgong Panaji Patna Pondicherry Port Blair Pune Puri Raipur Rajamundry Rajkot Ranchi Sambalpur Shillong

m

10 17.7 10 19.2 10 00.3 11 05.3 10 03.2 10 46.4 10 28.2 10 08.4 10 13.8 10 21.3 10 26.8 10 17.6 10 04.9 10 43.0 10 05.9 10 00.9 10 47.0 10 38.3 10 10.7 10 17.9 10 17.3 10 03.8 10 20.4 10 21.4 10 03.3 10 37.1 10 21.7 11 15.6 10 03.0 10 38.3 10 25.1 10 27.1 9 59.6 10 36.8 10 32.2 10 58.0

Position Angles at Eclipse Begins P V 295 287 284 273 275 276 279 287 280 256 264 292 283 276 261 270 273 268 286 272 279 269 285 266 277 269 290 301 272 279 274 282 263 273 275 272

47 33 26 320 9 8 17 31 19 326 40 42 23 7 341 360 357 345 29 1 17 357 29 346 12 348 39 114 2 19 5 24 346 360 7 343

Annular phase Begins (IST) h 12 -

Greatest Eclipse (IST)

m

h

m

01.4 -

11 11 11 12 11 12 12 11 11 12 12 11 11 12 11 11 12 12 11 12 11 11 11 12 11 12 11 12 11 12 12 12 11 12 12 12

41.9 55.1 28.0 53.3 39.5 35.5 13.5 38.5 52.6 01.8 11.8 46.5 37.1 32.0 44.3 37.5 36.1 26.0 43.4 01.6 58.4 42.0 59.0 05.8 38.8 24.9 56.0 53.4 40.5 26.0 10.9 10.6 35.8 25.0 19.6 46.6

Magnitude

Maximum Obscuration

0.329 0.458 0.460 0.835 0.617 0.725 0.619 0.439 0.554 0.997 0.879 0.377 0.498 0.722 0.868 0.697 0.782 0.841 0.461 0.711 0.582 0.720 0.499 0.830 0.589 0.825 0.423 0.393 0.675 0.641 0.699 0.564 0.819 0.753 0.697 0.826

21.9% 34.9% 35.1% 78.9% 52.6% 65.5% 52.8% 32.9% 45.4% 98.6% 84.4% 26.6% 39.1% 65.0% 83.0% 62.1% 72.4% 79.7% 35.2% 63.7% 48.6% 64.8% 39.3% 78.3% 49.3% 77.7% 31.2% 28.1% 59.5% 55.4% 62.3% 46.5% 77.0% 68.8% 62.1% 77.8%

Annular phase Ends (IST) h m 12 -

02.1 -

Partial Eclipse Ends (IST)

Position Angles at Eclipse Ends

h

m

P

V

13 13 13 14 13 14 13 13 13 13 13 13 13 14 13 13 14 14 13 13 13 13 13 13 13 14 13 14 13 14 13 13 13 14 14 14

15.3 37.9 09.7 28.8 28.3 17.0 59.4 20.2 39.6 47.4 58.5 24.3 21.8 14.5 33.8 27.5 17.5 10.0 26.5 50.7 45.8 32.3 43.4 54.1 26.9 09.3 36.7 18.8 30.3 09.3 58.4 55.7 25.5 09.6 05.3 24.5

38 50 45 81 57 73 63 46 56 83 78 43 49 72 72 62 76 78 48 67 58 64 53 74 55 77 48 54 61 66 68 59 68 73 69 80

260 295 256 4 301 349 329 273 307 16 1 274 279 348 350 311 356 360 283 335 316 321 305 353 296 358 291 316 312 337 338 321 332 349 341 2

‘ - - ‘ indicates annular phase of eclipse is not visible corresponding to the places where only partial eclipse occurs ‘*’ Places where annular phase of eclipse occurs

Duration of Eclipse h m 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

58 19 09 23 25 31 31 12 26 26 32 07 17 31 28 27 30 32 16 33 28 29 23 33 24 32 15 03 27 31 33 29 26 33 33 27

328

ECLIPSES, 2020 THE ANNULAR ECLIPSE OF THE SUN, JUNE 21 PHASES OF ECLIPSE VISIBLE FROM CERTAIN PLACES OF INDIA AND ITS NEIGHBOURHOOD Places

Partial Eclipse Begins (IST) h

Shimla Sibsagar Silchar Siliguri Silvassa *Sirsa Srinagar Sringeri *Suratgarh Tamelong Thanjavur Thiruvanantapuram Tiruneveil Trichur Udaipur Ujjain Vadodara Varanasi Vijayawada Chittagong Colombo Dhaka Islamabad Karachi Kathmandu Lahore Rwalpindi Thimpu Yangon

m

10 23.5 11 06.7 11 01.0 10 47.3 10 02.4 10 16.9 10 24.2 10 06.7 10 14.5 11 04.8 10 20.3 10 15.1 10 18.6 10 10.7 10 07.8 10 10.9 10 04.6 10 31.0 10 21.7 10 59.9 10 30.8 10 54.1 10 21.8 9 57.2 10 39.5 10 19.9 10 21.1 10 52.6 11 19.0

Position Angles at Eclipse Begins P V 254 271 274 269 268 255 248 282 255 274 291 294 293 288 262 266 265 268 281 277 300 274 247 255 264 251 247 267 290

322 294 349 341 355 327 310 22 327 335 41 44 45 34 343 350 349 348 22 11 60 358 310 333 335 318 310 330 135

Annular phase Begins (IST) h 11 11 -

Greatest Eclipse (IST)

m

h

m

55.9 52.5 -

12 12 12 12 11 11 11 11 11 12 11 11 11 11 11 11 11 12 12 12 11 12 11 11 12 11 11 12 13

03.4 54.0 49.7 35.5 40.1 56.1 59.7 40.6 52.9 53.1 51.8 40.0 45.9 40.5 47.2 52.1 43.2 17.8 03.4 49.0 54.6 43.3 56.0 30.0 26.1 57.0 55.3 40.3 04.1

Magnitude

Maximum Obscuration

Annular phase Ends (IST) h m

0.967 0.879 0.803 0.856 0.741 0.996 0.861 0.514 0.998 0.814 0.394 0.346 0.356 0.420 0.858 0.798 0.795 0.821 0.558 0.749 0.286 0.779 0.848 0.952 0.906 0.922 0.852 0.893 0.585

95.6% 84.4% 74.9% 81.6% 67.4% 98.6% 82.2% 40.9% 98.6% 76.4% 28.3% 23.5% 24.5% 30.9% 81.8% 74.3% 73.9% 77.2% 45.9% 68.3% 18.0% 72.0% 80.5% 93.6% 87.8% 89.8% 81.1% 86.1% 48.8%

11 11 -

56.6 53.3 -

Partial Eclipse Ends (IST)

Position Angles at Eclipse Ends

h

m

P

V

13 14 14 14 13 13 13 13 13 14 13 13 13 13 13 13 13 14 13 14 13 14 13 13 14 13 13 14 14

47.9 28.8 26.6 16.7 30.4 42.3 40.6 26.2 39.2 28.7 30.8 14.9 21.9 21.2 36.8 42.2 33.5 04.0 49.5 26.1 23.8 22.4 36.5 16.7 09.3 40.5 36.1 19.6 33.3

85 84 79 80 65 82 90 51 81 80 45 39 41 45 72 70 68 76 58 76 37 77 90 75 82 86 90 83 68

21 9 0 4 322 16 39 287 17 2 283 260 270 273 350 342 335 356 316 355 268 357 43 17 7 29 43 8 341

‘ - - ‘ indicates annular phase of eclipse is not visible corresponding to the places where only partial eclipse occurs ‘*’ Places where annular phase of eclipse occurs

Duration of Eclipse h m 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3

24 22 26 29 28 25 16 20 25 24 10 00 03 10 29 31 29 33 28 26 53 28 15 19 30 21 15 27 14

329

ECLIPSES, 2020 ANNULAR SOLAR ECLIPSE, JUNE 21, 2020 LOCAL CIRCUMSTANCES RELATING TO PLACES FROM WHERE ANNULAR PHASE IS VISIBLE Places

Chamoli Dehradun Joshimath Kurukshetra Sirsa Suratgarh

Annular phase Begins (IST) h m 12 08.7 12 05.0 12 09.5 12 01.4 11 55.9 11 52.5

Greatest Eclipse (IST) h 12 12 12 12 11 11

m 09.1 05.3 09.8 01.8 56.1 52.9

Maximum Obscuration

98.6% 98.6% 98.6% 98.6% 98.6% 98.6%

Annular phase Ends (IST) h m 12 09.4 12 05.6 12 10.2 12 02.1 11 56.4 11 53.3

Duration of Annularity

m 0 0 0 0 0 0

s 38 31 39 39 36 45

330

ECLIPSES, 2020 II- Total eclipse of the Sun December 14, 2020, Monday Not Visible in India. Area of Visibility The eclipse is visible in the region covering Southern Pacific Ocean, Galapogos Islands, South America, (except N. Parts), Parts of Antarctica and parts of S.W. Africa. ELEMENTS OF THE ECLIPSE Universal Time of Conjunction in Right Ascension : December 14d 16h 18m 12s.35 MOON h m 17 30

Right Ascension Hourly Motion

 Declination Hourly Motion Equatorial Horizontal Parallax True Semi-diameter

- 23

' 33 -5 60 16

SUN h m 17 30

s 06.77 158.63



" 22.44 14.32. 10.30 23.40

-23

' 15 16

s 06.77 11.06 " 32.89 -7.89 08.93 14.49

CIRCUMSTANCES OF THE ECLIPSE

Eclipse begins Central eclipse begins Greatest eclipse* Central eclipse ends Eclipse ends

Universal Time d h m 14 13 34.0 14 14 32.8 14 16 13.5 14 17 54.1 14 18 53.0

Indian Standard Time d h m 14 19 04.0 14 20 02.8 14 21 43.5 14 23 24.1 15 00 23.0

Latitude  -2 -7 -40 -23 -18

' 06.5 46.0 20.2 37.0 01.8

Longitude  -115 -132 -67 +11 -06

*Magnitude of the eclipse = 1.0245, Maximum duration of total phase = 2 min 14s

' 40.8 50.4 57.5 02.9 28.2

331

TOTAL SOLAR ECLIPSE OF DECEMBER 14, 2020 Longitude West of Greenwich

L Longitude it d West W t off Greenwich G i h

140o

110o

120o

130o

100o

90o

80o

70o

60o

50o

30o

40o

20o

NORTH AMERICA

PACIFIC OCEAN

10o

ATLANTIC OCEAN

at

at

SOUTH AMERICA

150o

AFRICA

of Maximum

0o

170o

LAST CONTACT

Sunset

Ecclipse

1400

160o

10o

180o 20o 170o

ANTARCTICA

30o

160o

AUSTRALIA 150o

140o

130o

110o

90o 80o 70o

60o

50o

Longitude East of Greenwich

40o

Longitude East of Greenwich The timings of beginning and ending are expressed in UT

332

ECLIPSES, 2020 BESSELIAN ELEMENTS OF THE TOTAL ECLIPSE OF THE SUN DECEMBER 14 Terrestrial Co-ordinates of the Centre Time of Shadow on the (TT) Fundamental Plane h m x y 13

14

15

16

17

18

19

00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00

-1.871460 -1.777628 -1.683790 -1.589947 -1.496100 -1.402248 -1.308391 -1.214531 -1.120667 -1.026799 -0.932929 -0.839055 -0.745178 -0.651299 -0.557418 -0.463535 -0.369650 -0.275764 -0.181876 -0.087988 +0.005901 +0.099791 +0.193680 +0.287570 +0.381459 +0.475347 +0.569235 +0.663121 +0.757006 +0.850889 +0.944771 +1.038650 +1.132526 +1.226400 +1.320271 +1.414139 +1.508003

-0.010551 -0.025029 -0.039498 -0.053957 -0.068407 -0.082846 -0.097276 -0.111696 -0.126106 -0.140506 -0.154896 -0.169275 -0.183645 -0.198005 -0.212354 -0.226693 -0.241022 -0.255340 -0.269648 -0.283946 -0.298233 -0.312509 -0.326776 -0.341031 -0.355276 -0.369510 -0.383733 -0.397946 -0.412148 -0.426339 -0.440519 -0.454688 -0.468846 -0.482994 -0.497130 -0.511255 -0.525368

Radius of Penumbra and Umbra on the Fundamental Plane l1 l2

Direction of the Axis of Shadow * sin d

cos d

-0.394772 -0.394777 -0.394783 -0.394788 -0.394793 -0.394799 -0.394804 -0.394810 -0.394815 -0.394820 -0.394826 -0.394831 -0.394836 -0.394842 -0.394847 -0.394852 -0.394858 -0.394863 -0.394868 -0.394873 -0.394879 -0.394884 -0.394889 -0.394895 -0.394900 -0.394905 -0.394910 -0.394916 -0.394921 -0.394926 -0.394931 -0.394937 -0.394942 -0.394947 -0.394952 -0.394957 -0.394963

+0.918779 +0.918777 +0.918775 +0.918772 +0.918770 +0.918768 +0.918765 +0.918763 +0.918761 +0.918758 +0.918756 +0.918754 +0.918751 +0.918749 +0.918747 +0.918745 +0.918742 +0.918740 +0.918738 +0.918736 +0.918733 +0.918731 +0.918729 +0.918726 +0.918724 +0.918722 +0.918720 +0.918717 +0.918715 +0.918713 +0.918711 +0.918708 +0.918706 +0.918704 +0.918702 +0.918700 +0.918697

 16 18 21 23 26 28 31 33 36 38 41 43 46 48 51 53 56 58 61 63 66 68 71 73 76 78 81 83 86 88 91 93 96 98 101 103 106

μ ' 16 46 16 46 16 46 16 46 16 46 16 46 16 46 16 46 16 45 15 45 15 45 15 45 15 45 15 45 15 45 15 45 15 45 15 45 15

" 34.8 32.7 30.6 28.5 26.4 24.3 22.2 20.1 18.0 15.9 13.8 11.7 09.6 07.5 05.4 03.3 01.2 59.1 57.0 54.9 52.8 50.7 48.6 46.5 44.4 42.3 40.2 38.1 36.0 33.9 31.8 29.7 27.6 25.5 23.4 21.3 19.2

+0.542564 +0.542592 +0.542620 +0.542647 +0.542673 +0.542698 +0.542723 +0.542747 +0.542771 +0.542794 +0.542816 +0.542837 +0.542858 +0.542878 +0.542898 +0.542917 +0.542935 +0.542953 +0.542969 +0.542986 +0.543001 +0.543016 +0.543031 +0.543044 +0.543057 +0.543070 +0.543081 +0.543092 +0.543103 +0.543113 +0.543122 +0.543131 +0.543139 +0.543146 +0.543153 +0.543159 +0.543164

tanf1= 0.00475784

tanf2= 0.00473417

TT

hr

-0.002457 -0.002429 -0.002402 -0.002375 -0.002349 -0.002323 -0.002298 -0.002274 -0.002250 -0.002228 -0.002205 -0.002184 -0.002163 -0.002143 -0.002123 -0.002105 -0.002086 -0.002069 -0.002052 -0.002036 -0.002020 -0.002005 -0.001991 -0.001977 -0.001964 -0.001952 -0.001940 -0.001929 -0.001918 -0.001909 -0.001899 -0.001891 -0.001883 -0.001875 -0.001869 -0.001863 -0.001857

Variations per minute d

 ' 13 -23 15 14 -23 15 15 -23 15 16 -23 15 17 -23 15 18 -23 15 ξ = 0.004364 ρcos φ'cos (μ+λ)

x' " 06 14 21 28 35 42

y'

μ' ' "

+0.009 383 -0.001 448 15 +0.009 386 -0.001 442 15 +0.009 388 -0.001 436 15 +0.009 389 -0.001 430 15 +0.009 389 -0.001 423 15 +0.009 388 -0.001 417 15  = 0.004364 ξsin d

*d stands for declination and μ stands for hour angle

00 00 00 00 00 00

333

ECLIPSES, 2020 PATH OF CENTRAL PHASE DURING THE TOTAL ECLIPSE OF THE SUN DECEMBER 14 Terrestrial Time (TT)

Northern Limit Latitude

Central Line

Longitude

Latitude

Southern Limit

Longitude

Latitude

Longitude

Duration of totality m s º ' -------132 56.2

Limit h m 14 40 50

' 37.3

º ' -132 44.6

º ' -7 46.0

º ' -132 50.4

º ' -7 54.7

-16 29.3 21 33.0

-114 59.1 -106 24.7

-16 34.3 -21 42.3

-115 21.3 -106 45.2

-16 39.1 -21 51.4

15 00 10 20 30 40 50

-25 28 30 33 35 36

17.4 21.8 59.2 15.7 14.4 56.9

-100 19.0 95 13.9 90 39.1 86 20.1 82 08.0 77 57.0

-25 28 31 33 35 37

29.5 36.2 15.5 33.7 33.9 17.7

-100 95 90 86 82 78

39.0 33.2 57.7 37.5 23.9 11.0

- 25 28 31 33 35 37

41.5 50.4 31.7 51.6 53.3 38.4

16 00 10 20 30 40 50

-38 39 40 41 41 41

24.0 35.9 32.2 12.3 35.1 39.0

-73 69 64 60 55 50

42.9 22.5 53.2 12.9 19.5 10.8

-38 39 40 41 41 42

45.8 58.5 55.3 35.5 58.1 01.3

-73 69 64 60 55 50

54.6 31.5 59.2 15.6 18.7 06.4

-39 40 41 41 42 42

07.6 21.1 18.4 58.7 21.0 23.6

-74 69 65 60 55 50

17 00 10 20 30 40 50

-41 40 39 37 34 30

22.0 40.8 30.6 42.7 57.8 05.8

-44 38 32 25 16 -4

43.8 53.9 33.0 25.0 51.1 20.0

-41 41 39 37 35 30

43.1 00.3 47.9 57.1 08.3 09.5

-44 38 32 25 16 -3

35.8 42.6 18.7 08.1 31.8 56.3

-42 41 40 38 35 30

04.2 19.7 05.1 11.4 18.7 12.9

Limit

-23

29.3

+10 57.3

-23 36.8

+11

03.0

-23 44.4

º -7

Central Line

-115 43.6 -107 05.8

0 1

53 10

-100 59.0 95 52.7 91 16.4 86 55.1 82 40.0 78 25.2

1 1 1 1 1 2

23 34 43 51 57 01

06.5 40.7 05.3 18.3 17.8 01.8

2 2 2 2 2 1

04 06 05 03 00 55

-44 38 32 24 16 -3

27.7 31.1 04.2 51.0 12.4 32.4

1 1 1 1 1 0

48 39 29 17 02 42

+11

08.7

-------

334

ECLIPSES, 2020 PENUMBRAL ECLIPSE OF THE MOON,

January 10, 2020, Friday

CIRCUMSTANCES OF THE ECLIPSE Universal Indian Position Angle The Moon being Time Standard from the North in the Zenith in Time Point of Moon’s Latitude Longitude Limb (N.E.S.W)** Moon enters penumbra Middle of the eclipse* Moon leaves penumbra

d 10 10 10

h 17 19 21

m 06.0 10.2 14.4

d h m 10 22 36.0 11 00 40.2 11 02 44.4

 136 230

 23 22 22

'  04 104 58 75 50 46

' 28 18 08

* Penumbral magnitude of eclipse : 0.921

** N.E.S.W stands for North, East, South and West Note : - A penumbral eclipse of the Moon is not to be taken as an eclipse of the Moon in the ordinary sense, as the Moon is not covered by the real shadow of the Earth during such an eclipse.

335

ECLIPSES, 2020 PENUMBRAL ECLIPSE OF THE MOON, June

5, 2020, Friday

CIRCUMSTANCES OF THE ECLIPSE Universal Indian Position Angle The Moon being Time Standard from the North in the Zenith in Time Point of Moon’s Latitude Longitude Limb (N.E.S.W)** Moon enters penumbra Middle of the eclipse* Moon leaves penumbra

d 05 05 05

h 17 19 21

m 43.5 25.1 06.7

d h m 05 23 13.5 06 00 55.1 06 02 36.7

 154 229

'  -21 15 -21 34 -21 52

 93 69 45

' 22 35 49

* Penumbral magnitude of eclipse: 0.593

** N.E.S.W stands for North, East, South and West Note : - A penumbral eclipse of the Moon is not to be taken as an eclipse of the Moon in the ordinary sense, as the Moon is not covered by the real shadow of the Earth during such an eclipse.

336

ECLIPSES, 2020 PENUMBRAL ECLIPSE OF THE MOON, July

5, 2020, Sunday

CIRCUMSTANCES OF THE ECLIPSE Universal Indian Position Angle The Moon being Time Standard from the North in the Zenith in Time Point of Moon’s Latitude Longitude Limb (N.E.S.W)** Moon enters penumbra Middle of the eclipse* Moon leaves penumbra

d 5 5 5

h 03 04 05

m 04.5 30.0 55.5

d 5 5 5

h m 08 34.5 10 00.0 11 35.5

 29 330

'  -24 04 -24 03 -24 00

 -46 -65 -84

' 07 25 44

* Penumbral magnitude of eclipse: 0.380

** N.E.S.W stands for North, East, South and West Note : - A penumbral eclipse of the Moon is not to be taken as an eclipse of the Moon in the ordinary sense, as the Moon is not covered by the real shadow of the Earth during such an eclipse.

337

ECLIPSES, 2020 PENUMBRAL ECLIPSE OF THE MOON, November

30, 2020. Monday

CIRCUMSTANCES OF THE ECLIPSE Universal Indian Position Angle The Moon being Time Standard from the North in the Zenith in Time Point of Moon’s Latitude Longitude Limb (N.E.S.W)** Moon enters penumbra Middle of the eclipse* Moon leaves penumbra

d 30 30 30

h 07 09 11

m 29.9 42.9 55.9

d h m 30 12 59.9 30 15 12.9 30 17 25.9

 30 300

 20 20 21

'  28 -115 52 -147 15 -179

' 47 26 05

* Penumbral magnitude of eclipse: 0.855

** N.E.S.W stands for North, East, South and West Note: - A penumbral eclipse of the Moon is not to be taken as an eclipse of the Moon in the ordinary sense, as the Moon is not covered by the real shadow of the Earth during such an eclipse.

338

OCCULTATIONS, 2020 PLANETS BY THE MOON Sl. No

Date and Ingress - Egress Times (U.T.)

Planet

Magnitude of Planet

1.

Jan – 23

h -- h 00.5 – 04.9

Jupiter

- 1.9

Madagascar, Kerguelen Islands, southern and eastern Australia, New Zealand, south and eastern Melanesia, south western Polynesia.

2.

Feb – 18

11.6 – 15.3

Mars

1.2

North America (except north western Canada and Alaska), most of Central America, Caribbean, northernmost South America, Southernmost tip of Greenland, Azores.

3.

Feb – 19

18.3 – 21.1

Jupiter

-1.9

Antarctica, America.

4.

Feb – 20

06.3 – 09.8

Pluto

14.4

South easternmost South America, Antarctica, Kerguelen Islands, south westernmost tip of Australia.

5.

Mar – 18

06.6 – 10.3

Mars

0.9

Southernmost South America, South Georgia, Antarctica, Kerguelen Islands.

6.

Mar – 18

13.4 – 16.1

Pluto

14.3

Most of Antarctica.

7.

Apr – 14

21.5 – 22.2

Pluto

14.3

Part of Antarctic Peninsula.

8.

Jun – 19

06.8 – 10.3

Venus

-4.4

Azores, Canary Islands, north and eastern Canada, Greenland, north western half of Europe, northern and central Russia, northern Mongolia.

9.

Aug – 02

05.0 – 06.6

Pluto

14.3

Most of East Antarctica.

10.

Aug – 09

06.7 – 10.6

Mars

-1.3

Most of West Antarctica, south eastern South America, Ascension Island.

11.

Aug – 29

10.4 – 11.7

Pluto

14.3

Queen Maud Land, most of West Antarctica.

12.

Sep – 06

02.4 – 07.1

Mars

-1.9

Central and north eastern South America, Cape Verde Is., northern Africa, southernmost Europe.

13.

Oct – 03

02.2 – 05.9

Mars

-2.5

South and south easternmost South America, most of West Antarctica, Ascension Island, south western Africa.

14.

Dec – 12

19.3 – 23.0

Venus

-3.9

Easternmost Russia, Hawaii, western North America.

Area of Visibility

southernmost

South

339

OCCULTATIONS, 2020 ELEMENTS OF OCCULTATIONS OF PLANETS Sl. No.

T0 (U.T. of Conj. in R.A.) d

Y

H0

h

m

h

m

x

Body Occulted

y

Right Ascension h m s



Declination  

1.

Jan – 23

02

41.1

-08

00.9

-0.3820

0.5623

-0.0029 18

50

53.6

-22 -51

2.

Feb – 18

13

17.1

05

04.0

0.8008

0.5383

-0.0442 18

06

13.5

-23 -39 -42.8

3.

Feb – 19

19

35.7

10

17.4

-0.9986

0.5551

0.0230 19

16

15.5

-22 -16 -09.1

4.

Feb – 20

07

51.7

-01

52.3

-0.8065

0.5594

0.0502 19

44

05.9

-22 -01 -33.4

5.

Mar – 18

08

18.4

00

32.3

-0.7957

0.5304

0.0370 19

32

42.2

-22 -26 -48.3

6.

Mar – 18

14

33.8

06

34.5

-1.0209

0.5566

0.0544 19

46

50.7

-21 -57 -40.9

7.

Apr – 14

21

37.1

15

24.1

-1.2618

0.5610

0.0568 19

48

15.4

-21 -57 -15.8

8.

Jun – 19

08

54.0

22

28.7

0.8049

0.5588

0.1528 04

18

35.8

18

9.

Aug – 02

05

36.2

06

41.0

-1.1944

0.5767

0.0520 19

41

26.4

-22 -26 -05.1

10.

Aug – 09

08

00.1

27

48.3

-0.8369

0.4851

0.2160 01

26

02.8

04

11.

Aug – 29

10

50.8

13

45.2

-1.2269

0.5712

0.0508 19

39

10.0

-22 -33 -36.9

12.

Sep – 06

04

46.1

25

60.0

0.0297

0.5022

0.2174 01

50

17.6

06

47

54.0

13.

Oct – 03

03

25.7

02

40.2

-0.8065

0.5175

0.2272 01

35

54.0

06

06

44.8

14.

Dec – 12

20

39.8

10

31.0

0.7851

0.5343

-0.1789 15

38

00.7

-18 -02 -40.0

33

43

-58.5

32.1

33.8

340

OCCULTATIONS, 2020 ELEMENTS (contd.) Sl. No. 1.

l

a

0.2726

1.00

0.2729

1.00

0.2726

1.00

2. 3. 4. 0.2725

1.00

5.

0.2730

1.00

6.

0.2725

1.00

7.

0.2725

1.00

8.

0.2747

1.00

9.

0.2725

1.00

10.

0.2737

1.00

11.

0.2725

1.00

12.

0.2741

1.00

13.

0.2743

1.00

14.

0.2729

1.00

PART - V ASTRONOMICAL PHENOMENA AND MISCELLANEOUS TABLES

342

PHENOMENA, 2020 ELONGATIONS AND MAGNITUDES OF PLANETS AT 0h U.T. Date Jan.

Feb.

Mar.

Apr.

May

June

-3 2 7 12 17

Mercury Venus Mag. Mag. Date Elong. Elong. ° ° W. 8 -0.8 E. 34 -3.9 June 5 -1.0 35 -4.0 July 3 -1.2 36 -4.0 2 -1.4 E. 37 -4.0 5 -1.3 38 -4.0

30 5 10 15 20

Mercury Venus Mag. Mag. Elong. Elong. ° ° E. 5 … E. 33 -4.7 8 +4.7 37 -4.7 13 +2.9 39 -4.7 18 +1.6 41 -4.7 20 +0.6 43 -4.6

22 W. 27 1 6 11

8 11 14 17 18

-1.1 E. -1.1 -1.0 -0.9 -0.6

39 39 40 41 42

-4.1 -4.1 -4.1 Aug. -4.1 -4.2

25 E. 30 4 9 W. 14

20 18 14 9 4

-0.1 E. -0.7 -1.1 -1.4 -1.8

44 45 45 46 46

-4.6 -4.6 -4.5 -4.5 -4.4

16 W. 21 E. 26 2 7

16 10 4 11 18

+0.4 E. +2.6 … +3.3 +1.6

43 43 44 45 45

-4.2 -4.2 -4.3 -4.3 Sept. -4.3

19 W. 24 29 3 8

2 6 11 14 18

-1.9 E. -1.3 -0.8 -0.5 -0.3

46 45 45 45 44

-4.4 -4.3 -4.3 -4.3 -4.2

12 E. 17 22 27 1 W.

24 26 28 28 27

+0.8 E. +0.4 +0.2 +0.1 0

46 46 46 46 46

-4.4 -4.4 -4.5 -4.5 -4.6 Oct.

13 W. 18 23 E. 28 3

20 23 24 26 26

-0.2 E. -0.1 -0.1 +0.0 +0.0

43 43 42 41 40

-4.2 -4.2 -4.1 -4.1 -4.1

6 W. 11 16 21 26

25 22 19 15 10

-0.1 E. -0.2 -0.4 -0.7 -1.1

46 45 44 43 41

-4.6 -4.6 -4.7 -4.7 -4.7

8 E. 13 18 23 28

25 22 16 6 5

+0.1 E. +0.4 +1.5 +4.1 +4.5 W.

39 38 37 36 35

-4.1 -4.0 -4.0 -4.0 -4.0

1 W. 6 11 16 21

5 1 7 13 18

-1.8 E. -2.3 -1.6 -1.1 -0.7

38 35 31 26 20

-4.7 Nov. -4.7 -4.7 -4.6 -4.4

2 E. 7 12 17 22

14 18 19 18 15

+1.1 W. -0.3 -0.7 -0.7 -0.7

34 33 32 31 30

-4.0 -4.0 -3.9 -3.9 -3.9

26 W. 31 5 10 E. 15

21 23 24 23 20

-0.4 E. +0.0 +0.5 +1.0 +1.7

14 6 2 10 17

-4.1 … Dec. … -4.1 -4.2

27 W. 2 7 12 17

13 10 7 5 2

-0.7 W. -0.8 -0.9 -1.0 -1.2

29 27 26 25 24

-3.9 -3.9 -3.9 -3.9 -3.9

20 E. 25 30 E.

16 10 5

+2.7 E. +4.1 … E.

23 29 33

-4.4 -4.6 -4.7

22 W. 27 32 W.

2 4 7

-1.3 W. -1.1 -1.0 W.

23 22 20

-3.9 -3.9 -3.9

Conjunctiond h d h Superior: Jan. 10 15 May 4 22 Inferior: Feb. 26 02 Jul. 1 03

d Jun.

h … 3 18

d h Aug. 17 15 Oct. 25 18

d h Dec. 20 03 …

d

h … …

N.B.- E. means that the planet is in the east of the Sun and W. means that it is in the west of the Sun by the amount of the arc stated.

343

PHENOMENA, 2020 ELONGATIONS AND MAGNITUDES OF PLANETS AT 0h UT Date Jan.

Feb.

Mar.

Apr. May

June

July Aug.

Sept. Oct.

Nov.

Dec.

-8 2 12 22 1

Mars Elong. ° W. 38 42 45 49 52

Mag. +1.6 +1.6 +1.5 +1.4 +1.4

Jupiter Saturn Uranus Neptune Pluto Elong. Mag. Elong. Elong. Elong. Elong. Mag. ° ° ° ° ° W. 4 -1.8 W. 20 +0.5 E. 122 E. 75 E. 21 4 -1.8 10 +0.5 112 65 11 12 -1.8 1 +0.5 101 55 W. 2 20 -1.9 8 +0.6 91 45 8 28 -1.9 17 +0.6 81 36 18

11 W. 21 2 12 22

55 59 62 65 68

+1.3 W. +1.2 +1.1 +1.0 +0.9

36 44 52 60 69

-1.9 W. -1.9 -2.0 -2.0 -2.1

26 35 44 53 62

+0.6 E. +0.7 +0.7 +0.7 +0.7

71 E. 62 52 42 W. 33

26 W. 16 6 3 13

28 38 48 57 67

1 W. 11 21 1 11

71 74 77 79 82

+0.8 W. +0.7 +0.5 +0.4 +0.3 E.

77 86 95 104 114

-2.1 W. -2.2 -2.3 -2.3 -2.4

71 80 90 99 109

+0.7 E. +0.6 +0.6 W. +0.6 +0.5

23 W. 14 5 4 13

22 W. 32 41 51 60

77 87 96 106 116

21 W. 31 10 20 30

85 88 91 94 98

+0.1 E. +0.0 -0.2 -0.3 -0.5

123 133 143 154 165

-2.5 W. -2.6 -2.6 -2.7 -2.7 E.

119 128 138 148 159

+0.5 W. +0.4 +0.4 +0.3 +0.2

22 W. 32 41 50 59

70 W. 79 89 98 108

126 135 145 155 165

10 W. 20 30 E. 9 19

101 105 110 115 122

-0.7 E. -0.8 -1.0 -1.3 -1.5

175 174 163 152 142

-2.7 E. -2.7 -2.7 -2.7 -2.6

169 179 171 160 150

+0.2 W. +0.1 +0.1 +0.2 +0.2

68 W. 77 87 96 106

117 W. 127 E. 137 146 156

174 176 166 156 146

29 E. 8 18 28 8

129 138 148 159 171

-1.7 E. -2.0 -2.2 -2.4 -2.6

132 122 112 102 93

-2.6 E. -2.5 -2.4 -2.4 -2.3

140 130 120 110 100

+0.3 W. +0.3 +0.4 +0.4 +0.5

116 W. 125 E. 135 145 156

166 E. 176 174 164 154

137 127 117 107 97

18 E. 28 7 17 27

174 162 151 140 131

-2.6 E. -2.3 -1.9 -1.6 -1.3 W.

84 75 67 58 50

-2.3 E. -2.2 -2.1 -2.1 -2.0

91 81 72 62 53

+0.5 W. +0.6 E. +0.6 +0.6 +0.6

166 E. 176 173 163 152

144 E. 133 123 113 103

87 78 68 58 48

7 E. 17 27 37 E.

123 116 110 104

-1.0 W. 42 -2.0 E. 44 +0.6 E. 142 E. 93 E. 38 -0.7 34 -2.0 34 +0.6 132 83 28 -0.4 26 -2.0 25 +0.6 121 73 18 -0.1 W. 18 -2.0 W. 16 +0.6 E. 111 E. 63 E. 9 d h d h d h d h d h d h …. Apr. 26 09 Mar. 8 12 Jan. 13 13 Jan. 13 15 Dec. 27 18 Conjunction: Opposition: Oct. 13 23 Jul. 14 08 Oct. 31 16 Sept.11 20 July 15 19 Jul. 20 22 Magnitudes at opposition: Uranus +5.7; Neptune +7.8; Pluto +14.5 N.B. - E. means that the planet is in the east of the Sun and W. means that it is in the west of the Sun by the amount of the arc stated.

344

PHENOMENA, 2020 CONJUNCTIONS, OPPOSITIONS ETC. OF PLANETS WITH THE SUN (IN LONGTITUDE) UNIVERSAL TIME

h 15 00 13 00 21 01 11 03 02 05

MERCURY m 17 02 56 (18˚.2) 54 07 44 47 58 06 (27˚.8) 49

Superior conjunction Heliacal rising E. Greatest elongation E. Retrograde Heliacal setting E. Inferior conjunction Heliacal rising W. Direct Greatest elongation W. Heliacal setting W.

Jan. Jan. Feb. Feb. Feb. Feb. Mar. Mar. Mar. Apr.

d 10 26 10 17 20 26 2 10 24 18

Superior conjunction Heliacal rising E. Greatest elongation E. Retrograde Heliacal setting E. Inferior conjunction Heliacal rising W. Direct Greatest elongation W. Heliacal setting W.

May May June June June July July July July Aug.

4 13 4 18 22 1 10 12 22 8

21 08 13 05 01 02 04 08 15 09

41 32 07 (23˚.6) 01 24 53 26 22 12 (20˚.1) 17

d … … 24 13 31 3 8 25 13 …

h … … 22 06 00 17 13 06 00 …

Superior conjunction Heliacal rising E. Greatest elongation E. Retrograde Heliacal setting E. Inferior conjunction Heliacal rising W. Direct Greatest elongation W. Heliacal setting W.

Mar. May May June June June Aug.

d 17 2 1 14 17 25 30 3 10 1

h 15 03 16 00 08 18 13 17 17 17

m 10 29 06 (25˚.8) 50 41 23 16 58 03 (19˚.1) 23

20 … … … … … … … … …

03 … … … … … … … … …

25 … … … … … … … … …

VENUS m … … 13 (46˚.1) 42 12 44 52 51 14 (45˚.8) …

d … … … … … … … … … …

h … … … … … … … … … …

m … … … … … … … … … …

EARTH d h m 5 07 37 Equinoxes Mar. 4 11 17 Solstices June

d h m 20 03 50 20 21 44

Perihelion Aphelion

Jan. July

Conjunction Heliacal rising W. Retrograde Opposition Direct Heliacal setting E.

MARS d h … … … … Sept. 9 22 Oct. 13 23 Nov. 14 00 … …

Aug. Sept. Oct. Oct. Oct. Oct. Oct. Nov. Nov. Dec. Dec.

SUPERIOR PLANETS JUPITER m d h … Dec. 27 18 … Jan. 9 01 21 May 14 14 26 July 14 07 36 Sept. 13 00 … … …

m 25 03 31 59 41 …

Sept. Dec.

d h m 22 13 31 21 10 02

SATURN d h Jan. 13 15 Jan. 30 00 May 11 04 July 20 22 Sept. 29 05 … …

m 16 21 09 28 12 …

345

PHENOMENA, 2020 CONJUNCTIONS, OPPOSITIONS ETC. OF PLANETS WITH THE SUN (IN LONGITUDE) UNIVERSAL TIME SUPERIOR PLANETS

URANUS d h Apr. 26 09 Aug. 15 14 Oct. 31 15 Jan. 11 01

Conjunction Retrograde Opposition Direct

m 01 26 53 48

NEPTUNE d h Mar. 8 12 June 23 04 Sept. 11 20 Nov. 29 00

m 24 31 26 37

Jan. Apr. July Oct.

PLUTO d h 13 13 25 18 15 19 4 13

m 17 52 09 33

N.B.- The heliacal risings and settings have been calcuted for 23° 11' north latitude. Here E. means east of the Sun or the western horizon and W. means west of the Sun or the eastern horizon.

PHENOMENA, 2020 CONJUNCTION OF PLANETS WITH THE MOON AND OTHER PLANETS (IN LONGITUDE) UNIVERSAL TIME

Jan.

Feb.

Mar.

Apr.

d 2 12 20 23 24 25 28 18 19 20

h 16 09 19 02 02 19 11 13 19 14

m 42 51 47 45 08 07 02 17 50 18

Mercury conj. Jupiter Mercury conj. Saturn Moon conj. Mars Moon conj. Jupiter Moon conj. Saturn Moon conj. Mercury Moon conj. Venus Moon conj. Mars Moon conj. Jupiter Moon conj. Saturn

24 27 18 18 19 20 21 28 31 14

00 17 08 10 00 11 20 14 18 23

39 06 33 48 48 35 39 21 31 47

Moon conj. Mercury Moon conj. Venus Moon conj. Mars Moon conj. Jupiter Moon conj. Saturn Mars conj. Jupiter Moon conj. Mercury Moon conj. Venus Mars conj. Saturn Moon conj. Jupiter

15 16 21 26

10 05 20 16

21 42 06 39

Moon conj. Saturn Moon conj. Mars Moon conj. Mercury Moon conj. Venus

May

June

July

Aug.

Sept.

d 12 12 15 22 24 24 8 9 13 19

h 10 19 04 08 03 11 18 03 02 08

m 30 18 06 41 15 09 06 17 13 40

Moon conj. Jupiter Moon conj. Saturn Moon conj. Mars Mercury conj. Venus Moon conj. Venus Moon conj. Mercury Moon conj. Jupiter Moon conj. Saturn Moon conj. Mars Moon conj. Venus

22 5 6 11 17 19 1 2 9 15

08 22 09 21 06 04 23 13 08 13

01 13 35 16 41 19 57 59 36 27

Moon conj. Mercury Moon conj. Jupiter Moon conj. Saturn Moon conj. Mars Moon conj. Venus Moon conj. Mercury Moon conj. Jupiter Moon conj. Saturn Moon conj. Mars Moon conj. Venus

19 29 29 6

05 01 17 04

38 56 18 45

Moon conj. Mercury Moon conj. Jupiter Moon conj. Saturn Moon conj. Mars

346

PHENOMENA, 2020 --- contd. CONJUNCTION OF PLANETS WITH THE MOON AND OTHER PLANETS (IN LONGITUDE) UNIVERSAL TIME d Sept. 14 19 25 25 Oct. 3 14 17 22 23 29

h 06 02 07 21 03 02 21 17 04 18

m 53 08 12 26 57 55 52 44 35 33

Moon conj. Venus Moon conj. Mercury Moon conj. Jupiter Moon conj. Saturn Moon conj. Mars Moon conj. Venus Moon conj. Mercury Moon conj. Jupiter Moon conj. Saturn Moon conj. Mars

d Nov. 12 13 19 19 25 Dec. 12 14 17 17 21 23

h 23 21 09 15 23 20 10 05 06 18 22

m 31 44 43 51 39 59 41 34 28 21 51

Moon conj. Venus Moon conj. Mercury Moon conj. Jupiter Moon conj. Saturn Moon conj. Mars Moon conj. Venus Moon conj. Mercury Moon conj. Jupiter Moon conj. Saturn Jupiter conj. Saturn Moon conj. Mars

CONJUNCTIONS OF PLANETS WITH BRIGHT STARS (IN R.A.)

Jan. Apr. May June July Aug. Aug.

d 17 17 17 8 12 2 19

h 04 19 08 08 06 05 20

m 05 48 52 20 39 30 56

Mars 4˚.82 N. of Antares Venus 10˚.13 N. of Aldebaran Mercury 7˚.36 N. of Aldebaran Venus 4˚.92 N. of Aldebaran Venus 0˚.96 N. of Aldebaran Mercury 6˚.64 S. of Pollux Mercury 1˚.36 N. of Regulus

d h m Sept. 1 16 57 Sept. 22 08 52 Oct. 3 23 41 Nov. 15 13 23 Dec. 7 20 00 Dec. 23 00 48

Venus 8˚.68 S. of Pollux Mercury 0˚.30 N. of Spica Venus 0˚.09 S. of Regulus Venus 4˚.13 N. of Spica Mercury 4˚.39 N. of Antares Venus 5˚.65 N. of Antares

347

ASTRONOMICAL DIARY, 2020 UNIVERSAL TIME h 1 10 15 04 18 07 23 15

m 30 27 16 45 22 37 29 17

10 19

21

11 12 13 13 13 15 17 17 19 20

07 04 13 15 20 14 04 12 11 19

22 31 17 16 20 50 05 58 36 12

Uranus stationary in RA Mercury 2.1° S of Saturn Pluto in conjunction with Sun Saturn in conjunction with Sun Moon at perigee Moon greatest lat. N 5˚12' Mars 4.8˚ N. of Antares LAST QUARTER Mercury greatest helio lat. S. Mars 2.3˚ S of Moon

22 20 23 02

32 41

23 24 24 25 27 28 28

06 21 01 18 19 06 07

29 29 Feb. 1 1 2 6 7 9 10 10 11 12 12 15 15 16 18

Jan.

d 2 2 2 3 4 5 9 10

Moon at apogee Moon greatest lat. S 5˚ 16' Mercury 1.5° S of Jupiter FIRST QUARTER Uranus 4.7˚ N of Moon Earth at Perihelion Moon in ascending node Mercury in superior conjunction 1˚ 56' S of Sun FULL MOON Penumbral Lunar Eclipse

d h Feb. 19 19

m 36

Jupiter 0.9˚ N of Moon Occultation Saturn 1.8 ° N of Moon Mercury greatest helio lat. N. NEW MOON Mercury 8.6˚ N of Moon Neptune 4.1° N of Moon Moon greatest lat. S 5˚ 00' Jupiter in descending node Mercury in inferior conjunction 3˚ 43' N of Sun

20 22 23 23 24 25 25 26

13 10 15 18 15 15 15 01

39 17 32 43 14 46 56 44

26 27 28 Mar. 2 4 8 9 9 9 10

11 11 11 19 14 12 08 14 17 06

34 52 51 57 59 24 11 33 48 28

Moon at apogee Venus 6.3˚N of Moon Uranus 4.3° N of Moon FIRST QUARTER Moon in ascending node Neptune in conjunction with Sun Mercury stationary in RA Venus 2.4˚N. of Uranus FULL MOON Moon at perigee

54 42 39 13 25 20 28

Moon in descending node Jupiter 0.4˚ N of Moon Occultation Uranus in square with Sun NEW MOON Saturn 1.5° N of Moon Mercury 1.3˚ N of Moon Venus 0.1° S of Neptune Neptune 4.1˚ N of Moon Venus 4.1 ˚ N of Moon

10 16 16 17 18

09 09 19 01 08

06 34 58 00 18

18 18 20 20

10 23 02 03

18 56 08 50

Moon greatest lat. N 4˚57' LAST QUARTER Mercury in descending node Moon in descending node Mars 0.7˚ N of Moon Occultation Jupiter 1.5 ° N of Moon Saturn 2.1 ° N of Moon Venus at perihelion Vernal Equinox

13 21 03 16 01 08 13 07 13 20

55 27 01 60 42 58 02 33 56 27

Moon greatest lat. S 5˚ 10' Moon at apogee Uranus 4.6˚ N of Moon Mars in descending node FIRST QUARTER Moon in ascending node Mercury in ascending node FULL MOON Mercury greatest elong. E. (18.2˚) Moon at perigee

20 21 22 23 24 24 24 24 26 27

06 17 23 16 02 09 15 22 20 04

22 48 23 12 06 28 24 13 42 43

Mars 0.7 ° S of Jupiter Mercury 3.6 ° N of Moon Neptune 4.1˚ N of Moon Moon greatest lat. S 4˚ 56' Mercury greatest elong. W. (27.8˚) NEW MOON Moon at apogee Venus greatest elong. E. (46.1˚) Uranus 4.1° N of Moon Mercury at aphelion

17 05 15 05 22 10 13

47 05 37 33 17 15 17

19 00

12

Moon greatest lat. N 5˚03' Mercury at perihelion Saturn in descending node Venus in ascending node LAST QUARTER Mercury stationary in RA Mars 0.8˚ S of Moon Occultation Moon in descending node

28 30 31 31 Apr. 1 3 6 7 8

10 09 16 10 10 15 12 18 02

39 31 52 58 21 13 20 07 35

Venus 6.8˚ N of Moon Venus 1.9˚ N of Moon Moon in ascending node Mars 0.9° S of Saturn FIRST QUARTER Mercury 1.4° S of Neptune. Moon greatest lat. N 5˚01' Moon at perigee FULL MOON

348

ASTRONOMICAL DIARY, 2020 UNIVERSAL TIME d Apr. 10 13 14 14 14 15 15 16 16 17

h 17 02 11 22 23 09 10 04 10 19

m 40 59 03 56 05 18 58 33 49 48

Venus greatest helio lat. N. Moon in descending node Pluto in square with Sun LAST QUARTER Jupiter 2.0° N of Moon Saturn 2.5° N of Moon Jupiter in square with Sun Mars 2.0° N of Moon Mercury greatest helio lat. S. Venus 10.1˚ N. of Aldebaran

d May 30 31 Jun. 3 3

h 03 06 03 17

m 30 38 28 44

4 5 5

13 19 19

07 06 12

6

18

11

FIRST QUARTER Moon greatest lat. N 5˚10' Moon at perigee Venus in inferior conjunction 0˚ 29' N of Sun Mercury greatest elong. E. (23.6˚) Venus in descending node FULL MOON Penumbral Lunar Eclipse Moon in descending node

19 19 20 21 21 23 23 26 26 26

07 16 19 07 17 02 05 09 12 15

09 38 00 00 16 26 51 01 58 25

Neptune 4.2˚ N of Moon Moon greatest lat. S 5˚ 00' Moon at apogee Saturn in square with Sun Mercury 3.1° N of Moon NEW MOON Uranus 4.0° N of Moon Uranus in conjunction with Sun Pluto stationary in RA Venus 6.1° N of Moon

6 8 8 9 11 12 12 12 12 13

19 08 17 02 09 23 23 12 19 06

11 20 21 12 38 18 55 24 08 24

Mars in square with Sun Venus 5.0˚ N. of Aldebaran Jupiter 2.2° N of Moon Saturn 2.7° N of Moon Neptune in square with Sun Neptune 4.5˚ N of Moon Mars 2.8° N of Moon Mars 1.7˚ S. of Neptune Mercury in descending node LAST QUARTER

27 30 May 1 3 4

17 20 02 15 21

55 38 24 33 41

13 15 17 17 19

09 00 01 19 08

42 57 48 35 54

22 02 45 53

Moon in ascending node FIRST QUARTER Mercury 0.3° S of Uranus Moon greatest lat. N 5˚04' Mercury in superior conjunction 0˚ 06' S of Sun Mercury in ascending node Moon at perigee FULL MOON Mars 7.3˚ N of Moon

20 21 21 22

21 04 06 07

44 23 41 18

Moon greatest lat. S 5˚ 15' Moon at apogee Uranus 3.9° N of Moon Mercury stationary in RA Venus 0.7˚ S of Moon Occultation Summer solstice Moon in ascending node NEW MOON, Solar Eclipse Mercury 3.9° N of Moon

5 6 7 7

12 03 10 10

10 10 11 12 12 13 14 14 15 16

04 09 09 09 18 10 14 18 02 15

20 02 26 41 11 15 03 27 01 03

Mercury at perihelion Moon in descending node Saturn stationary in RA Jupiter 2.3° N of Moon Saturn 2.7° N of Moon Venus stationary in RA LAST QUARTER Jupiter stationary in RA Mars 2.8° N of Moon Neptune 4.4˚ N of Moon

23 23 24 27 28 30 1

03 18 18 09 08 02 02

58 25 11 20 16 15 53

4 4

03 11

18 17

17 17 18 20 20 22 22 24 24 24

06 08 07 09 15 07 17 02 10 21

24 52 44 34 35 56 39 42 52 35

Moon greatest lat. S 5˚ 08' Mercury 7.4˚ N. of Aldebaran Moon at apogee Mercury greatest helio lat. N. Uranus 3.9° N of Moon Mercury 0.9˚ S. of Venus NEW MOON Venus 3.7° N of Moon Mercury 2.8° N of Moon Moon in ascending node

5

04

44

5 6 8 10 10 10 11 12

21 08 01 07 13 14 19 06

39 38 19 28 32 35 38 39

July

Mercury at aphelion Neptune stationary in RA Venus stationary in RA Moon greatest lat. N 5˚13' FIRST QUARTER Moon at perigee Mercury in inferior conjunction 4˚ 27' S of Sun Moon in descending node Earth at Aphelion FULL MOON Penumbral Lunar Eclipse Jupiter 1.9° N of Moon Saturn 2.5° N of Moon Mars greatest helio lat. S. Neptune 4.4˚ N of Moon Moon greatest lat. S 5˚ 13' Venus at aphelion Mars 2.0° N of Moon Venus 1.0˚ N. of Aldebaran

349

ASTRONOMICAL DIARY, 2020 UNIVERSAL TIME d 12 12 12 13 14 14 15 17 18 19

h 06 19 23 10 07 11 19 07 12 03

m 50 26 29 02 59 52 09 26 33 54

Mercury stationary in RA Moon at apogee LAST QUARTER Mercury greatest helio lat. S. Jupiter in opposition with Sun Uranus 3.8° N of Moon Pluto in opposition with Sun Venus 3.1° S of Moon Moon in ascending node Mercury 3.9° S of Moon

20 20 22 22 24 25 27 31 Aug. 1 1

17 22 09 15 11 05 12 09 11 15

33 28 00 12 49 00 33 32 45 31

NEW MOON Saturn in opposition with Sun Saturn 0.0˚ S of Moon Mercury greatest elong. W. (20.1˚) Moon greatest lat. N 5˚11' Moon at perigee FIRST QUARTER Moon in descending node Mercury in ascending node Venus greatest helio lat. S.

1 2 2 2 3 3 6 6 6 9

23 05 11 13 09 15 03 14 16 08

33 30 18 10 00 59 37 51 35 00

Jupiter 1.5° N of Moon Mercury 6.6˚ S. of Pollux Uranus in square with Sun Saturn 2.3° N of Moon Mars at perihelion FULL MOON Mercury at perihelion Neptune 4.3˚ N of Moon Moon greatest lat. S 5˚ 04' Mars 0.8˚ N of Moon Occultation

9 10 11 13 14 15 15 16 17

13 20 16 00 19 13 16 08 15

49 51 45 14 24 00 53 51 10

Moon at apogee Uranus 3.5° N of Moon LAST QUARTER Venus greatest elong. W. (45.8˚) Moon in ascending node Venus 4.0° S of Moon Uranus stationary in RA Mercury greatest helio lat. N. Mercury in superior conjunction 1˚ 46' N of Sun

19 19 19 20 21 25 27 29 29

02 03 20 14 10 17 11 01 16

42 46 56 16 56 58 53 36 32

NEW MOON Mercury 2.8° N of Moon Mercury 1.4˚ N. of Regulus Moon greatest lat. N 5˚01' Moon at perigee FIRST QUARTER Moon in descending node Jupiter 1.4° N of Moon Saturn 2.2° N of Moon

July

Sept.

Oct.

d 1 2 2 3 6

h 16 05 20 06 04

m 57 22 55 08 46

6 7 8

06 03 18

29 54 27

Venus 8.7˚ S. of Pollux FULL MOON Neptune 4.2˚ N of Moon Moon greatest lat. S 4˚ 57' Mars 0.03° N of Moon Occultation Moon at apogee Uranus 3.3° N of Moon Mercury in descending node

9 10 10 11 12 14 16 17 18

17 09 23 20 23 04 17 11 06

46 26 06 26 55 43 04 00 23

Mars stationary in RA LAST QUARTER Moon in ascending node Neptune in opposition with Sun Jupiter stationary in RA Venus 4.5° S of Moon Moon greatest lat. N 4˚55' NEW MOON Uranus 0.4˚ N of Moon

18 18 19 22 22 23 24 25 25

13 21 03 08 13 12 01 06 20

47 53 15 52 31 33 55 48 38

Moon at perigee Mercury 6.4° S of Moon Mercury at aphelion Mercury 0.3˚ N. of Spica Autumnal Equinox Moon in descending node FIRST QUARTER Jupiter 1.6° N of Moon Saturn 2.3° N of Moon

26 26 29 30 30 1 1 3

17 22 02 01 06 16 21 03

51 30 52 44 39 06 05 26

Venus 7.8˚ S of Moon Venus in ascending node Saturn stationary in RA Neptune 4.2° N of Moon Moon greatest lat. S 4˚ 57' Mercury greatest elong. E. (25.8˚) FULL MOON Mars 0.7˚ N of Moon Occultation

3 3 4 4 6 8 9 10 11

17 23 05 08 14 00 09 00 13

22 41 42 57 17 30 16 40 35

Moon at apogee Venus 0.1˚ S. of Regulus Pluto stationary in RA Uranus 3.2° N of Moon Mars nearest to Earth Moon in ascending node Mercury greatest helio lat. S. LAST QUARTER Jupiter in square with Sun

13 13 14 14

23 23 04 08

26 56 18 22

Mars in opposition with Sun Venus 4.4° S of Moon Mercury stationary in RA Moon greatest lat. N 5˚00'

350

ASTRONOMICAL DIARY, 2020 UNIVERSAL TIME h 10 19 23 18 13 15 17 03 13

m 12 31 47 36 58 55 12 42 23

25 18

23

27 27 28 29 30 30 31

06 07 11 16 18 23 12

16 28 03 17 45 03 50

Mercury in inferior conjunction 0˚ 55' S of Sun Neptune 4.4˚ N of Moon Moon greatest lat. S 5˚ 04' Mercury in ascending node Mars 3.0° N of Moon Moon at apogee Venus at perihelion Uranus 3.2° N of Moon

31 31 Nov. 2 3 4 8 10 10 12

14 15 02 08 02 13 11 17 08

49 53 53 25 40 46 55 03 08

12 13 14 15 15 15 17 19 19 21

21 20 11 05 13 19 00 08 14 10

30 44 43 07 23 25 07 56 51 31

Oct.

d 15 16 16 17 18 20 22 23 23

d Nov. 22 23 23 25 27 27 29 30

h 04 12 09 19 24 16 09 09

m 45 01 45 47 28 59 02 30

Dec.

1 2 5 7 7 8 9 12

07 03 17 15 20 00 19 20

46 28 41 17 00 37 41 40

Moon in ascending node Mars in ascending node Mercury in descending node Moon greatest lat. N 5˚14' Mercury 4.4° N of Antares. LAST QUARTER Neptune in square with Sun Venus 0.8˚ S of Moon Occultation

FULL MOON Uranus in opposition with Sun Mercury at perihelion Mercury stationary in RA Moon in ascending node LAST QUARTER Moon greatest lat. N 5˚13' Mercury greatest elong. W. (19.1˚) Mercury greatest helio lat. N.

12 14 14 14 16 17 17 20

20 10 11 16 02 04 05 03

41 33 03 17 31 29 19 25

Moon at perigee Mercury 1.0° S of Moon Moon in descending node NEW MOON, Solar Eclipse Mercury at aphelion Jupiter 2.9° N of Moon Saturn 3.1° N of Moon Mercury in superior conjunction 1˚ 27' S of Sun

Venus 3.1° S of Moon Mercury 1.7° S of Moon Moon at perigee NEW MOON Venus 4.1˚ N. of Spica Mars stationary in RA Moon in descending node Jupiter 2.5° N of Moon Saturn 2.9° N of Moon Venus greatest helio lat. N.

20 20 21 21 21 23 23 24 24 28 30

20 13 10 13 23 00 18 16 22 15 03

05 26 02 31 41 48 32 30 40 03 28

Neptune 4.6˚ N of Moon Moon greatest lat. S 5˚ 16' Winter solstice Jupiter 0.1° S of Saturn FIRST QUARTER Venus 5.7˚ N. of Antares Mars 5.6˚ N of Moon Moon at apogee Uranus 3.4° N of Moon Moon in ascending node FULL MOON

Pluto in square with Sun NEW MOON Moon at perigee Mercury 6.8° S of Moon Saturn in square with Sun Moon in descending node Jupiter 2.0° N of Moon Saturn 2.6° N of Moon FIRST QUARTER

FIRST QUARTER Neptune 4.5˚ N of Moon Moon greatest lat. S 5˚ 14' Mars 4.9° N of Moon Moon at apogee Uranus 3.3° N of Moon Neptune stationary in RA FULL MOON Penumbral Lunar Eclipse

351

TABLE-I CONVERSION OF MEAN SOLAR INTO SIDEREAL TIME CORRECTION TO BE ADDED TO A MEAN TIME INTERVAL MINUTES SECONDS HOURS _______________ ________________________________ _________________________________ Mean Correction Mean Correction Mean Correction Mean Correction Mean Correction Time Time Time Time Time h m s m s m s s s s s 1 0 09.856 1 0.164 31 5.093 1 .003 31 .085 2 0 19.713 2 0.329 32 5.257 2 .005 32 .088 3 0 29.569 3 0.493 33 5.421 3 .008 33 .090 4 0 39.426 4 0.657 34 5.585 4 .011 34 .093 5 0 49.282 5 0.821 35 5.750 5 .014 35 .096 6 7 8 9 10

0 1 1 1 1

59.139 6 08.995 7 18.852 8 28.708 9 38.565 10

0.986 1.150 1.314 1.478 1.643

36 37 38 39 40

5.914 6.078 6.242 6.407 6.571

6 7 8 9 10

.016 .019 .022 .025 .027

36 37 38 39 40

.099 .101 .104 .107 .110

11 12 13 14 15

1 1 2 2 2

48.421 58.278 08.134 17.991 27.847

11 12 13 14 15

1.807 1.971 2.136 2.300 2.464

41 42 43 44 45

6.735 6.900 7.064 7.228 7.392

11 12 13 14 15

.030 .033 .036 .038 .041

41 42 43 44 45

.112 .115 .118 .120 .123

16 17 18 19 20

2 2 2 3 3

37.704 47.560 57.417 07.273 17.129

16 17 18 19 20

2.628 2.793 2.957 3.121 3.285

46 47 48 49 50

7.557 7.721 7.885 8.049 8.214

16 17 18 19 20

.044 .047 .049 .052 .055

46 47 48 49 50

.126 .129 .131 .134 .137

21 22 23 24

3 3 3 3

26.986 36.842 46.699 56.555

21 22 23 24 25

3.450 3.614 3.778 3.943 4.107

51 52 53 54 55

8.378 8.542 8.707 8.871 9.035

21 22 23 24 25

.057 .060 .063 .066 .068

51 52 53 54 55

.140 .142 .145 .148 .151

26 27 28 29 30

4.271 4.435 4.600 4.764 4.928

56 57 58 59 60

9.199 9.364 9.528 9.692 9.856

26 27 28 29 30

.071 .074 .077 .079 .082

56 57 58 59 60

.153 .156 .159 .162 .164

Local Apparent Sidereal time for any given local mean time = mean Sid. Time for 0h U.T. (Pages 13 to 16) — reduction for longitude of place + local mean time reckoned from midnight + correction for local mean time added (Table-I) + Equation of Equinoxes.

Local apparent Sidereal Time for any hour of Universal Time. = Sid. Time for 0h U.T. (Pages 13 to 16) + longitude of place (in time ) + Universal Time + correction for U.T. added (Table-I) + Equation of Equinoxes.

N.B. The longitude of place is to be taken in time and regarded positive for places East of Greenwich. The reduction of Sidereal Time for the longitude of place may be taken from the above table and with the same sign as that of longitude. The correction for the L.M.T. or U.T. added should also be taken from the above table. For details, see the examples given under the EXPLANATION.

352

TABLE-II CONVERSION OF SIDEREAL INTO MEAN SOLAR TIME CORRECTION TO BE SUBTRACTED FROM A SIDEREAL TIME INTERVAL MINUTES SECONDS HOURS _________________ __________________________________ _________________________________ Sidereal Correction Sidereal Correction Sidereal Correction Sidereal Correction Sidereal Correction Time Time Time Time Time h m s m s m s s s s s 1 0 09.830 1 0.164 31 5.079 1 .003 31 .085 2 0 19.659 2 0.328 32 5.242 2 .005 32 .087 3 0 29.489 3 0.491 33 5.406 3 .008 33 .090 4 0 39.318 4 0.655 34 5.570 4 .011 34 .093 5 0 49.148 5 0.819 35 5.734 5 .014 35 .096 6 7 8 9 10

0 1 1 1 1

58.977 08.807 18.636 28.466 38.296

6 7 8 9 10

0.983 1.147 1.311 1.474 1.638

36 37 38 39 40

5.898 6.062 6.225 6.389 6.553

6 7 8 9 10

.016 .019 .022` .025 .027

36 37 38 39 40

.098 .101 .104 .106 .109

11 12 13 14 15

1 1 2 2 2

48.125 57.955 07.784 17.614 27.443

11 12 13 14 15

1.802 1.966 2.130 2.294 2.457

41 42 43 44 45

6.717 6.881 7.045 7.208 7.372

11 12 13 14 15

.030 .033 .035 .038 .041

41 42 43 44 45

.112 .115 .117 .120 .123

16 17 18 19 20

2 2 2 3 3

37.273 47.103 56.932 06.762 16.591

16 17 18 19 20

2.621 2.785 2.949 3.113 3.277

46 47 48 49 50

7.536 7.700 7.864 8.027 8.191

16 17 18 19 20

.044 .046 .049 .052 .055

46 47 48 49 50

.126 .128 .131 .134 .137

21 22 23 24

3 3 3 3

26.421 36.250 46.080 55.909

21 22 23 24 25

3.440 3.604 3.768 3.932 4.096

51 52 53 54 55

8.355 8.519 8.683 8.847 9.010

21 22 23 24 25

.057 .060 .063 .066 .068

51 52 53 54 55

.139 .142 .145 .147 .150

26 27 28 29 30

4.259 4.423 4.587 4.751 4.915

56 57 58 59 60

9.174 9.338 9.502 9.666 9.830

26 27 28 29 30

.071 .074 .076 .079 .082

56 57 58 59 60

.153 .156 .158 .161 .164

Local Mean Time for any given local apparent Otherwise, L.M.T. for any given Sidereal Time Sidereal Time may be obtained as follows:= Time of preceding transit of First Point of Given Sidereal Time Aries (pages 13 to 16) — Sidereal Time for 0h U.T. (pages 13 to 16) + reduction for longitude of place + reduction for longitude of place + given local apparent Sidereal Time — Equation = Sidereal interval since 0h L.M.T. of Equinoxes This Sidereal interval corrected by the above — correction for Sidereal Time added (Table-II). table gives the required local mean time. or, Universal Time for any given Sidereal Time may be obtained as follows:Given Sidereal Time —longitude of place —Sidereal Time for 0h U.T. = Sidereal interval since 0h U.T. This interval converted into Mean Solar Time by the above table gives the Universal Time required. N.B. The reduction for longitude of place is of the same sign as that of the longitude, i.e. positive for places East of Greenwich and negative for West. See Example under EXPLANATION.

353

TABLE-III CONVERSION OF ARC TO TIME  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3

m 00 04 08 12 16 20 24 28 32 36 40 44 48 52 56 00 04 08 12 16 20 24 28 32 36 40 44 48 52 56 00 04 08 12 16 20 24 28 32 36 40 44 48 52 56 00 04 08 12

DEGREES  h m 49 3 16 50 3 20 51 3 24 52 3 28 53 3 32 54 3 36 55 3 40 56 3 44 57 3 48 58 3 52 59 3 56 60 4 00 61 4 04 62 4 08 63 4 12 64 4 16 65 4 20 66 4 24 67 4 28 68 4 32 69 4 36 70 4 40 71 4 44 72 4 48 73 4 52 74 4 56 75 5 00 76 5 04 77 5 08 78 5 12 79 5 16 80 5 20 81 5 24 82 5 28 83 5 32 84 5 36 85 5 40 86 5 44 87 5 48 88 5 52 89 5 56 90 6 00 91 6 04 92 6 08 93 6 12 94 6 16 95 6 20 96 6 24 97 6 28

 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

h m 6 32 6 36 6 40 6 44 6 48 6 52 6 56 7 00 7 04 7 08 7 12 7 16 7 20 7 24 7 28 7 32 7 36 7 40 7 44 7 48 7 52 7 56 8 00 8 04 8 08 8 12 8 16 8 20 8 24 8 28 8 32 8 36 8 40 8 44 8 48 8 52 8 56 9 00 9 04 9 08 9 12 9 16 9 20 9 24 9 28 9 32 9 36 9 40 9 44

MINUTES  m s 0 0 00 1 0 04 2 0 08 3 0 12 4 0 16 5 0 20 6 0 24 7 0 28 8 0 32 9 0 36 10 0 40 11 0 44 12 0 48 13 0 52 14 0 56 15 1 00 16 1 04 17 1 08 18 1 12 19 1 16 20 1 20 21 1 24 22 1 28 23 1 32 24 1 36 25 1 40 26 1 44 27 1 48 28 1 52 29 1 56 30 2 00 31 2 04 32 2 08 33 2 12 34 2 16 35 2 20 36 2 24 37 2 28 38 2 32 39 2 36 40 2 40 41 2 44 42 2 48 43 2 52 44 2 56 45 3 00 46 3 04 47 3 08 48 3 12

 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

s 0.000 0.067 0.133 0.200 0.267 0.333 0.400 0.467 0.533 0.600 0.667 0.733 0.800 0.867 0.933 1.000 1.067 1.133 1.200 1.267 1.333 1.400 1.467 1.533 1.600 1.667 1.733 1.800 1.867 1.933 2.000 2.067 2.133 2.200 2.267 2.333 2.400 2.467 2.533 2.600 2.667 2.733 2.800 2.867 2.933 3.000 3.067 3.133 3.200

SECONDS s  0.00 0.000 .01 .001 .02 .001 .03 .002 .04 .003 .05 .003 .06 .004 .07 .005 .08 .005 .09 .006 0.10 0.007 .11 .007 .12 .008 .13 .009 .14 .009 .15 .010 .16 .011 .17 .011 .18 .012 .19 .013 0.20 0.013 .21 .014 .22 .015 .23 .015 .24 .016 .25 .017 .26 .017 .27 .018 .28 .019 .29 .019 0.30 0.020 .31 .021 .32 .021 .33 .022 .34 .023 .35 .023 .36 .024 .37 .025 .38 .025 .39 .026 0.40 0.027 .41 .027 .42 .028 .43 .029 .44 .029 .45 .030 .46 .031 .47 .031 .48 .032

 0.50 .51 .52 .53 .54 .55 .56 .57 .58 .59 0.60 .61 .62 .63 .64 .65 .66 .67 .68 .69 0.70 .71 .72 .73 .74 .75 .76 .77 .78 .79 0.80 .81 .82 .83 .84 .85 .86 .87 .88 .89 0.90 .91 .92 .93 .94 .95 .96 97 .98

s 0.033 .034 .035 .035 .036 .037 .037 .038 .039 .039 0.040 .041 .041 .042 .043 .043 .044 .045 .045 .046 0.047 .047 .048 .049 .049 .050 .051 .051 .052 .053 0.053 .054 .055 .055 .056 .057 .057 .058 .059 .059 0.06 .061 .061 .062 .063 .063 .064 .065 .065

354

TABLE-III ---- contd. CONVERSION OF ARC TO TIME  147 148 149 150 151 152 153 154 155 156 157

h 9 9 9 10 10 10 10 10 10 10 10

m 48 52 56 00 04 08 12 16 20 24 28

DEGREES  h m 158 10 32 159 10 36 160 10 40 161 10 44 162 10 48 163 10 52 164 10 56 165 11 00 166 11 04 167 11 08 168 11 12

 169 170 171 172 173 174 175 176 177 178 179

MINUTES  m s 3 16 49 50 3 20 51 3 24 52 3 28 53 3 32 54 3 36 55 3 40 56 3 44 57 3 48 58 3 52 59 3 56

h m 11 16 11 20 11 24 11 28 11 32 11 36 11 40 11 44 11 48 11 52 11 56

 49 50 51 52 53 54 55 56 57 58 59

s 3.267 3.333 3.400 3.467 3.533 3.600 3.667 3.733 3.800 3.867 3.933

SECONDS s  0.49 0.033 0.50 0.033

 0.99 1.00

s 0.066 0.067

TABLE-IV CONVERSION OF TIME TO ARC 0h m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7

 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30

1h  15 15 15 15 16 16 16 16 17 17 17 17 18 18 18 18 19 19 19 19 20 20 20 20 21 21 21 21 22 22 22

 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30

2h  30 30 30 30 31 31 31 31 32 32 32 32 33 33 33 33 34 34 34 34 35 35 35 35 36 36 36 36 37 37 37

 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30

3h  45 45 45 45 46 46 46 46 47 47 47 47 48 48 48 48 49 49 49 49 50 50 50 50 51 51 51 51 52 52 52

 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30

4h  60 60 60 60 61 61 61 61 62 62 62 62 63 63 63 63 64 64 64 64 65 65 65 65 66 66 66 66 67 67 67

 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30

5h  75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82

 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30

SECONDS s 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7

 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30

s 0.00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.10 .11 .12 .13 .14 .15 .16 .17 .18 .19 .20 .21 .22 .23 .24 .25 .26 .27 .28 .29 .30

 0.00 0.15 0 30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 3.00 3.15 3.30 3.45 3.60 3.75 3.90 4.05 4.20 4.35 4.50

s 0.50 .51 .52 .53 .54 .55 .56 .57 .58 .59 0.60 .61 .62 .63 .64 .65 .66 .67 .68 .69 0.70 .71 .72 .73 .74 .75 .76 .77 .78 .79 0.80

 7.50 7.65 7.80 7.95 8.10 8.25 8.40 8.55 8.70 8.85 9.00 9.15 9.30 9.45 9.60 9.75 9.90 10.05 10.20 10.35 10.50 10.65 10.80 10.95 11.10 11.25 11.40 11.55 11.70 11.85 12.00

355

TABLE-IV ---- contd. CONVERSION OF TIME TO ARC 0h m 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12 13 13 13 13 14 14 14 14

 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45

1h  22 23 23 23 23 24 24 24 24 25 25 25 25 26 26 26 26 27 27 27 27 28 28 28 28 29 29 29 29

 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45

2h  37 38 38 38 38 39 39 39 39 40 40 40 40 41 41 41 41 42 42 42 42 43 43 43 43 44 44 44 44

 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45

3h  52 53 53 53 53 54 54 54 54 55 55 55 55 56 56 56 56 57 57 57 57 58 58 58 58 59 59 59 59

 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45

4h  67 68 68 68 68 69 69 69 69 70 70 70 70 71 71 71 71 72 72 72 72 73 73 73 73 74 74 74 74

 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45

5h   82 45 83 00 83 15 83 30 83 45 84 00 84 15 84 30 84 45 85 00 85 15 85 30 85 45 86 00 86 15 86 30 86 45 87 00 87 15 87 30 87 45 88 00 88 15 88 30 88 45 89 00 89 15 89 30 89 45

s 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12 13 13 13 13 14 14 14 14

 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45 00 15 30 45

SECONDS s  0.31 4.65 .32 4.80 .33 4.95 .34 5.10 .35 5.25 .36 5.40 .37 5.55 .38 5.70 .39 5.85 .40 6.00 .41 6.15 .42 6.30 .43 6.45 .44 6.60 .45 6.75 .46 6.90 .47 7.05 .48 7.20 .49 7.35 0.50 7.50

h 6 = 12 = 18 =

s 0.81 .82 .83 .84 .85 .86 .87 .88 .89 .90 .91 .92 .93 .94 .95 .96 .97 .98 0.99 1.00

 12.15 12.30 12.45 12.60 12.75 12.90 13.05 13.20 13.35 13.50 13.65 13.80 13.95 14.10 14.25 14.40 14.55 14.70 14.85 15.00

 90 180 270

TABLE - V CONVERSION OF HOURS, MINUTES AND SECONDS TO DECIMALS OF A DAY

m 0 1 2 3 4 5 6 7 8 9 10 11

0h

1h

2h

3h

d 0.000 000 .000 694 .001 389 .002 083 .002 778 .003 472 .004 167 .004 861 .005 556 .006 250 0.006 944 .007 639

d 0.041 667 .042 361 .043 056 .043 750 .044 444 .045 139 .045 833 .046 528 .047 222 .047 917 0.048 611 .049 306

d 0.083 333 .084 028 .084 722 .085 417 .086 111 .086 806 .087 500 .088 194 .088 889 .089 583 0.090 278 .090 972

d 0.125 000 .125 694 .126 389 .127 083 .127 778 .128 472 .129 167 .129 861 .130 556 .131 250 0.131 944 0.132 639

4h d 0.166 667 .167 361 .168 056 .168 750 .169 444 .170 139 .170 833 .171 528 .172 222 .172 917 0.173 611 .174 306

5h d 0.208 333 .209 028 .209 722 .210 417 .211 111 .211 806 .212 500 .213 194 .213 889 .214 583 0.215 278 .215 972

SECONDS s 0 1 2 3 4 5 6 7 8 9 10 11

d 0.000 000 .000 012 .000 023 .000 035 .000 046 .000 058 .000 069 .000 081 .000 093 .000 104 0.000 116 .000 127

356

TABLE - V ---- contd. CONVERSION OF HOURS, MINUTES AND SECONDS TO DECIMALS OF A DAY

m 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

0h

1h

2h

3h

d 0.008 333 .009 028 .009 722 .010 417 .011 111 .011 806 .012 500 .013 194 0.013 889 .014 583 .015 278 .015 972 .016 667 .017 361 .018 056 .018 750 .019 444 .020 139 0.020 833 .021 528 .022 222 .022 917 .023 611 .024 306 .025 000 .025 694 .026 389 .027 083 0.027 778 .028 472 .029 167 .029 861 .030 556 .031 250 .031 944 .032 639 .033 333 .034 028 0.034 722 .035 417 .036 111 .036 806 .037 500 .038 194 .038 889 .039 583 .040 278 0.040 972

d 0.050 000 .050 694 .051 389 .052 083 .052 778 .053 472 .054 167 .054 861 0.055 556 056 250 .056 944 .057 639 .058 333 .059 028 .059 722 .060 417 .061 111 .061 806 0.062 500 .063 194 .063 889 .064 583 .065 278 .065 972 .066 667 .067 361 .068 056 .068 750 0.069 444 .070 139 .070 833 .071 528 .072 222 .072 917 .073 611 .074 306 .075 000 .075 694 0.076 389 .077 083 .077 778 .078 472 .079 167 .079 861 .080 556 .081 250 .081 944 0.082 639

d 0.091 667 .092 361 .093 056 .093 750 .094 444 .095 139 .095 833 .096 528 0.097 222 .097 917 .098 611 .099 306 .100 000 .100 694 .101 389 .102 083 .102 778 .103 472 0.104 167 .104 861 .105 556 .106 250 .106 944 .107 639 .108 333 .109 028 .109 722 .110 417 0.111 111 .111 806 .112 500 .113 194 .113 889 .114 583 .115 278 .115 972 .116 667 .117 361 0.118 056 .118 750 .119 444 .120 139 .120 833 .121 528 .122 222 .122 917 .123 611 0.124 306

d 0.133 333 .134 028 .134 722 .135 417 .136 111 .136 806 .137 500 .138 194 0.138 889 .139 583 .140 278 .140 972 .141 667 .142 361 .143 056 .143 750 .144 444 .145 139 0.145 833 .146 528 .147 222 .147 917 .148 611 .149 306 .150 000 .150 694 .151 389 .152 083 0.152 778 .153 472 .154 167 .154 861 .155 556 .156 250 .156 944 .157 639 .158 333 .159 028 0.159 722 .160 417 .161 111 .161 806 .162 500 .163 194 .163 889 .164 583 .165 278 0.165 972

4h d 0.175 000 .175 694 .176 389 .177 083 .177 778 . 178 472 .179 167 .179 861 0.180 556 .181 250 .181 944 182 639 .183 333 .184 028 .184 722 .185 417 .186 111 .186 806 0.187 500 .188 194 .188 889 .189 583 .190 278 .190 972 .191 667 .192 361 .193 056 .193 750 0.194 444 .195 139 .195 833 .196 528 .197 222 .197 917 .198 611 .199 306 .200 000 .200 694 0.201 389 .202 083 .202 778 .203 472 .204 167 .204 861 .205 556 .206 250 .206 944 0.207 639

5h d 0.216 667 .217 361 .218 056 .218 750 .219 444 .220 139 .220 833 .221 528 0.222 222 .222 917 .223 611 .224 306 .225 000 .225 694 .226 389 .227 083 .227 778 .228 472 0.229 167 .229 861 .230 556 .231 250 .231 944 .232 639 .233 333 .234 028 .234 722 .235 417 0.236 111 .236 806 .237 500 .238 194 .238 889 .239 583 .240 278 .240 972 .241 667 .242 361 0.243 056 .243 750 .244 444 .245 139 .245 833 .246 528 .247 222 .247 917 .248 611 0.249 306

SECONDS s 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

d 0.000 139 .000 150 .000 162 .000 174 .000 185 .000 197 .000 208 .000 220 0.000 231 .000 243 .000 255 .000 266 .000 278 .000 289 .000 301 .000 312 .000 324 .000 336 0.000 347 .000 359 .000370 .000 382 .000 394 .000 405 .000 417 .000 428 .000 440 .000 451 0.000 463 .000 475 .000 486 .000 498 .000 509 .000 521 .000 532 .000 544 .000 556 .000 567 0.000 579 .000 590 .000 602 .000 613 .000 625 .000 637 .000 648 .000 660 .000 671 0.000 683

357

TABLE - V ---- contd. CONVERSION OF HOURS, MINUTES AND SECONDS TO DECIMALS OF A DAY

m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

6h

7h

8h

9h

d 0.250 000 .250 694 .251 389 .252 083 .252 778 .253 472 .254 167 .254 861 .255 556 .256 250 0.256 944 .257 639 .258 333 .259 028 .259 722 .260 417 .261 111 .261 806 .262 500 .263 194 0.263 889 .264 583 .265 278 .265 972 .266 667 .267 361 .268 056 .268 750 .269 444 .270 139 0.270 833 .271 528 .272 222 .272 917 .273 611 .274 306 .275 000 .275 694 276 389 .277 083 0.277 778 .278 472 279 167 .279 861 .280 556 .281 250 0.281 944

d 0.291 667 .292 361 .293 056 .293 750 .294 444 .295 139 .295 833 .296 528 .297 222 .297 917 0.298 611 .299 306 .300 000 .300 694 .301 389 .302 083 .302 778 .303 472 .304 167 .304 861 0.305 556 .306 250 .306 944 .307 639 .308 383 .309 028 .309 722 .310 417 .311 111 .311 806 0.312 500 .313 194 .313 889 .314 583 .315 278 .315 972 .316 667 .317 361 .318 056 .318 750 0.319 444 .320 139 .320 833 .321 528 .322 222 .322 917 0.323 611

d 0.333 333 .334 028 .334 722 .335 417 .336 111 .336 806 .337 500 338 194 .338 889 .339 583 0.340 278 .340 972 .341 667 .342 361 .343 056 .343 750 .344 444 .345 139 .345 833 .346 528 0.347 222 .347 917 .348 611 .349 306 .350 000 .350 694 .351 389 .352 083 .352 778 .353 472 0.354 167 .354 861 .355 556 .356 250 .356 944 .357 639 .358 333 .359 028 .359 722 .360 417 0.361 111 .361 806 .362 500 .363 194 .363 889 .364 583 0.365 278

d 0.375 000 .375 694 .376 389 .377 083 .377 778 .378 472 .379 167 .379 861 .380 556 .381 250 0.381 944 .382 639 .383 333 384 028 .384 722 .385 417 .386 111 .386 806 .387 500 .388 194 0.388 889 .389 583 .390 278 .390 972 .391 667 .392 361 .393 056 .393 750 .394 444 .395 139 0.395 833 .396 528 .397 222 .397 917 .398 611 .399 306 .400 000 .400 694 .401 389 .402 083 0.402 778 .403 472 .404 167 .404 861 .405 556 .406 250 0.406 944

10 h d 0.416 667 . 417 361 .418 056 .418 750 .419 444 .420 139 .420 833 .421 528 .422 222 .422 917 0.423 611 .424 306 .425 000 .425 694 .426 389 .427 083 .427 778 .428 472 .429 167 .429 861 0.430 556 .431 250 .431 944 .432 639 .433 333 .434 028 .434 722 .435 417 .436 111 .436 806 0.437 500 .438 194 .438 889 .439 583 .440 278 .440 972 .441 667 .442 361 .443 056 .443 750 0.444 444 .445 139 .445 833 .446 528 .447 222 .447 917 0.448 611

11 h d 0.458 333 .459 028 .459 722 .460 417 .461 111 .461 806 .462 500 . 463 194 . 463 889 .464 583 0.465 278 .465 972 .466 667 .467 361 .468 056 .468 750 .469 444 .470 139 .470 833 .471 528 0.472 222 .472 917 .473 661 .474 306 .475 000 .475 694 .476 389 .477 083 .477 778 .478 472 0.479 167 .479 861 .480 556 .481 250 .481 944 .482 639 .483 333 .484 028 .484 722 .485 417 0.486 111 .486 806 .487 500 .488 194 .488 889 .489 583 0.490 278

SECONDS s 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

d 0.000 000 .000 012 .000 023 .000 035 .000 046 .000 058 .000 069 .000 081 .000 093 .000 104 0.000 116 .000 127 .000 139 .000 150 .000 162 .000 174 .000 185 .000 197 .000 208 .000 220 0.000 231 .000 243 .000 255 .000 266 .000 278 .000289 .000 301 .000 312 .000 324 .000 336 0.000 347 .000 359 .000 370 .000 382 .000 394 .000 405 .000 417 .000 428 .000 440 .000 451 0.000 463 .000 475 .000 486 .000 498 .000 509 .000 521 0.000 532

358

TABLE - V ---- contd. CONVERSION OF HOURS, MINUTES AND SECONDS TO DECIMALS OF A DAY

m 47 48 49 50 51 52 53 54 55 56 57 58 59

6h

7h

8h

9h

d 0.282 639 .283 333 .284 028 0.284 722 .285 417 .286 111 .286 806 .287 500 .288 194 .288 889 .289 583 .290 278 0.290 972

d 0.324 306 .325 000 .325 694 0.326 389 .327 083 .327 778 .328 472 .329 167 .329 861 .330 556 .331 250 .331 944 0.332 639

d 0.365 972 .366 667 .367 361 0.368 056 .368 750 .369 444 . 370 139 .370 833 .371 528 .372 222 .372 917 .373 611 0.374 306

d 0.407 639 .408 333 .409 028 0.409 722 .410 417 .411 111 .411 806 .412 500 .413 194 .413 889 .414 583 .415 278 0.415 972

10 h d 0.449 306 .450 000 .450 694 0.451 389 .452 083 .452 778 .453 472 .454 167 .454 861 .455 556 .456 250 .456 944 0.457 639

11 h d 0.490 972 .491 667 .492 361 0.493 056 .493 750 .494 444 .495 139 .495 833 .496 528 .497 222 .497 917 .498 611 0.499 306

SECONDS s 47 48 49 50 51 52 53 54 55 56 57 58 59

d 0.000 544 .000 556 .000 567 0.000 579 .000 590 .000 602 .000 613 .000 625 .000 637 .000 648 .000 660 .000 671 0.000 683

TABLE - VI CONVERSION OF MINUTES AND SECONDS TO DECIMALS OF A DEGREE 0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

 0.00000 0028 0056 0083 0111 0139 0167 0194 0222 0250 0.00278 0306 0333 0361 0389 0417 0444 0472 0500 0528 0.00556 0583 0611 0639 0667 0.00694

1  0.01667 1694 1722 1750 1778 1806 1833 1861 1889 1917 0.01944 1972 2000 2028 2056 2083 2111 2139 2167 2194 0.02222 2250 2278 2306 2333 0.02361

2  0.03333 3361 3389 3417 3444 3472 3500 3528 3556 3583 0.03611 3639 3667 3694 3722 3750 3778 3806 3833 3861 0.03889 3917 3944 3972 4000 0.04028

3  0.05000 5028 5056 5083 5111 5139 5167 5194 5222 5250 0.05278 5306 5333 5361 5389 5417 5444 5472 5500 5528 0.05556 5583 5611 5639 5667 0.05694

4  0.06667 6722 6750 6778 6806 6833 6861 6889 6917 0.06944 6972 7000 7028 7056 7083 7111 7139 7167 7194 0.07222 7250 7278 7306 7333 0.07361

5  0.08333 8361 8389 8417 8444 8472 8500 8528 8556 8583 0.08611 8639 8667 8694 8722 8750 8778 8806 8833 8861 0.08889 8917 8944 8972 9000 0.09028

 0 6 12 18 24 30 36 42 48 54

 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

359

TABLE - VI ---- contd. CONVERSION OF MINUTES AND SECONDS TO DECIMALS OF A DEGREE 0  26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

1

 0.00722 0750 0778 0806 0.00833 0861 0889 0917 0944 0972 1000 1028 1056 1083 0.01111 1139 1167 1194 1222 1250 1278 1306 1333 1361 0.01389 1417 1444 1472 1500 1528 1556 1583 1611 0.01639

2

 0.02389 2417 2444 2472 0.02500 2528 2556 2583 2611 2639 2667 2694 2722 2750 0.02778 2806 2833 2861 2889 2917 2944 2972 3000 3028 0.03056 3083 3111 3139 3167 3194 3222 3250 3278 0.03306

3

 0.04056 4083 4111 4139 0.04167 4194 4222 4250 4278 4306 4333 4361 4389 4417 0.04444 4472 4500 4528 4556 4583 4611 4639 4667 4694 0.04722 4750 4778 4806 4833 4861 4889 4917 4944 0.04972

4

 0.05722 5750 5778 5806 0.05833 5861 5889 5917 5944 5972 6000 6028 6056 6083 0.06111 6139 6167 6194 6222 6250 6278 6306 6333 6361 0.06389 6417 6444 6472 6500 6528 6556 6583 6611 0.06639

5

 0.07389 7417 7444 7472 0.07500 7528 7556 7583 7611 7639 7667 7694 7722 7750 0.07778 7806 7833 7861 7889 7917 7944 7972 8000 8028 0.08056 8083 8111 8139 8167 8194 8222 8250 8278 0.08306

 0.09056 9083 9111 9139 0.09167 9194 9222 9250 9278 9306 9333 9361 9389 9417 0.09444 9472 9500 9528 9556 9583 9611 9639 9667 9694 0.09722 9750 9778 9806 9833 9861 9889 9917 9944 0.09972

In units of the fifth decimal of a Degree.   0.00 0 .01 1 .05 2 .09 3 .12 4 .16 5 .19 6 .23 7 .26 8 .30 9 .34 10 .37 11 .41 12 .45 13 .48 14 .52 15 .55 16 .59 17 .62 18 .66 19 .70 20 .73 21 .77 22 .81 23 .84 24 .88 25 .91 26 .95 27 0.98 28 1.00

In critical cases ascend

TABLE - VII INTERPOLATION COEFFICIENTS n

B

0.00 .01 .02 .03 .04 0.05

0.00000 .00248 .00490 .00728 .00960 0.01188

E0  0.00000 .00328 .00647 .00955 .01254 0.01544

E1  0.00000 .00167 .00333 .00500 .00666 0.00831

n 0.05 .06 .07 .08 .09 0.10

B 0.01188 0.01410 .01628 .01840 .02048 0.02250

E0  0.01544 0.01824 .02094 .02355 .02607 0.02850

E1  0.00831 0.00996 .01161 .01325 .01488 0.01650

360

TABLE - VII ---- contd. INTERPOLATION COEFFICIENTS n

B

0.10 .11 .12 .13 .14 .15 .16 .17 .18 .19 0.20 .21 .22 .23 .24 .25 .26 .27 .28 .29 0.30 .31 .32 .33 .34 .35 .36 .37 .38 .39 0.40 .41 .42 .43 .44 .45 .46 .47 .48 .49 0.50 .51 .52 .53 .54 0.55

0.02250 .02448 .02640 .02828 .03010 .03188 .03360 .03528 .03690 .03848 0.04000 .04148 .04290 .04428 .04560 .04688 .04810 .04928 .05040 .05148 0.05250 .05348 .05440 .05528 .05610 .05688 .05760 .05828 .05890 .05948 0.06000 .06048 .06090 .06128 .06160 .06188 .06210 .06228 .06240 .06248 0.06250 .06248 .06240 .06228 .06210 0.06188

E0 0.02850 .03084 .03309 .03525 .03732 .03931 .04122 .04304 .04477 .04643 0.04800 .04949 .05091 .05224 .05350 .05469 .05580 .05683 .05779 .05868 0.05950 .06025 .06093 .06154 .06208 .06256 .06298 .06333 .06361 .06384 0.06400 .06410 .06415 .06413 .06406 .06394 .06376 .06352 .06323 .06289 0.06250 .06206 .06157 .06103 .06044 0.05981

E1 0.01650 .01811 .01971 .02130 .02288 .02444 .02598 .02751 .02903 .03052 0.03200 .03346 .03489 .03631 .03770 .03906 .04040 .04172 .04301 .04427 0.04550 .04670 .04787 .04901 .05012 .05119 .05222 .05322 .05419 .05511 0.05600 .05685 .05765 .05842 .05914 .05981 .06044 .06103 .06157 .06206 0.06250 .06289 .06323 .06352 .06376 0.06394

n 0.55 .56 .57 .58 .59 0.60 .61 .62 .63 .64 .65 .66 .67 .68 .69 0.70 .71 .72 .73 .74 .75 .76 .77 .78 .79 0.80 .81 .82 .83 .84 .85 .86 .87 .88 .89 0.90 .91 .92 .93 .94 .95 .96 .97 .98 0.99 1.00

B 0.06188 0.06160 .06128 .06090 .06048 0.06000 .05948 .05890 .05828 .05760 .05688 .05610 .05528 .05440 .05348 0.05250 .05148 .05040 .04928 .04810 .04688 .04560 .04428 .04290 .04148 0.04000 . 03848 .03690 .03528 .03360 .03188 .03010 .02828 .02640 .02448 0.02250 .02048 .01840 .01628 .01410 .01188 .00960 .00728 .00490 .00248 0.00000

E0 0.05981 0.05914 .05842 .05765 .05685 0.05600 .05511 .05419 .05322 .05222 .05119 .05012 .04901 .04787 .04670 0.04550 .04427 .04301 .04172 .04040 .03906 .03770 .03631 .03489 .03346 0.03200 .03052 .02903 .02751 .02598 .02444 .02288 .02130 .01971 .01811 0.01650 .01488 .01325 .01161 .00996 .00831 .00666 .00500 .00333 .00167 0.00000

E1 0.06394 0.06406 .06413 .06415 .06410 0.06400 .06384 .06361 .06333 .06298 .06256 .06208 .06154 .06093 .06025 0.05950 .05868 .05779 .05683 .05580 .05469 .05350 .05224 .05091 .04949 0.04800 .04643 .04477 .04304 .04122 .03931 .03732 .03525 .03309 .03084 0.02850 .02607 .02355 .02094 .01824 .01544 .01254 .00955 .00647 .00328 0.00000

N.B. – The coefficients are all negative. For details about Bessel’s and Everett’s interpolation formula, please see Explanation

361

TABLE - VIII EVERETT COEFFICIENTS OF THE SECOND DIFFERENCES (The coefficients are all negative) n 0.000 .001 .002 .003 .004 .005 .006 .007 .008 .009 .010 .011 .012 .013 .014 .015 .016 .017 .018 .019 .020 .021 .022 .023 .024 .025 .026 .027 .028 .029 .030 .031 .032 .033 .034 .035 .036 .037 .038 .039 .040 .041 .042 .043 .044 .045 .046 .047 .048 .049 0.050

E0 

E1 

0.0002 0.0001 .0005 .0002 .0008 .0004 .0012 .0006 .0015 .0007 .0018 .0009 .0021 .0011 .0025 .0012 .0028 .0014 .0031 .0016 .0034 .0017 .0038 .0019 .0041 .0021 .0044 .0022 .0047 .0024 .0050 .0026 .0054 .0027 .0057 .0029 .0060 .0031 .0063 .0032 .0066 .0034 .0069 .0036 .0072 .0037 .0076 .0039 .0079 .0041 .0082 .0042 .0085 .0044 .0088 .0046 .0091 .0047 .0094 .0049 .0097 .0051 .0100 .0052 .0103 .0054 .0106 .0056 .0109 .0057 .0112 .0059 .0115 .0061 .0118 .0062 .0121 .0064 .0124 .0066 .0127 .0067 .0130 .0069 .0133 .0071 .0136 .0072 .0139 .0074 .0141 .0076 .0144 .0077 .0147 .0079 .0150 .0081 0.0153 0.0082 E1 

E0 

1.000 0.999 .998 .997 .996 .995 .994 .993 .992 .991 .990 .989 .988 .987 .986 .985 .984 .983 .982 .981 .980 .979 .978 .977 .976 .975 .974 .973 .972 .971 .970 .969 .968 .967 .966 .965 .964 .963 .962 .961 .960 .959 .958 .957 .956 .955 .954 .953 .952 .951 0.950 n

n E0  0.050 0.0156 .051 .0159 .052 .0161 .053 .0164 .054 .0167 .055 .0170 .056 .0173 .057 .0175 .058 .0178 .059 .0181 .060 .0184 .061 .0186 .062 .0189 .063 .0192 .064 .0195 .065 .0197 .066 .0200 .067 .0203 .068 .0205 .069 .0208 .070 .0211 .071 .0213 .072 .0216 .073 .0219 .074 .0221 .075 .0224 .076 .0226 .077 .0229 .078 .0232 .079 .0234 .080 .0237 .081 .0239 .082 .0242 .083 .0244 .084 .0247 .085 .0249 .086 .0252 .087 .0255 .088 .0257 .089 .0259 .090 .0262 .091 .0264 .092 .0267 .093 .0269 .094 .0272 .095 .0274 .096 .0277 .097 .0279 .098 .0281 .099 0.0284 0.100 E1 

E1 0.0084 .0086 .0087 .0089 .0091 .0092 .0094 .0096 .0097 .0099 .0100 .0102 .0104 .0105 .0107 .0109 .0110 .0112 .0114 .0115 .0117 .0119 .0120 .0122 .0123 .0125 .0127 .0128 .0130 .0132 .0133 .0135 .0137 .0138 .0140 .0141 .0143 .0145 .0146 .0148 .0150 .0151 .0153 .0154 .0156 .0158 .0159 .0161 .0163 0.0164 E0

n E0  E1  0.900 0.950 0.100 0.0286 0.0166 .949 .101 .899 .0289 .0167 .948 .102 .898 .0291 .0169 .947 .103 .897 .0293 .0171 .946 .104 .896 .0296 .0172 .945 .105 .895 .0298 .0174 .944 .106 .894 .0300 .0175 .943 .107 .893 .0303 .0177 .942 .108 .892 .0305 .0179 .941 .109 .891 .0307 .0180 .940 .110 .890 .0310 .0182 .939 .111 .889 .0312 .0184 .938 .112 .888 .0314 .0185 .937 .113 .887 .0316 .0187 .936 .114 .886 .0319 .0188 .935 .115 .885 .0321 .0190 .934 .116 .884 .0323 .0192 .933 .117 .883 .0325 .0193 .932 .118 .882 .0328 .0195 .931 .119 .881 .0330 .0196 .930 .120 .880 .0332 .0198 .929 .121 .879 .0334 .0200 .928 .122 .878 .0336 .0201 .927 .123 .877 .0339 .0203 .926 .124 .876 .0341 .0204 .925 .125 .875 .0343 .0206 .924 .126 .874 .0345 .0207 .923 .127 .873 .0347 .0209 .922 .128 .872 .0349 .0211 .921 .129 .871 .0351 .0212 .920 .130 .870 .0354 .0214 .919 .131 .869 .0356 .0215 .918 .132 .868 .0358 .0217 .917 .133 .867 .0360 .0219 .916 .134 .866 .0362 .0220 .915 .135 .0364 .0222 .865 .914 .136 .0366 .0223 .864 .913 .137 .0368 .0225 .863 .912 .138 .0370 .0226 .862 .911 .139 .0372 .0228 .861 .910 .140 .0374 .0230 .860 .909 .141 .0376 .0231 .859 .908 .142 .0378 .0233 .858 .907 .143 .0380 .0234 .857 .906 .144 .0382 .0236 .856 .905 .145 .0384 .0237 .855 . 904 .146 .0386 .0239 .854 .903 .147 .0388 .0240 .853 .902 .148 .0390 .0242 .852 .901 .149 0.0392 0.0244 .851 0.900 0.150 0.850 n n E1  E0 

Formula : f n = f0 + n Δ1/2' + E0 Δ0 + E1 Δ1

362

TABLE - VIII ---- contd. EVERETT COEFFICIENTS OF THE SECOND DIFFERENCES (The coefficients are all negative) n E0  E1  0.850 0.150 0.0394 0.0245 .151 .849 .0396 .0247 .152 .848 .0398 .0248 .153 .847 .0400 .0250 .154 .846 .0402 .0251 .155 .845 .0404 .0253 .156 .844 .0406 .0254 .157 .843 .0407 .0256 .158 .842 .0409 .0258 .159 .841 .0411 .0259 .160 .840 .0413 .0261 .161 .839 .0415 .0262 .162 .838 .0417 .0264 .163 .837 .0419 .0265 .164 .836 .0420 .0267 .165 .835 .0422 .0268 .166 .834 .0424 .0270 .167 .833 .0426 .0271 .168 .832 .0428 .0273 .169 .831 .0429 .0274 .170 .830 .0431 .0276 .171 .829 .0433 .0277 .172 .828 .0435 .0279 .173 .827 .0437 .0280 .174 .826 .0438 .0282 .175 .825 .0440 .0283 .176 .824 .0442 .0285 .177 .823 .0443 .0287 .178 .822 .0445 .0288 .179 .821 .0447 .0290 .180 .820 .0449 .0291 .181 .819 .0450 .0293 .182 .818 .0452 .0294 .183 .817 .0454 .0296 .184 .816 .0455 .0297 .185 .0457 .0299 .815 .186 .0459 .0300 .814 .187 .0460 .0302 .813 .188 .0462 .0303 .812 .189 .0463 .0304 .811 .190 .0465 .0306 .810 .191 .0467 .0307 .809 .192 .0468 .0309 .808 .193 .0470 .0310 .807 .194 .0471 .0312 .806 .195 .0473 .0313 .805 .196 .0475 .0315 .804 .197 .0476 .0316 .803 .198 .0478 .0318 .802 .199 0.0479 0.0319 .801 0.200 0.800 n E1  E0 

n 0.200 .202 .204 .206 .208 .210 .212 .214 .216 .218 .220 .222 .224 .226 .228 .230 .232 .234 .236 .238 .240 .242 .244 .246 .248 .250 .252 .254 .256 .258 .260 .262 .264 .266 .268 .270 .272 .274 .276 .278 .280 .282 .284 .286 .288 .290 .292 .294 .296 .298 0.300

E0 

E1

n 0.800 0.300 0.0482 0.0321 .798 .304 .0324 .0485 .796 .308 .0327 .0488 .794 .312 .0330 .0491 .792 .316 .0333 .0493 .790 .320 .0336 .0496 .788 .324 .0339 .0499 .786 .328 .0342 .0502 .784 .332 .0345 .0505 .782 .336 .0347 .0508 .780 .340 .0350 .0510 .778 .344 .0353 .0513 .776 .348 .0356 .0516 .774 .352 .0359 .0519 .772 .356 .0362 .0521 .770 .360 .0364 .0524 .768 .364 .0367 .0526 .766 .368 .0370 .0529 .764 .372 .0373 .0531 .762 .376 .0376 .0534 .760 .380 .0378 .0536 .758 .384 .0381 .0539 .756 .388 .0384 .0541 .754 .392 .0387 .0543 .752 .396 .0389 .0546 .750 .400 .0392 .0548 .748 .404 .0395 .0550 .746 .408 .0397 .0553 .744 .412 .0400 .0555 .742 .416 .0403 .0557 .740 .420 .0405 .0559 .738 .424 .0408 .0561 .736 .428 .0411 .0563 .734 .432 .0413 .0565 .732 .436 .0416 .0567 .730 .440 .0418 .0569 .728 .444 .0421 .0571 .726 .448 .0424 .0573 .724 .452 .0426 .0575 .722 .456 .0429 .0577 .720 .460 .0431 .0579 .718 .464 .0434 .0581 .716 .468 .0436 .0582 .714 .472 .0439 .0584 .712 .476 .0441 .0586 .710 .480 .0444 .0588 .708 .484 .0446 .0589 .706 .488 .0449 .0591 .704 .492 .0451 .0593 0.0594 0.0454 .702 .496 0.700 0.500 n E1  E0

E0 

E1 

0.0597 .0600 .0602 .0605 .0608 .0611 .0613 .0615 .0618 .0620 .0622 .0624 .0626 .0627 .0629 .0631 .0632 .0633 .0634 .0636 .0637 .0638 .0638 .0639 .0640 .0640 .0641 .0641 .0641 .0641 .0641 .0641 .0641 .0641 .0641 .0640 .0640 .0639 .0639 .0638 .0637 .0636 .0635 .0634 .0633 .0632 .0630 .0629 .0627 0.0626

0.0457 .0462 .0467 .0472 .0476 .0481 .0486 .0490 .0495 .0499 .0503 .0508 .0512 .0516 .0520 .0524 .0528 .0532 .0536 .0540 .0544 .0547 .0551 .0555 .0558 .0562 .0565 .0568 .0572 .0575 .0578 .0581 .0584 .0587 .0590 .0593 .0595 .0598 .0601 .0603 .0606 .0608 .0610 .0613 .0615 .0617 .0619 .0621 .0622 0.0624

E1 

E0 

N. B. -- The table is to be used like a critical table without interpolation

0.700 .696 .692 .688 .684 .680 .676 .672 .668 .664 .660 .656 .652 .648 .644 .640 .636 .632 .628 .624 .620 .616 .612 .608 .604 .600 .596 .592 .588 .584 .580 .576 .572 .568 .564 .560 .556 .552 .548 .544 .540 .536 .532 .528 .524 .520 .516 .512 .508 .504 0.500 n

363

TABLE - IX JULIAN DAY NUMBER DAYS ELAPSED AT GREENWICH NOON OF JANUARY 0 Yr. A.D. 100 200 300 400 500 600 700 800 900 1000 175 7582 179 4107 183 0632 186 7157 190 3682 194 0207 197 6732 201 3257 204 9782 208 6307 0 20 176 4887 180 1412 183 7937 187 4462 191 0987 194 7512 198 4037 202 0562 205 7087 209 3612 40 177 2192 180 8717 184 5242 188 1767 191 8292 195 4817 199 1342 202 7867 206 4392 210 0917 60 177 9497 181 6022 185 2547 188 9072 192 5597 196 2122 199 8647 203 5172 207 1697 210 8222 80 178 6802 182 3327 185 9852 189 6377 193 2902 196 9427 200 5952 204 2477 207 9002 211 5527 Yr. A.D. 0 20 40 60 80 100

1100

1200

1300

1400

1500

1600

1700

1800 1900 2000 * * * 212 2832 215 9357 219 5882 223 2407 226 8932 230 5447 234 1971 237 8495 241 5020 245 1544 213 0137 216 6662 220 3187 223 9712 227 6237 231 2752 234 9276 238 5806 242 2324 245 8849 213 7442 217 3967 221 0492 224 7017 228 3542 232 0057 235 6581 239 3105 242 9629 246 6154 214 4747 218 1272 221 7797 225 4322 229 0847 232 7362 236 3886 240 0410 243 6934 247 3459 215 2052 218 8577 222 5102 226 1627 229 8152 233 4667 237 1191 240 7715 244 4239 248 0764 † 215 9357 219 5882 223 2407 226 8932 230 5447 234 1971 237 8495 241 5020 245 1544 248 8069

NUMBER OF DAYS TO BE ADDED TO REDUCE TO THE BEGINNING OF EACH MONTH Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Jan. 0 Feb. 0 Mar. 0 Apr. 0 May 0 Jun. 0 July 0 Aug. 0 Sept. 0 Oct. 0 Nov. 0 Dec. 0 * * 0 31 60 91 121 152 182 213 244 274 305 335 366 397 425 456 486 517 547 578 609 639 670 700 731 762 790 821 851 882 912 943 974 1004 1035 1065 1096 1127 1155 1186 1216 1247 1277 1308 1339 1369 1400 1430 1461 1492 1521 1552 1582 1613 1643 1674 1705 1735 1766 1796 1827 1858 1886 1917 1947 1978 2008 2039 2070 2100 2131 2161 2192 2223 2251 2282 2312 2343 2373 2404 2435 2465 2496 2526 2557 2588 2616 2647 2677 2708 2738 2769 2800 2830 2861 2891 2922 2953 2982 3013 3043 3074 3104 3135 3166 3196 3227 3257 3288 3319 3347 3378 3408 3439 3469 3500 3531 3561 3592 3622 3353 3684 3712 3743 3773 3804 3834 3865 3896 3926 3957 3987 4018 4049 4077 4108 4138 4169 4199 4230 4261 4291 4322 4352 4383 4414 4443 4474 4504 4535 4565 4596 4627 4657 4688 4718 4749 4780 4808 4839 4869 4900 4930 4961 4992 5022 5053 5083 5114 5145 5173 5204 5234 5265 5295 5326 5357 5387 5418 5448 5479 5510 5538 5569 5599 5630 5660 5691 5722 5752 5783 5813 5844 5875 5904 5935 5965 5996 6026 6057 6088 6118 6149 6179 6210 6241 6269 6300 6330 6361 6391 6422 6453 6483 6514 6544 6575 6606 6634 6665 6695 6726 6756 6787 6818 6848 6879 6909 6940 6971 6999 7030 7060 7091 7121 7152 7183 7213 7244 7274 † From 1582 October 15 to 1599 December 31 inclusive, Gregorian calendar, the numbers given by the above tables must be diminished by 10. * The numbers given for the years 1700, 1800 and 1900 which are not leap years, are for January - 1 and consequently the numbers 0 and 31 for January 0 and February 0 of these years must be increased by 1 and read as 1 and 32 respectively. N.B. To find the Julian Day Number for a B.C. date, first express the year astronomically, i.e. diminish it by 1 and put a negative sign before it. Then make the number positive by adding the smallest multiple of 1000. The Julian Day Number for the date thus obtained diminished by 365250 for each multiple of 1000 added will give the required Julian Day Number for the B.C. date in question. The Julian Day is completed at noon. In order to obtain the Julian Day Number for 0h U.T., diminish the figure obtained from the above tables by 0.5. The tables give the Day Numbers upto 1582, Oct. 4 for the Julian calendar and from 1582, Oct. 15 onward for the Gregorian calendar.

364

TABLE – X ATMOSPHERIC REFRACTION MEAN REFRACTION FOR TEMPERATURE 25 C AND PRESSURE 1000 mb Apparent Altitude   -1 00 0 00 +0 10 20 30 0 40 0 50 1 00 10 20 30 1 40 1 50 2 00 10 20 30 2 40 2 50 3 00 10 20 30 3 40 3 50 4 00 10 20 30 4 40 4 50 5 00 10 20 30 5 40 5 50 6 00 6 10

Mean Refraction   46 17.5 30 59.6 29 09.3 27 28.9 25 57.8 24 34.6 23 18.3 22 07.9 21 02.6 20 02.4 19 07.0 18 15.6 17 28.2 16 44.0 16 02.6 15 24.0 14 48.0 14 14.4 13 42.9 13 13.5 12 45.8 12 19.6 11 55.0 11 31.9 11 10.0 10 49.5 10 30.1 10 11.7 9 54.2 9 37.5 9 21.6 9 06.5 8 52.1 8 38.6 8 25.5 8 13.0 8 01.2 7 49.8 7 39.0

Apparent Altitude   6 10 20 30 40 6 50 7 00 7 10 20 30 40 7 50 8 00 8 10 20 30 40 8 50 9 00 9 10 20 30 40 9 50 10 00 10 30 11 00 11 30 12 00 12 30 13 00 13 30 14 00 14 30 15 00 15 30 16 00 16 30 17 00 17 30

Mean Refraction   7 39.0 7 28.5 7 18.5 7 08.9 6 59.7 6 50.8 6 42.3 6 34.1 6 26.3 6 18.7 6 11.4 6 04.4 5 57.6 5 51.2 5 44.7 5 38.6 5 32.6 5 26.8 5 21.3 5 15.9 5 10.6 5 05.5 5 00.6 4 55.9 4 42.4 4 30.0 4 18.7 4 08.1 3 58.4 3 49.3 3 40.8 3 32.9 3 25.6 3 18.6 3 12.1 3 06.0 3 00.2 2 54.8 2 49.6

Apparent Altitude   17 30 18 00 18 30 19 00 19 30 20 00 21 00 22 00 23 00 24 00 25 00 26 00 27 00 28 00 29 00 30 00 31 00 32 00 33 00 34 00 35 00 36 00 37 00 38 00 39 00 40 00 41 00 42 00 43 00 44 00 45 00 46 00 47 00 48 00 49 00 50 00 51 00 52 00 53 00

Mean Refraction   2 49.6 2 44.7 2 40.0 2 35.6 2 31.4 2 27.3 2 19.8 2 12.9 2 06.6 2 00.8 1 55.4 1 50.4 1 45.7 1 41.3 1 37.2 1 33.4 1 29.8 1 26.3 1 23.1 1 20.0 1 17.1 1 14.3 1 11.7 1 09.1 1 06.8 1 04.4 1 02.2 1 00.0 0 57.9 0 56.0 0 54.1 0 52.2 0 50.4 0 48.7 0 47.0 0 45.4 0 43.8 0 42.2 0 40.8

Apparent Altitude  53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

Mean Refraction   0 40.8 39.3 37.9 36.5 35.1 33.8 0 32.6 31.2 30.0 28.8 27.6 26.4 0 25.2 24.1 23.0 21.9 20.8 19.7 0 18.6 17.6 16.5 15.5 14.5 13.5 0 12.5 11.5 10.5 09.5 08.6 07.6 0 06.6 05.7 04.7 03.8 02.8 01.9 0 00.9 0 00.0

Rule: True altitude of a celestial object = Its apparent or observed altitude - refraction. N.B.-The figures of mean refraction given in the above table are for temperature 25 C and pressure 1000 mb. (750.06 mm. Or 29.530 inches of mercury barometer). For other values of temperature and pressure, corrections form the tables on the following two pages are to be taken and applied to the mean refraction.

365

TABLE - Xa ATMOSPHERIC REFRACTION CORRECTION OF MEAN REFRACTION FOR DIFFERENT VALUES OF TEMPERATURE Apparent Altitude   - 1 00 0 00 + 0 30 1 00 1 30 2 00 2 30 3 00 3 30 4 00 4 30 5 00 6 00 7 00 8 00 9 00 10 00 11 00 12 00 13 00 14 00 15 00 16 00 17 00 18 00 19 00 20 00 25 00 30 00 35 00 40 00 45 00 50 00 55 00 60 00 65 00 70 00 75 00 80 00 85 00 90 00

- 10 C (14 F)   + 13 31.7 7 16.3 5 39.4 4 27.7 3 38.4 3 00.9 + 2 32.9 2 12.7 1 56.6 1 43.2 1 32.5 1 23.7 + 1 10.2 1 00.3 0 52.7 0 46.8 0 43.0 0 39.4 + 0 35.7 0 33.1 0 30.4 0 28.4 0 26.4 0 24.8 + 0 23.3 0 22.1 0 20.9 0 16.3 0 13.1 0 10.8 + 0 09.0 0 07.5 0 06.0 0 05.3 0 04.4 0 03.6 + 0 02.8 0 02.0 0 01.4 0 00.7 + 0 00.0

0 C (32 F)   + 9 17.8 5 04.8 3 57.4 3 07.8 2 33.1 2 07.0 + 1 48.1 1 33.2 1 21.9 1 12.5 1 05.0 0 58.9 + 0 49.4 0 42.5 0 37.1 0 32.9 0 29.6 0 26.9 + 0 24.3 0 22.6 0 21.0 0 19.6 0 18.2 0 17.2 + 0 16.2 0 15.2 0 14.3 0 11.2 0 09.0 0 07.4 + 0 06.2 0 05.2 0 04.4 0 03.6 0 03.0 0 02.4 + 0 01.9 0 01.4 0 00.9 0 00.4 + 0 00.0

10 C (50 F)   + 5 13.4 2 53.4 2 15.6 1 47.8 1 27.9 1 13.1 + 1 02.1 0 53.8 0 47.3 0 42.0 0 37.9 0 35.0 + 0 30.0 0 25.6 0 21.4 0 19.1 0 17.1 0 15.6 + 0 14.2 0 13.2 0 12.1 0 11.3 0 10.3 0 09.9 + 0 09.3 0 08.8 0 08.3 0 06.5 0 05.2 0 04.3 + 0 03.6 0 03.0 0 02.5 0 02.1 0 01.8 0 01.4 + 0 01.1 0 00.8 0 00.5 0 00.2 + 0 00.0

20 C (68 F)   + 1 37.7 0 54.8 0 42.8 0 34.7 0 27.8 0 23.4 + 0 19.6 0 17.2 0 15.1 0 13.5 0 12.0 0 10.9 + 0 09.1 0 07.9 0 06.9 0 06.1 0 05.4 0 05.0 + 0 04.6 0 04.2 0 03.9 0 03.6 0 03.4 0 03.2 + 0 03.0 0 02.7 0 02.5 0 02.1 0 01.7 0 01.4 + 0 01.2 0 01.0 0 00.8 0 00.7 0 00.6 0 00.5 + 0 00.4 0 00.3 0 00.2 0 00.1 + 0 00.0

25 C (77 F)   0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0 0 00.0

30 C (86 F)   - 1 32.6 0 52.1 0 41.2 0 32.1 0 27.1 0 22.4 - 0 19.5 0 16.7 0 14.6 0 12.9 0 11.7 0 10.6 - 0 09.0 0 07.6 0 06.6 0 05.9 0 05.3 0 04.8 - 0 04.4 0 04.0 0 03.7 0 03.5 0 03.3 0 03.1 - 0 02.9 0 02.7 0 02.6 0 02.0 0 01.6 0 01.3 - 0 01.1 0 00.9 0 00.8 0 00.7 0 00.6 0 00.5 - 0 00.4 0 00.3 0 00.2 0 00.1 - 0 00.0

40 C (104 F)   - 4 22.5 2 29.6 1 58.4 1 33.8 1 18.1 1 05.0 - 0 56.0 0 48.2 0 42.4 0 37.6 0 33.9 0 30.7 - 0 25.8 0 22.1 0 19.4 0 17.2 0 15.5 0 14.1 - 0 12.8 0 11.9 0 11.0 0 10.2 0 09.5 0 08.9 - 0 08.4 0 07.9 0 07.5 0 05.9 0 04.7 0 03.9 - 0 03.2 0 02.7 0 02.3 0 02.0 0 01.6 0 01.3 - 0 01.0 0 00.7 0 00.4 0 00.2 - 0 00.0

50 C (122 F)   - 6 54.8 3 58.2 3 09.1 2 30.7 2 05.2 1 44.5 - 1 29.9 1 17.5 1 08.3 1 00.6 0 54.5 0 49.5 - 0 41.5 0 35.7 0 31.3 0 27.8 0 25.0 0 22.8 - 0 20.7 0 19.2 0 17.7 0 16.5 0 15.4 0 14.4 - 0 13.5 0 12.8 0 12.1 0 09.4 0 07.6 0 06.3 - 0 05.2 0 04.4 0 03.7 0 03.1 0 02.5 0 02.1 - 0 01.6 0 01.2 0 00.8 0 00.4 - 0 00.0

366

TABLE - Xb ATMOSPHERIC REFRACTION PRESSURE CORRECTION OF REFRACTION FOR DIFFERENT VALUES OF PRESSURE

mb 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050

PRESSURE

1

mm 495.0 502.5 510.0 517.5 525.0 532.5 540.0 547.5 555.0 562.6 570.1 577.6 585.1 592.6 600.1 607.6 615.1 622.6 630.1 637.6 645.1 652.6 660.1 667.6 675.1 682.6 690.1 697.6 705.1 712.6 720.1 727.6 735.1 742.6 750.1 757.6 765.1 772.6 780.1 787.6

 - 20.4 19.8 19.2 18.6 18.0 17.4 - 16.8 16.2 15.6 15.0 14.4 13.8 - 13.2 12.6 12.0 11.4 10.8 10.2 - 9.6 9.0 8.4 7.8 7.2 6.6 - 6.0 5.4 4.8 4.2 3.6 3.0 - 2.4 1.8 1.2 - 0.6 0.0 + 0.6 1.2 1.8 2.4 + 3.0

Inch 19.49 19.79 20.08 20.38 20.67 20.97 21.26 21.56 21.85 22.15 22.44 22.74 23.03 23.33 23.62 23.92 24.22 24.51 24.81 25.10 25.40 25.69 25.99 26.28 26.58 26.87 27.17 27.46 27.76 28.05 28.35 28.64 28.94 29.24 29.53 29.83 30.12 30.42 30.71 31.01

AMOUNT OF REFRACTION CORRECTED FOR PRESSURE 2 3 5 10 20 30  - 40.8 39.7 38.4 37.2 36.0 34.8 - 33.5 32.4 31.2 30.0 28.9 27.6 - 26.4 25.2 24.0 22.8 21.6 20.4 - 19.2 18.0 16.8 15.6 14.4 13.2 - 12.0 10.8 9.6 8.4 7.2 6.0 - 4.8 3.6 2.4 - 1.2 0.0 + 1.2 2.4 3.6 4.8 + 6.0

 - 61.3 59.5 57.7 55.9 54.1 52.3 - 50.6 48.7 46.9 45.1 43.3 41.5 - 39.7 37.9 36.0 34.3 32.4 30.7 - 28.9 27.0 25.2 23.4 21.6 19.8 - 18.0 16.2 14.4 12.6 10.8 9.0 - 7.2 5.4 3.6 - 1.8 0.0 + 1.8 3.6 5.4 7.2 + 9.0

 -1 1 1 1 1 1 -1 1 1 1 1 1 -1 1 1 0 0 0 -0 0 0 0 0 0 -0 0 0 0 0 0 -0 0 0 -0 0 +0 0 0 0 +0

    42.3 - 3 26.5 - 7 39.3 3 20.4 6 36.3 3 14.3 6 33.3 3 08.2 6 30.3 3 02.2 6 27.3 2 56.1 6 24.3 - 2 50.0 - 5 21.2 2 43.9 5 18.2 2 37.8 5 15.2 2 31.8 5 12.3 2 25.8 5 09.2 2 19.7 4 06.2 - 2 13.6 - 4 03.2 2 07.6 4 00.2 2 01.4 4 57.2 1 55.4 3 54.2 1 49.3 3 51.2 1 43.3 3 48.2 - 1 37.2 - 3 45.1 1 31.1 3 42.1 1 25.0 2 39.1 1 19.0 2 36.1 1 12.9 2 33.1 1 06.8 2 30.1 - 1 00.7 - 2 27.1 0 54.7 1 24.1 0 48.6 1 21.1 0 42.5 1 18.1 0 36.4 1 15.0 0 30.3 1 12.0 - 0 24.3 - 0 09.0 0 18.2 0 06.0 0 12.1 0 03.0 - 0 06.1 - 0 00.0 0 00.0 0 03.1 + 0 06.1 + 0 06.0 0 12.2 0 09.0 0 18.2 0 12.0 0 24.3 0 15.0 + 0 30.3 + 0

 04.9 52.5 39.8 27.4 14.9 02.5 50.0 37.4 24.9 12.4 00.2 47.5 35.0 22.5 09.9 57.5 44.9 32.5 20.0 07.4 54.9 42.5 30.0 17.5 04.9 52.5 39.9 27.5 15.0 02.4 49.9 37.5 25.0 12.5 00.0 12.5 25.1 37.5 50.0 62.4

 - 10 10 10 10 9 9 -9 8 8 8 7 7 -7 6 6 6 5 5 -5 4 4 4 3 3 -3 2 2 2 1 1 -1 0 0 -0 0 +0 0 0 0 +0

 59.1 39.8 20.2 00.9 41.5 22.2 02.8 43.3 23.9 04.6 45.6 25.9 06.5 47.2 27.6 08.3 48.9 29.6 10.2 50.7 31.3 12.0 52.6 33.3 13.7 54.3 35.0 15.7 50.3 36.9 17.4 58.2 38.7 19.4 00.0 19.5 38.9 58.2 77.6 96.9

60  - 24 23 22 22 21 20 - 20 19 18 17 17 16 - 15 15 14 13 12 12 - 11 10 10 9 8 7 -7 6 5 5 4 3 -2 2 1 -0 0 +0 1 2 2 +3

 19 36 53 10 27 45 01 18 35 53 21 27 44 01 18 35 52 10 27 43 01 18 35 52 09 26 43 01 17 34 51 09 26 43 00 43 26 09 52 24

367

TABLE - XI FACTORS FOR COMPUTING THE GEOCENTRIC COORDINATES OF A PLACE   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

S

C

0.993306 0.993307 0.993310 0.993315 0.993322 0.993331 0.993342 0.993355 0.993370 0.993387 0.993406 0.993427 0.993449 0.993474 0.993500 0.993528 0.993558 0.993590 0.993623 0.993658 0.993695 0.993733 0.993773 0.993814 0.993856 0.993900 0.993945 0.993992 0.994039 0.994088 0.994138 0.994189 0.994241 0.994293 0.994347 0.994401 0.994456 0.994512 0.994568 0.994625 0.994682 0.994740 0.994798 0.994856 0.994914 0.994972

1.000000 1.000001 1.000004 1.000009 1.000016 1.000025 1.000037 1.000050 1.000065 1.000082 1.000101 1.000122 1.000145 1.000169 1.000196 1.000224 1.000254 1.000286 1.000320 1.000355 1.000392 1.000430 1.000470 1.000511 1.000554 1.000598 1.000644 1.000691 1.000739 1.000788 1.000838 1.000889 1.000941 1.000994 1.001048 1.001103 1.001158 1.001214 1.001271 1.001328 1.001386 1.001444 1.001502 1.001560 1.001619 1.001678

  45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

 sin  = (S+H) sin  H = 0.156779  elevation in meters 10-6

S

C

0.994972 0.995031 0.995089 0.995147 0.995205 0.995262 0.995320 0.995377 0.995433 0.995489 0.995544 0.995599 0.995652 0.995705 0.995758 0.995809 0.995859 0.995908 0.995956 0.996002 0.996048 0.996092 0.996135 0.996176 0.996216 0.996255 0.996291 0.996327 0.996360 0.996392 0.996422 0.996451 0.996477 0.996502 0.996525 0.996546 0.996565 0.996582 0.996597 0.996610 0.996622 0.996631 0.996638 0.996643 0.996646 0.996647

1.001678 1.001737 1.001795 1.001854 1.001912 1.001970 1.002028 1.002085 1.002142 1.002198 1.002254 1.002309 1.002363 1.002416 1.002468 1.002520 1.002570 1.002620 1.002668 1.002715 1.002761 1.002805 1.002848 1.002890 1.002930 1.002969 1.003006 1.003041 1.003075 1.003107 1.003138 1.003166 1.003193 1.003218 1.003241 1.003262 1.003281 1.003299 1.003314 1.003327 1.003338 1.003348 1.003355 1.003360 1.003363 1.003364

 cos  = (C+H) cos  H = 0.047786  elevation in feet 10-6

368

TABLE - XII CONVERSION OF GEOGRAPHIC TO GEOCENTRIC COORDINATES 

 - 

   0 0 00.0 1 - 0 24.1 2 0 48.2 3 1 12.2 4 1 36.1 5 1 59.9 6 2 23.6 7 2 47.0 8 3 10.3 9 3 33.4 10 - 3 56.2 11 4 18.7 12 4 40.9 13 5 02.8 14 5 24.3 15 5 45.4 16 6 06.0 17 6 26.3 18 6 46.1 19 7 05.4 20 - 7 24.1 21 7 42.4 22 8 00.0 23 8 17.1 24 8 33.6 25 8 49.5 26 9 04.7 27 9 19.3 28 9 33.2 29 9 46.4 30 - 9 58.9 31 10 10.7 32 10 21.7 33 10 32.0 34 10 41.5 35 10 50.2 36 10 58.1 37 11 05.3 38 11 11.6 39 11 17.1 40 -11 21.8 41 11 25.7 42 11 28.7 43 11 30.9 44 11 32.2 45 -11 32.7



ONE DEGREE OF Latitude Longitude Kilometers Kilometers

1.000000 0.999999 0.999996 0.999991 0.999984 0.999975 0.999964 0.999951 0.999936 0.999919 0.999900 0.999879 0.999856 0.999832 0.999805 0.999777 0.999747 0.999716 0.999682 0.999647 0.999611 0.999573 0.999533 0.999492 0.999449 0.999405 0.999360 0.999314 0.999266 0.999217 0.999167 0.999116 0.999064 0.999011 0.998958 0.998903 0.998848 0.998792 0.998736 0.998679 0.998622 0.998564 0.998506 0.998447 0.998389 0.998331

110.57 110.58 110.58 110.58 110.58 110.58 110.59 110.59 110.60 110.60 110.61 110.62 110.62 110.63 110.64 110.65 110.66 110.67 110.68 110.69 110.70 110.72 110.73 110.74 110.76 110.77 110.79 110.80 110.82 110.84 110.85 110.87 110.89 110.90 110.92 110.94 110.96 110.98 111.00 111.02 111.03 111.05 111.07 111.09 111.11 111.13

111.32 111.30 111.25 111.17 111.05 110.90 110.71 110.50 110.24 109.96 109.64 109.29 108.90 108.49 108.03 107.55 107.03 106.49 105.91 105.29 104.65 103.97 103.26 102.52 101.75 100.95 100.12 99.26 98.36 97.44 96.49 95.50 94.49 93.45 92.39 91.29 90 16 89.01 87.83 86.63 85.39 84.14 82.85 81.54 80.21 78.85

  45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

 -   - 11 11 11 11 11 11 11 11 11 10 - 10 10 10 10 10 10 9 9 9 9 -8 8 8 8 7 7 7 6 6 6 -5 5 5 4 4 3 3 3 2 2 -2 1 1 0 -0 0

 32.7 32.4 31.2 29.2 26.3 22.6 18.1 12.7 06.5 59.5 51.7 43.1 33.7 23.5 12.6 00.9 48.5 35.4 21.5 07.0 51.8 36.0 19.5 02.4 44.7 26.4 07.6 48.3 28.4 08.1 47.4 26.2 04.6 42.6 20.3 57.7 34.7 11.6 48.1 24.5 00.7 36.7 12.7 48.5 24.3 00.0



ONE DEGREE OF Latitude Longitude Kilometers Kilometers

0.998331 0.998272 0.998214 0.998155 0.998097 0.998039 0.997982 0.997925 0.997868 0.997812 0.997756 0.997702 0.997648 0.997594 0.997542 0.997491 0.997440 0.997391 0.997343 0.997296 0.997250 0.997206 0.997163 0.997121 0.997081 0.997042 0.997005 0.996970 0.996936 0.996904 0.996874 0.996845 0.996818 0.996793 0.996770 0.996749 0.996730 0.996713 0.996697 0.996684 0.996673 0.996664 0.996656 0.996651 0.996648 0.996647

111.13 111.15 111.17 111.19 111.21 111.23 111.25 111.27 111.29 111.31 111.32 111.34 111.36 111.38 111.40 111.41 111.43 111.45 111.46 111.48 111.49 111.51 111.52 111.54 111.55 111.56 111.57 111.59 111.60 111.61 111.61 111.62 111.63 111.64 111.65 111.66 111.67 111.67 111.68 111.68 111.69 111.69 111.69 111.69 111.69 111.69

 and  are the geographic and geocentric latitude respectively  = radius of the earth. 1 kilometre = 0.621372 miles.

78.85 77.46 76.06 74.63 73.17 71.70 70.20 68.68 67.14 65.58 63.99 62.39 60.77 59.13 57.48 55.80 54.11 52.40 50.67 48.93 47.18 45.40 43.62 41.82 40.01 38.19 36.35 34.50 32.65 30.78 28.90 27.02 25.12 23.22 21.31 19.39 17.47 15.54 13.61 11.67 9.73 7.79 5.85 3.90 1.95 0.00

369

LATITUDE AND LONGITUDE OF PLACES Longitude Place

Altitude Latitude (Metre)

In arc

In time

Reduction of Greenwich Sid. Time

s     h m s Agartala 16 +23 31.8 + 91 09.0 +6 04 36 +59.89 Agra 160 +27 05.6 + 77 34.8 +5 10 19 +50.98 Ahmedabad 49 +23 03.0 + 72 40.2 +4 50 41 +47.75 Aizawl 1097 +23 26.4 + 92 43.2 +6 10 53 +60.93 Ajmer 486 +26 16.2 + 74 22.2 +4 57 29 +48.87 Alibag (Obs.) 7 +19 00.0 + 72 30.6 +4 50 02 +47.65 Mumbai, Aligarh 187 +27 31.8 + 78 2.44 +5 12 10 +51.28 Allahabad 96 +25 16.2 + 81 26.4 +5 25 46 +53.51 Amritsar 231 +31 22.8 + 74 31.2 +4 58 05 +48.97 Bangalore 921 +12 34.8 + 77 21.0 +5 09 24 +50.83 Bangkok, Thailand 16 +13 25.0 +100 18.0 +6 41 12 +65.91 Baroda 35 +22 12.0 + 73 9.6 +4 52 38 +48.07 Bhopal 506 +23 10.2 + 77 12.6 +5 08 50 +50.73 Bhuj 105 +23 09.0 + 69 24.0 +4 37 36 +45.60 Bhubaneswar 46 +20 00.0 + 85 30.0 +5 42 00 +56.18 Bikaner 224 +28 01.0 + 73 10.8 +4 52 43 +48.09 Bilaspur,(H.P) 502 +31 11.4 + 76 30.0 +5 06 00 +50.27 6 -34 21.0 - 58 12.0 - 3 52 48 -38.24 Buenos Aires (Naval Obs.), Argentina Cairo 68 +30 01.0 + 31 09.0 +2 04 36 +20.47 Canberra (Mount 767 -35 10.2 +149 10.5 +9 56 42 +98.02 Stromlo), Australia Cape Town (Ast. 18 -33 33.6 + 18 15.0 +1 13 00 +11.99 Obs.), S. Africa Chandigarh 347 +30 25.2 + 76 32.0 +5 06 08 +50.29 Chennai (or 7 +13 00.0 + 80 06.6 +5 20 26 +52.64 Madras) Obs. Chittagong, 27 +22 12.6 + 91 31.8 +6 06 07 +60.14 Bangladesh Colaba Obs. 14 +19 04.2 + 72 31.0 +4 50 04 +47.65 Mumbai, (Bombay) Colombo (Obs.), 6 + 6 33.6 + 79 33.6 +5 18 14 +52.28 Srilanka Cuttack 26 +20 16.8 + 85 33.6 +5 42 14 +56.42 Dacca,Bangladesh 7 +23 25.8 + 90 15.6 +6 01 02 +59.31 Darjeeling 2128 +27 02.0 + 88 10.8 +5 52 43 +57.94 Dehra Dun 682 +30 11.3 + 78 01.2 +5 12 05 +51.27 Delhi 220 +28 21.0 + 77 07.2 +5 08 29 +50.68 Dibrugarh 106 +27 17.4 + 94 06.0 +6 16 24 +61.83 Gangtok 1768 +27 12.0 + 88 22.2 +5 53 29 +58.07 Guwahati 55 +26 3.6.0 + 91 21.0 +6 05 24 +60.03 Gauribidanur 686 +13 36.2 + 77 26.1 +5 09 44 +50.88 (Radio Astr. Obs.) Gaya 111 +24 27.0 + 84 34.2 +5 38 17 +55.57 1 metre = 3.2808 feet

Reduction of L.M.T. to Indian Standard Time m s -34 36 +19 51 +39 19 -40 53 +32 31 +39 58

 sin 

 cos 

+0.39677 +0.45272 +0.38912 +0.39540 +0.43996 +0.33350

0.91734 0.89091 0.92064 0.91812 0.89738 0.94586

+17 +04 +31 +20 - 71 +37 +21 +52 - 12 +37 +24 ..

47 14 55 36 12 22 10 24 00 17 00 ..

+0.45946 +0.42429 +0.51771 +0.21641 +0.23052 +0.37549 +0.39106 +0.39072 +0.33987 +0.46695 +0.51491 -0.56107

0.88743 0.90487 0.85454 0.97629 0.97289 0.92632 0.91989 0.91997 0.94007 0.88349 0.85629 0.82649

.. ..

.. ..

+0.49733 0.86662 -0.57285 0.81845

..

..

-0.54967

0.83416

+23 52 + 9 34

+0.50340 0.86312 +0.22348 0.97454

- 36 07

+0.37565 0.92625

+39 56

+0.32465 0.94546

+11 46

+011348

0.99350

- 12 - 31 - 22 +17 +21 - 46 - 23 - 35 +20

+0.34443 +0.39518 +0.45193 +0.49995 +0.47205 +0.45575 +0.45448 +0.43666 +0.23369

0.93839 0.91803 0.89166 0.86520 0.88076 0.88734 0.89029 0.89892 0.97223

14 02 43 55 31 24 29 24 16

- 8 17

+0.41137 0.91086

370

LATITUDE AND LONGITUDE OF PLACES Longitude Place

Geneva (Obs.), Switzerland Greenwich (Royal Obs.). Hanle/ Mt.Saraswati (Indian Ast. Obs.) Haridwar Heidelberg Obs., Germany Helwan (Obs.), Egypt Herstmonceux (Royal Obs.), Sussex, U.K. Hyderabad (Nizamiah Obs.) Imphal India, Central Station of Indore Istambul (Univ. Obs.), Turkey IUCAA Giravali Obs., Pune Jabalpur Jaipur Jakarta, Indonesia Jamshedpur Japal Rangapur (Obs.), Jodhpur Johannesberg, South Africa Kabul, Afghanistan Kanchipuram Kanpur Karachi, Pakistan Kathmandu, Nepal Kavalur (Vainu Bappu Obs.), Kodaikanal (Solar Obs.) Kohima Kolkata (Alipore Obs.), (Calcutta) Kolkata (Presi. Coll. Obs.) Kurnool

Altitude Latitude (Metre)

In arc

In time

h m s     465 +46 07.8 + 6 04.2 +0 24 17 47 +51 28.6

s + 3.99

Reduction of L.M.T.  sin   cos  to Indian Standard Time m s .. .. +0.71739 0.69428

0 00 00.0

0.00

4467 +32 46.8 + 78 57.9 +5 15 51.6

+51.89

+14 8.4 +0.53870 0.84217

274 +29 34.8 + 78 08.0 +5 12 32.0 570 +49 14.0 + 8 25.2 +0 33 41.0

+51.34 + 5.53

+ 17 28 +0.49076 0.87041 .. .. +0.75382 0.65430

116 +29 51.5 + 31 22.8 +2 05 31.2

+20.62

..

..

+0.49494 0.86800

31 +50 52.0 + 0 20.3 +0 01 21.0

+ 0.22

..

..

+0.77205 0.63241

554 +17 25.9 + 78 27.2 +5 13 49.0

+51.55

+ 16 11 +0.29768 0.95444

801 +24 26.4 + 93 34.8 +6 14 19.0 - +23 11.0 + 82 30.0 +5 30 00.0

+61.49 +54.21

- 44 19 +0.41126 0.91103 0 00 +0.39124 0.91973

556 +22 26.4 + 75 30.0 +5 02 00.0 65 +41 00.7 + 28 57.9 +1 55 51.6

+49.61 +19.03

+ 28 00 +0.37938 0.92481 .. .. +0.65277 0.75567

1000 +18 19.2 + 73 30.6 +4 54 02.0

+48.3

+35 58

+0.31237 0.94978

17.0 05.0 00.0 26.0 55.0

+52.29 +49.62 +69.98 +56.58 +51.73

+ 11 + 27 .. - 14 + 15

+0.39026 +0.44431 -0.10590 +0.38016 +0.29216

224 +26 10.8 + 73 00.6 +4 52 02.0 1806 - 26 10.9 + 28 04.5 +1 52 18.0

+47.97 +18.45

+ 37 58 +0.43854 0.89803 .. .. -0.43868 0.89824

1766 76 126 4 1324 725

43.0 48.0 53.0 10.0 29.0 18.0

+45.46 +52.21 +52.71 +44.05 +55.93 +51.80

+ 53 + 12 + 9 + 61 - 10 + 14

2343 +10 13.8 + 77 28.1 +5 09 52.0

+50.90

+ 20 08 +0.17649 0.98457

1405 +25 24.0 + 94 04.8 +6 16 19.0 6 +22 19.2 + 88 12.0 +5 52 48.0

+61.82 +57.96

- 46 19 +0.42642 0.90409 - 22 48 +0.37742 0.92553

12 +22 23.4 + 88 16.2 +5 53 05.0

+58.00

- 23 05

281 +15 30.0 + 78 03.0 +5 12 12.0 1 metre = 3.2808 feet

+51.29

+ 17 48 +0.26552 0.96390

393 436 23 152 695

+23 +26 - 6 +22 +17

+34 +12 +26 +24 +27 +12

07.2 33.0 07.2 29.4 05.9

0 00

Reduction of Greenwich Sid. Time

+ 79 + 75 +106 + 86 + 78

18.0 + 30.0 + 15.6 + 53.6 + 23.2 + 34.6 +

69 79 80 67 85 78

34.2 31.2 30.0 06.6 43.7

10.8 27.0 13.2 02.4 07.2 49.6

+5 +5 +7 +5 +5

+4 +5 +5 +4 +5 +5

18 02 06 44 14

36 17 20 28 40 15

..

..

43 55 .. 26 05

17 12 07 50 29 42

+0.77872 0.62412

+0.56051 +0.21503 +0.43978 +0.41836 +0.45733 +0.21635

0.92022 0.89520 0.99434 0.92442 0.95618

0.82721 0.97646 0.89740 0.90763 0.88874 0.97627

+0.37854 0.92506

371

LATITUDE AND LONGITUDE OF PLACES Longitude Place

Kyoto (Univ. Ast. Dept. Obs.), Japan Lahore, Pakistan Lucknow Maitri (Indian base station at Antarctica) Mangalore Moscow (Sternberg State Ast. Inst.), Russia Mount Abu (Gurushikhar Obs.) Mount Palomar (Obs.), U.S.A. Mount Wilson (Obs.), U.S.A. Mysore Nagpur Nainital (Aryabhatta Res. Inst. Of Obs. Sci.) New York (Rutherford Obs.), U.S.A. Ottawa, Canada Panaji Paris (Obs.), France Patiala Patna Peshawar, Pakistan Pondicherry Pune Porbandar Port Blair Puri Quetta, Pakistan Rajkot Rawalpindi, Pakistan Rome (Obs.), Italy San Fernando (Naval Obs.), Spain Shillong

h m s     +35 00.6 +135 20.4 +9 1 22.0

s +88.93

Reduction of L.M.T.  sin   cos  to Indian Standard Time m s .. .. +0.57052 0.81997

214 +31 22.2 + 74 15.6 +4 57 02.0 113 +26 31.2 + 80 33.6 +5 22 14.0 132 -70 46.0 + 11 45.0 +0 47 00.0

+48.80 +52.94 + 7.72

+ 32 58 + 7 46 .. ..

+0.51756 0.85269 +0.44383 0.89539 -0.94069 0.33041

22 +12 33.0 + 74 31.8 +4 58 07.0 195 +55 27.0 + 37 22.2 +2 29 29.0

+48.97 +24.56

+ 31 53 .. ..

+0.21587 0.97626 +0.82001 0.56843

1700 +24 23.4 + 72 25.8 +4 49 43.0

+47.59

1706 +33 21.4 -116 51.8 - 7 47 27.2

-76.79

..

..

+054687

1742 +34 13.0 -118 03.6 - 7 52 14.4

-77.58

..

..

+0.55931 0.82802

767 +12 10.8 + 76 25.2 +5 05 41.0 312 +21 05.4 + 79 04.2 +5 16 17.0 1927 +29 13.8 + 79 18.0 +5 17 12.0

+50.22 +51.96 +52.11

25 +40 25.8 - 74 00.6 - 4 56 02.0

-48.63

Altitude Latitude (Metre)

86

87 56 67 251 53 358 6 559 7 79 6 1673 132 510

+45 +15 +48 +30 +25 +34 +11 +18 +21 +11 +19 +30 +22 +33

16.2 18.0 30.0 12.0 21.6 01.0 34.8 19.0 22.2 24.0 28.8 07.2 10.8 22.2

In arc

+ + + + + + + + + + + + +

75 73 2 76 85 71 79 73 69 92 85 67 70 73

22.2 - 5 33.0 +4 12.0 +0 15.0 +5 03.6 +5 34.0 +4 29.4 +5 30.0 +4 29.4 +4 25.8 +6 29.4 +5 00.0 +4 33.6 +4 03.6 +4

In time

01 54 08 05 40 46 17 54 37 09 41 28 42 52

Reduction of Greenwich Sid. Time

29.0 -49.53 12.0 +48.33 49.0 + 1.45 00.0 +50.10 14.0 +55.89 15.0 +47.03 58.0 +52.23 00.0 +48 .30 58.0 +45.66 43.0 +60.74 58.0 +56.18 00.0 +44.03 14.0 +46 .36 14.0 +48.01

152 +41 33.0 + 12 16.8 +0 49 07.2 27 +36 28.0 - 6 12.2 -0 24 48.8

+40 17 +0.41053 0.91152

+ 24 19 + 13 43 + 12 48

..

.. + 35 .. + 25 - 10 + 43 + 12 + 36 + 52 - 39 - 11 + 62 + 47 + 37

0.83633

+0.20963 0.97775 +0.35760 0.93347 +0. 48558 0.87363

..

+0.64509 0.76228

.. 48 .. 00 14 45 02 00 02 43 58 00 46 46

+0.70688 +0.26217 +0.74535 +0.50010 +0.42570 +0.55630 +0. 19942 +0.31230 +0.36211 +0.19636 +0.33137 +0.49901 +0.37518 +0.54696

0.70497 0.96479 0.66387 0.86504 0.90420 0.82979 0.97978 0.94973 0.93166 0.98041 0.94311 0.86593 0.92646 0.83605

+ 8.07 - 4.08

.. .. .. ..

+0.65982 0.74950 +0.59108 0.80516

1500 +25 20.4 + 91 33.6 +6 06 14.0 +61.16 1 metre = 3.2808 feet

- 36 14

+0.42549 0.90455

372

LATITUDE AND LONGITUDE OF PLACES Longitude Place

Sholapur Siliguri Simla Singapore Srinagar St. Petersburg Univ. Obs., Russia Tehran, Iran Tokyo (Hydrographic Obs.), Japan Thiruvanantapuram Udaipur (Solar Obs.) Udhagamandalam (Ooty) (Rad. Astr.Centre) Ujjain Varanasi Visakhapatnam Washington (U. S. Naval Obs.), U.S.A. Yangon, Myanmar

Altitude Latitude (Metre)

476 127 2202 18 1586 3

 +17 +26 +31 + 1 +34 +59

 24.0 24.0 03.6 10.2 03.6 56.5

In arc

 + 75 + 88 + 77 +103 + 74 + 30

h  33.6 +5 13.2 +5 07.8 +5 30.6 +6 30.6 +4 17.7 +2

In time

m s 02 14 52 53 08 31 54 02 58 02 01 11

Reduction of Greenwich Sid. Time s +49.65 +57.97 +50. 68 +68.02 +48.96 +19.91

Reduction of L.M.T. to Indian Standard Time m s + 27 46 - 22 53 + 21 29 .. .. + 31 58 .. ..

+0.29715 +0.44196 +0.51312 +0.02028 +0.55704 +0.86189

0.95460 0.89632 0.85769 0.99980 0.82953 0.50214

+33.68 +90.98

61 + 8 17.4 + 76 34.2 +5 06 17 301 +24 21.0 + 73 25.2 +4 53 41

+50.31 +48.24

+ 23 43 + 36 19

+0.14323 0.98963 +0.40980 0.91161

2150 +11 22.9 + 76 40.0 +5 06 40

+50.38

+ 23 20

+0.19611 0.98079

+49.59 +54.54 +54.63 -50.62

+ 28 07 - 2 00 - 2 34 .. ..

+0.39002 +0.42288 +0.29763 +0.61984

28 +16 27.0 + 96 7.20 +6 24 29 +63.16 1 metre = 3.2808 feet

- 54 29

+0.28136 0.95933

+23 +25 +17 +38

06.3 10.8 25.8 33.0

+ + + -

75 83 83 77

28.2 +5 00.0 +5 08.4 +5 02.4 - 5

01 53 32 00 32 34 08 10

.. ..

 cos 

1200 +35 24.6 + 51 15.0 +3 25 00 41 +35 24.0 +138 27.0 +9 13 48

496 76 38 92

.. ..

 sin 

+0.57630 0.81610 +0.57605 0.81605

0.92033 0.90554 0.95438 0.78309

373

SEMI-DIURNAL AND SEMI-NOCTURNAL ARCS (FOR TRUE ALTITUDE = 0) Lat. Decli. º ' 0 00 5 00 10 00 15 00 20 00 23 00 25 00 28 00 30 00

0º

10º

20º

30º

35º

40º

45º

50º

52º

54º

56º

58º

60º

h m h m h m h m h m h m h m h m h m h m h m h m 6 00 6 00 6 00 6 00 6 00 6 00 6 00 6 00 6 00 6 00 6 00 6 00 6 00 6 04 6 07 6 12 6 14 6 17 6 20 6 24 6 26 6 28 6 30 6 32 6 00 6 07 6 15 6 23 6 28 6 34 6 41 6 49 6 52 6 56 7 01 7 06 6 00 6 11 6 22 6 36 6 43 6 52 7 02 7 14 7 20 7 27 7 34 7 42 6 00 6 15 6 30 6 49 6 59 7 11 7 25 7 43 7 51 8 00 8 11 8 22 6 00 6 18 6 36 6 58 7 11 7 25 7 43 8 05 8 15 8 27 8 40 8 56 6 00 6 19 6 39 7 02 7 16 7 32 7 51 8 15 8 27 8 40 8 55 9 13 6 00 6 22 6 45 7 12 7 27 7 46 8 08 8 37 8 52 9 08 9 28 9 59 6 00 6 23 6 49 7 18 7 35 7 56 8 21 8 54 9 11 9 30 9 55 10 30 When the latitude of the place and the declination of the heavenly body are of the same sign then the figure represent semi-diurnal arc, when of opposite signs then semi-nocturnal arc.

h m 6 00 6 35 7 11 7 51 8 36 9 15 9 35 10 28 12 00

AMPLITUDE OF RISING AND SETTING Lat. Decli. º ' 0 00 5 00 10 00 15 00 20 00 23 00 25 00 28 00 30 00

0º

10º

20º

(FOR TRUE ALTITUDE = 0) 30º 35º 40º 45º 50º

52º

54º

56º

58º

º ' º ' º ' º ' º ' º ' º ' º ' º ' º ' º ' º 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 5 00 5 05 5 19 5 47 6 06 6 32 7 05 7 48 8 08 8 32 8 58 9 10 00 10 09 10 39 11 34 12 14 13 06 14 13 15 40 16 23 17 11 18 05 19 15 00 15 14 15 59 17 23 18 25 19 45 21 28 23 45 24 52 26 07 27 34 29 20 00 20 19 21 21 23 16 24 41 26 31 28 56 32 09 33 45 35 35 37 42 40 23 00 23 50 25 03 27 21 29 04 31 18 34 15 38 15 40 16 42 37 45 22 48 25 00 25 25 26 44 29 13 31 04 33 29 36 42 41 06 43 21 45 58 49 06 52 28 00 28 28 29 58 32 50 34 58 37 48 41 36 46 55 49 41 53 00 57 06 62 30 00 30 31 32 09 35 16 37 37 40 45 45 00 51 04 54 18 58 17 63 24 70 The amplitude of rising and setting points of a heavenly body is measured from the East or the West point of the horizon towards the northern or southern direction as the case may be. The amplitude is of the same sign as that of declination of the body. Note - If true zenith distance of the heavenly body at the time of rising or setting be 90º + h, then the figures of the above two tables would require some correction according to the value of h (vide Explanation).

' 00 28 08 14 12 40 54 22 39

60º º 0 10 20 31 43 52 57 69 90

' 00 02 19 10 10 44 42 52 00

AUGMENTATION OF MOON'S SEMI-DIAMETER Moon 's Apparent Altitude Semidiameter   14 30 15 00 15 30 16 00 16 30 17 00

0º  0.1 0.1 0.1 0.1 0.2 0.2

6º

12º

18º

24º

30º

36º

42º

48º

54º

60º

66º

72º

78º

84º

90º

            1.5 2.9 4.3 5.6 6.9 8.1 9.2 10.2 11.1 11.8 12.5 13.0 1.6 3.1 4.6 6.0 7.3 8.6 9.8 10.9 11.8 12.7 13.4 13.9 1.7 3.3 4.9 6.4 7.9 9.2 10.5 11.6 12.7 13.5 14.3 14.9 1.9 3.6 5.2 6.8 8.4 9.8 11.2 12.4 13.5 14.4 15.2 15.9 2.0 3.8 5.6 7.3 8.9 10.5 11.9 13.2 14.4 15.4 16.2 16.9 2.1 4.0 5.9 7.7 9.5 11.1 12.6 14.0 15.3 16.3 17.2 17.9 The visible or apparent semi-diameter of the moon is augmented over the tabulated value due to moon's altitude above the horizon.

 13.4 14.3 15.3 16.3 17.4 18.4

 13.6 14.6 15.6 16.6 17.6 18.7

 13.7 14.6 15.6 16.7 17.7 18.8

374

NATURAL TRIGONOMETRIC FUNCTIONS ANGLE Arc Time h m  0 00 0 1 0 04 2 0 08 3 0 12 4 0 16 5 0 20 6 0 24 7 0 28 8 0 32 9 0 36 10 0 40 11 0 44 12 0 48 13 0 52 14 0 56 15 1 00 16 1 04 17 1 08 18 1 12 19 1 16 20 1 20 21 1 24 22 1 28 23 1 32 24 1 36 25 1 40 26 1 44 27 1 48 28 1 52 29 1 56 30 2 00 31 2 04 32 2 08 33 2 12 34 2 16 35 2 20 36 2 24 37 2 28 38 2 32 39 2 36 40 2 40 41 2 44 42 2 48 43 2 52 44 2 56 45 3 00

Sin

Cos

Tan

0.00000 .01745 .03490 .05234 .06976 .08716 .10453 .12187 .13917 .15643 .17365 0.19081 .20791 .22495 .24192 .25882 .27564 .29237 .30902 .32557 .34202 0.35837 .37461 .39073 .40674 .42262 .43837 .45399 .46947 .48481 .50000 0.51504 .52992 .54464 .55919 .57358 .58779 .60182 .61566 .62932 .64279 0.65606 .66913 .68200 .69446 0.70711 Cos

1.00000 0.99985 .99939 .99863 .99756 .99619 .99452 .99255 .99027 .98769 .98481 0.98163 .97815 .97437 .97030 .96593 .96126 .95630 .95106 .94552 .93969 0.93358 .92718 .92050 .91355 .90631 .89879 .89101 .88295 .87462 .86603 0.85717 .84805 .83867 .82904 .81915 .80902 .79864 .78801 .77715 .76604 0.75471 .74314 .73135 .71934 0.70711 Sin

0.00000 .01746 .03492 .05241 .06993 .08749 .10510 .12278 .14054 .15838 .17633 0.19438 .21256 .23087 .24933 .26795 .28675 .30573 .32492 .34433 .36397 0.38386 .40403 .42447 .44523 .46631 .48773 .50953 .53171 .55431 .57735 0.60086 .62487 .64941 .67451 .70021 .72654 .75355 .78129 .80978 .83910 0.86929 .90040 .93252 0.96569 1.00000 Cot

Cot

Infinity 57.28996 28.63625 19.08114 14.30067 11.43005 9.51436 8.14435 7.11537 6.31375 5.67128 5.14455 4.70463 4.33148 4.01078 3.73205 3.48741 3.27085 3.07768 2.90421 2.74748 2.60509 2.47509 2.35585 2.24604 2.14451 2.05030 1.96261 1.88073 1.80405 1.73205 1.66428 1.60033 1.53987 1.48256 1.42815 1.37638 1.32704 1.27994 1.23490 1.19175 1.15037 1.11061 1.07237 1.03553 1.00000 Tan

Sec

1.00000 .00015 .00061 .00137 .00244 .00382 .00551 .00751 .00983 .01247 .01543 1.01872 .02234 .02630 .03061 .03528 .04030 .04569 .05146 .05762 .06418 1.07115 .07853 .08636 .09464 .10338 .11260 .12233 .13257 .14335 .15470 1.16663 .17918 .19236 .20622 .22077 .23607 .25214 .26902 .28676 .30541 1.32501 .34563 .36733 .39016 1.41421 Cosec

Cosec

Infinity 57.29869 28.65371 19.10732 14.33559 11.47371 9.56667 8.20551 7.18530 6.39245 5.75877 5.24084 4.80973 4.44541 4.13357 3.86370 3.62796 3.42030 3.23607 3.07155 2.92380 2.79043 2.66947 2.55930 2.45859 2.36620 2.28117 2.20269 2.13005 2.06267 2.00000 1.94160 1.88708 1.83608 1.78829 1.74345 1.70130 1.66164 1.62427 1.58902 1.55572 1.52425 1.49448 1.46628 1.43956 1.41421 Sec

h m  6 00 90 5 56 89 5 52 88 5 48 87 5 44 86 5 40 85 5 36 84 5 32 83 5 28 82 5 24 81 5 20 80 5 16 79 5 12 78 5 08 77 5 04 76 5 00 75 4 56 74 4 52 73 4 48 72 4 44 71 4 40 70 4 36 69 4 32 68 4 28 67 4 24 66 4 20 65 4 16 64 4 12 63 4 08 62 4 04 61 4 00 60 3 56 59 3 52 58 3 48 57 3 44 56 3 40 55 3 36 54 3 32 53 3 28 52 3 24 51 3 20 50 3 16 49 3 12 48 3 08 47 3 04 46 3 00 45 Time Arc ANGLE

375

STANDARD TIMES LOCAL STANDARD TIME FOR EACH COUNTRY OR AREA THE AHEAD OF ( + ) OR BEHIND ( - ) U.T. OR G.M.T Country or Area

Aden Afghanistan Alaska - Day light Saving Time Albania - Day light Saving Time Aleutian Islands Algeria Angola Argentina Ascension Islands AustraliaCapital Territory (Canberra), Victoria, New South Wales, Queensland, Tasmania. South Australia, Northern Territory, Broken Hill Area - Day light Saving Time

Standard L.S.T Time at 12h U.T or 17-30 I.S.T. h +3 + 4 1/2 -9 -8 +1 +2 - 10

h 15 16 03 04 13 14 02

m 00 30 00 00 00 00 00

0 +1 -3 0

12 13 09 12

00 00 00 00

+ 10

22

00

+ 9 1/2

21

30

+ 10 1/2

22

30

+8 +9

20 21

00 00

Austral Islands

- 10

02

00

Austria Azores Bahrain Bangladesh

+1 -1 +3 +6

13 11 15 18

00 00 00 00

Western Australia - Day light Saving Time

Country or Area

Belgium Belize Bermuda Bhutan Bolivia BrazilEastern (including coast) Western Territory of Acre Bulgaria Cambodia Cameroon CanadaNewfoundland

East of Long. 63 W N W Territories (EaSt of Long. 68 W), New Brunswick Nova Scotia, Prince Edward Island Quebec (West of Long.63W), Ontario (East of Long 90 W) (Ottawa), Nunavut (East) and NW Territories ( Long.. W 68-85 ) Ontario (West of Long. 90 W), Manitoba, NW Territories (Long. W 85-102), East Saskatchewan, Nunavut (Central) Alberta Yukon Time Canary Island Cape Verde Islands

Standard L.S.T Time at 12h U.T or 17-30 I.S.T. h +1 - 6 -4 +6 -4

h 13 06 08 18 08

m 00 00 00 00 00

- 3*

09 00*

- 3* - 4* +2 +7 +1

09 08 14 19 13

00* 00* 00 00 00

- 3 1/2*

08 30*

- 4*

08 00*

- 5*

07 00*

- 6*

06 00*

- 7* - 8 +1 -1

05 00* 04 00 13 00 11 00

376

STANDARD TIMES LOCAL STANDARD TIME FOR EACH COUNTRY OR AREA THE AHEAD OF ( + ) OR BEHIND ( - ) U.T. OR G.M.T Country or Area

Standard L.S.T Time at 12h U.T or 17-30 I.S.T. h + 11 + 11 +1 - 4* +8

h 23 23 13 08 20

m 00 00 00 00* 00

+ 6 1/2 -5 +1 - 10

18 07 13 02

30 00 00 00

+ 1 -6 +1 - 5* +1 +2 +1 +1 -5 + 2*

13 06 13 07 13 14 13 13 07 14

00 00 00 00* 00 00 00 00 00 00*

Estonia

+2

14

00

El Salvador

- 6

06

00

Ethiopia Falkland Islands Fiji Finland France Germany

+3 -4 +12 +2 +1 +1

15 08 24 14 13 13

00 00 00 00 00 00

Caroline IslandsTruk, Ponape Central African Republic Chile China, People's Republic of Cocos-keeling Islands Colombia Congo Republic Cook Islands Corsica Costa Rica Croatia Cuba Czech Republic Cyprus Dahomey Republic (Africa ) Denmark Ecuador Egypt

Country or Area

Standard L.S.T Time at 12h U.T or 17-30 I.S.T.

h Ghana 0 Gibraltar + 1 Greece +2 Greenland Angmagssalik, -3 W. Coast Thule Area -4 Guam + 10 Guatemala -6 Guiana Dutch (Surinam) -3 French -3 Guyana Republic - 4 Haiti - 5 Hawaiian Islands - 10 Honduras - 6 Hong Kong + 8* Hungary + 1 Iceland 0 India + 5 1/2 Indonesia, Republic -ofSumatra, Java, West +7 & Central Kalimantan Bali, South & East +8 Kalimantan Irian Jaya, Maluku +9 Iran + 3 1/2 Iraq +3 Ireland, Republic of 0 Israel +2 Italy +1*

h 12 13 14

m 00 00 00

09 00 08 00 22 00 06 00 09 09 08 07 02 06 20 13 12 17

00 00 00 00 00 00 00* 00 00 30 --

19 00

20 00 21 00 15 30 15 00 12 00 14 00 13 00*

377

STANDARD TIMES LOCAL STANDARD TIME FOR EACH COUNTRY OR AREA THE AHEAD OF ( + ) OR BEHIND ( - ) U.T. OR G.M.T Country or Area

Standard L.S.T Time at 12h U.T or 17-30 I.S.T.

h Ivory Coast Japan (and Japan Is.) Jordan Kenya Korea (North & South ) Kuwait Laos Latvia Lebanon Liberia Libya Lithuania Luxembourg Madagascar Madeira Malawi Malaysia Maldives Island Malta Manchuria (China) Mariana Island Marquesas Islands Marshall Islands Mauritania Mauritius Mayanmar MexicoMexico City Sonora, Sinaloa, Nayarit, Baja California Sur Baja California

m 00 00 00 00 00 00

Country or Area

0 +9 +2 +3 +9 +3

h 12 21 14 15 21 15

+7 +2 + 2* 0 +2 +3 + 1 +3 - 1*

19 14 14 12 14 15 13 15 11

+2 +8 +5 +1 +8 + 10 - 9 1/2 + 12 0 +4 + 6 1/2

14 20 17 13 20 22 02 24 12 16 18

- 6 - 7

06 05

Monaco Mongolia Morocco Mozambique Nepal Netherlands (Holland) 00 New Caledonia 00 New Hebrides 00* New Zealand 00 Nicaragua 00 Niger 00 Nigeria 00 Norfolk Island 00 Norway 00* Oman (Masira, Muscat, Salalah) 00 Pakistan 00 Papua New Guinea 00 Paraguay 00 Peru 00 Philippines 00 Poland 30 Portugal 00 Puerto Rico 00 Reunion 00 Romania 30 Sakhalin Samoa 00 Sardinia 00

- 8

04

00

Standard Time

L.S.T at 12h U.T or 17-30 I.S.T.

h +1 +8 0* +2 + 5 3/4 +1

h 13 20 12 14 17 13

m 00 00 00* 00 45 00

+ 11 + 11 + 12 - 6 +1 +1 + 11 1/2 + 1* +4

23 23 24 06 13 13 23 13 16

00 00 00 00 00 00 30 00* 00

+5 + 10 - 4 - 5 +8 + 1* +1 - 4 +4 +2 + 11 - 11 +1

17 22 08 07 20 13 13 08 16 14 23 01 13

00 00 00 00 00 00* 00 00 00 00 00 00 00

378

STANDARD TIMES LOCAL STANDARD TIME FOR EACH COUNTRY OR AREA THE AHEAD OF ( + ) OR BEHIND ( - ) U.T. OR G.M.T Country or Area

Standard L.S.T Time at 12h U.T or 17-30 I.S.T. h

Saudi ArabiaJeddah Dhahran Senegal Serbia

+3 +4 0 +1

Sierra Leone Singapore Solomon Islands Somalia South Africa Spain Sri Lanka Sudan Sweden Switzerland Syria Tanzania *  

0 +8 + 11 +3 +2 + 1 + 5 1/2 +2 +1 +1 + 2* +3

h

Country or Area

m

Tangier 15 00 Thailand 16 00 Uganda 12 00 Ukraine 13 00 United Arab Emirates 12 00 USA Aleutian 20 30 USA Hawaii 23 00 USA Pacific 15 00 USA Mountain 14 00 USA Arizona 13 00 USA Central 17 30 USA Eastern 14 00 Uruguay 13 00 Uzbekistan 13 00 Zambia 14 00* Zimbabwe 15 00

Standard L.S.T Time at 12h U.T or 17-30 I.S.T. h 0 +7 +3 +2 +4

h 12 19 15 14 16

m 00 00 00 00 00

- 10* - 10* - 8* - 7* - 7* - 6* - 5* -3 +5 +2 +2

02 02 04 05 05 06 07 09 17 14 14

00* 00* 00* 00* 00* 00* 00* 00 00 00 00

During summer seasons clock time differs from Standard time. Winter time may be kept in these countries. This time is used throughout the year, but may differ from legal time.

PART - VI INDIAN CALENDAR AND EXPLANATION

380

INDIAN CALENDAR EXPLANATORY NOTE The astronomical data included in this section on Indian Calendar have been calculated in accordance with the recommendations of the Calendar Reform Committee, as outlined in its report, and the calculations have been done on the basis of the positions of the Sun, Moon and Planets, as contained in the main tables of the Ephemeris. However, the information on Luni- Solar Calendar in this section have been calculated on the basis of traditional Nirayana Calendric system following the Government’s decision not to disturb the traditional procedure in fixing the days of religious festivals. Certain additional data, which are required for the compilation of an Indian Panchang (Almanac), have also been furnished to meet the requirements of the numerous Panchang makers of this country. The tables of this section have been extended beyond December, 2020 and materials up to April 20, 2021 have been furnished in order to facilitate preparation of Almanacs for one complete Indian year. The longitudes of the Sun, Moon and Planets and certain other data relating to their positions for the period of 2021 covered by this calendar have also been given in separate table for the same purpose. All calculations contained in this section have been done for an adopted Central Station of India situated at 820 30/ longitude East of Greenwich and 230 11/ latitude North (latitude of Ujjain ) and accordingly the timings have been expressed in the local mean time of this Central Station, which is also the Indian Standard Time. This time (I.S.T.) is 5h 30 m ahead on the Universal Time or Greenwich Mean Time. The Calendar used in this section is the ‘National Calendar’ of India as recommended by the Calendar Reform Committee and introduced by the Government of India with effect from the 22 nd March 1957, corresponding to the 1st of Chaitra, 1879 Saka Era. Thereafter, Govt. of India has decided to introduce an all India Nirayana Solar Calendar in addition to the existing National Calendar. This new Calendar has been introduced with effect from 14th April, 2004 corresponding to 1st Vaisakha of 5105 Kali, Kali Era being the Era of this new Calendar and this Calendar have fixed number of days for its months. Dates of the Nirayana Calendar have been indicated in addition to the existing National Calendar. The months of these Calendars, the number of days assigned to each month of the two Calendars, and the dates of the Gregorian calendar corresponding to the first day of each month of both the Calendars are as follows :Months of the National Calendar Chaitra (30 days ; 31 days in a leap-year) Vaisakha (31 days) Jyaishtha (31 days) Ashadha (31 days) Sravana (31 days) Bhadra (31 days) Asvina (30 days) Kartika (30 days) Agrahayana (30 days) Pausha (30 days) Magha (30 days) Phalguna (30 days)

Gregorian date for 1st of the month March 22 ( March 21 in a leap-year) April 21 May 22 June 22 July 23 August 23 September 23 October 23 November 22 December 22 January 21 February 20

Months of the Nirayana Calendar Vaisakha (31 days) Jyaishtha (31 days) Ashadha (31 days) Sravana (31 days) Bhadra (31 days) Asvina (30 days) Kartika (30 days) Agrahayana (30 days) Pausha (30 days) Magha (30 days) Phalguna (30 days ; 31 days in a leap-year) Chaitra (30 days)

Gregorian date for 1st of the month April 14 May 15 June 15 July 16 August 16 September 16 October 16 November 15 December 15 January 14 February 13 March 15

Different items included in this section are elaborated below :The Sunrise and Sunset times, calculated for the Central Station, relate respectively to the appearance and disappearance of the upper limb of the Sun on the horizon. The amount of horizontal refraction taken for this purpose is 31/ and the semi-diameter of the Sun as 16/ , so that at the given times of Sunrise and Sunset, the centre of the Sun actually 47/ below the horizon. The apparent noon is the local mean time of the sun’s meridian passage, i.e., the mid-day reduced to the above standard meridian of India (82½0 E. Longitude).

381

INDIAN CALENDAR The ending moments of tithis, nakshatras and yogas have been given in Indian Standard Time and shown against their ordinal numbers. The phenomena being geocentric ones, their timings in I.S.T. are applicable for the whole of India without any modification. These timings reduced by a deduction of 5h 30m would give the G.M.T. applicable for all places on the earth. The tithi is based on the difference of longitude of the Moon and that of the Sun. A tithi is completed when the longitude of the Moon gains exactly 120 or its integral multiple on that of the Sun and as such there are 30 tithis in lunar month. A difference in longitude of 120 indicates the ending of the 1st tithi, 240 that of the 2nd tithi and so on. The number of tithis have been shown from Sukla 1 to Sukla 15 (full-moon) and again from Krishna 1 to Krishna 14 and Krishna 30 (new moon), using the symbols S and K for Sukla paksha (waxing Moon)and Krishna paksha (waning Moon) respectively. A nakshatra is completed when the nirayana longitude of the Moon as measured from the initial point attains a value of 13° 20/ or an integral multiple thereof. When this longitude is 13° 20/ the 1st nakshatra ends and so on. There are thus 27 nakshatras in a sidereal month and the nakshatra divisions occupy fixed positions in the sphere of stars. In the case of the Sun the calculation also has been done on the same basis. But in this case, the time of Sun’s entry into a nakshatra-division has been stated, whereas in the case of the Moon, the time of its exit from the division has been given. Like nakshatras, there are 27 yogas. Yoga is calculated from the sum of nirayana longitudes of the Sun and the Moon. When the sum amounts to 13° 20/, the first yoga ends; when it amounts to 26° 40/, the second yoga ends, and so on. Thus, in all 27 yogas cover 360°. Names of the nakshatras and yogas have been given at the bottom of the table. It will be seen that two of the names Vyatipata and Vaidhriti occur also under Phenomena, where they have been treated as special yogas and calculated by a somewhat different rule. The 27 yogas which have got very little astronomical significance have been included in this publication only to meet the needs of Panchang where the yoga is also one of the components. For the purpose of calculation of rasis, nakshatras and yogas, an initial point which occupies a fixed position on the ecliptic has been adopted as the origin for the measurement of longitudes. The position of this initial point coincides with the vernal equinoctial point of vernal equinox day of 285 A.D. For the purpose of assigning a precise position to it, the tropical longitude of this initial point has been adopted as 23° 15/ 00// for 0h on 21st March, 1956. The tropical longitude of this fixed initial point for any day is known as ayanamsa. The longitude of a celestial body measured from this initial point is known as nirayana longitude.

The entry into different rasis of the Moon and of the Sun have been shown at the bottom of the relevant pages of the calendar and the calculations have been done on the same basis as in the case of nakshatras, utilising the nirayana longitudes. Rasis, which cover arc of 300 of the zodiac belt, are measured along the ecliptic from the above-mentioned initial point. The tithi, nakshatra and yoga as are current at Sunrise at the Central Station, have been shown against the date with their ending moments in I. S. T. When the time of these or any other phenomena falls after midnight and before the next Sunrise, the time has been expressed after adding 24h to the I.S.T. without changing the date after midnight in order to maintain continuity of time-reckoning from one Sunrise to the next, in conformity with the system followed in Indian religious calendars. The solar months recommended for the religious calendar, such as, Saura Vaisakha, Saura Jyaishtha, etc., by the Calendar Reform Committee in 1955 have been reckoned from the moments when the apparent longitude of the Sun equals 23° 15/, 53° 15/ and so on. The calculation for this purpose thus has not been done with a variable ayanamsa, as in the case of rasis and nakshatras, but with a fixed ayanamsa of 23° 15/ . These months are shown for purpose of illustration only, but are not used in practice for actual luni-solar adjustment.

382

INDIAN CALENDAR The lunar months for determining the dates of religious festivals are reckoned from one New-Moon to the next (Sukladi system or mukhya mana). The lunar month for this purpose is named after the Nirayana or Sidereal solar month in which the initial New-Moon from which the month starts, falls. Phenomena mentioned in the table include New-Moon, Full-Moon, Sayana Vyatipata (when the sum of the tropical longitudes of the Sun and the Moon equals 1800), Sayana Vaidhriti (when the above sum amounts to 3600), eclipses, heliacal rising and setting of Venus, Mars and Jupiter and Jupiter’s transit into rasis. The principal festivals of different states have been fixed on the basis of the criterion stated here, but in doing so, the rules and conventions of the states concerned have been followed as far as practicable.

LIST OF HOLIDAYS The list of holidays for the Government of India as well as for the State Governments have been prepared in a consolidated form and the dates fixed for them, have been shown in a separate table under the head ‘Principal Festivals for Holidays’. The principal festivals of Moslems, Parsis, Jewish and Christians have also been shown separately.

AYANAMSA The value of ayanamsa has been given in the calendar for the first day of the month and also in a separate table at the end at interval of three days.

The Sayana Vyatipata and Sayana Vaidhriti, reported under the column “Phenomena”, are calculated on the basis of defination given in the report of Calendar Reform Committee. These are classified as the Calendar Reform Committee view and no way related to the ‘mahapata yoga’ defined in some Indian traditional texts (siddhantic treatises).

383

HELIACAL RISING AND SETTING OF PLANETS, 2021 (JANUARY TO APRIL) Planet

National Date

Mercury rises in the West Mercury sets in the West Mercury rises in the East Mercury sets in the East Venus sets in the East Venus rises in the West Jupiter sets in the West Jupiter rises in the East Saturn sets in the West Saturn rises in the East

Pausha Magha Magha Chaitra Magha Chaitra Pausha Magha Pausha Magha

17, 1942 Saka 14, 1942 Saka 24, 1942 Saka 10, 1943 Saka 28, 1942 Saka 18, 1943 Saka 26, 1942 Saka 23, 1942 Saka 19, 1942 Saka 20, 1942 Saka

Nirayana Date

Gregorian Date

Pausha 24, 5121 Kali Magha 21, 5121 Kali Phalguna 1, 5121 Kali Chaitra 17, 5121 Kali Phalguna 5, 5121 Kali Vaisakha 5, 5122 Kali Magha 3, 5121 Kali Magha 30, 5121 Kali Pausha 26, 5121 Kali Magha 27, 5121 Kali

Jan. Feb. Feb. Mar. Feb. Apr. Jan. Feb. Jan. Feb.

7, 2021 3, 2021 13, 2021 31, 2021 17, 2021 19, 2021 16, 2021 12, 2021 9, 2021 9, 2021

Time (I.S.T) h m 11 36 23 18 14 04 25 52 10 10 5 41 26 45 10 06 15 37 26 00

N.B.- Here East means the eastern horizon or west of the Sun and West means the western horizon or east of the Sun.

RETROGRESSION OF PLANETS, 2021 (JANUARY TO APRIL) Planet

Mercury Mercury Uranus

Retrograde Direct Direct

National Date

Nirayana Date

Gregorian Date

Time (I.S.T)

Magha 10, 1942 Saka Phalguna 2, 1942 Saka Pausha 24, 1942 Saka

Magha 17, 5121 Kali Phalguna 9, 5121 Kali Magha 1, 5121 Kali

Jan. 30, 2021 Feb. 21, 2021 Jan. 14, 2021

h 21 6 14

m 19 35 08

MEAN RAHU, 2021 Date

Longitude 0

Jan.

Jan.

-2 8 18 28

54 54 53 53

/

52 20 48 16

Date

Longitude

//

17 29 41 54

0

Feb.

Mar.

7 17 27 9

52 52 51 51

/

45 13 41 09

Longitude

//

06 18 30 43

ECLIPSES, 2021 (JANUARY TO APRIL) _

Date

Mar. Apr.

19 29 8 18 28

0

/

//

50 50 49 49 48

37 06 34 02 30

55 07 20 32 44

384

INDIAN CALENDAR SAKA ERA 1941

Makara : Tapas Winter (Sisira), 1st Month

Month of PAUSHA (30 days)

(Nirayana) 8 Pausha, 5120 Kali Era to (Nirayana) 7 Magha, 5120 Kali Era

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

h

m

Tithi No. Ending Moment h m

Sunset

Nakshatra No.

Ending Moment h m

1

2019 A.D. Sun Dec. 22

6 37.3

11

58.3

17

19.5

K 11 15

22.4

15

18

37.7

2 3 4 5

Mon Tue Wed Thu

23 24 25 26

6 6 6 6

37.8 38.3 38.7 39.2

11 11 11 12

58.8 59.3 59.8 00.3

17 17 17 17

20.0 20.5 21.1 21.6

12 13 14 K 30

13 12 11 10

42.0 18.8 17.6 43.1

16 17 18 19

17 16 16 16

6 7 8 9 10

Fri Sat Sun Mon Tue

6 6 6 6 6

39.6 40.0 40.4 40.7 41.1

12 12 12 12 12

00.8 01.3 01.8 02.3 02.7

17 17 17 17 17

22.2 22.8 23.4 24.0 24.6

S

1 2 3 4 5

10 11 12 13 16

39.7 10.2 15.9 54.8 01.7

20 21 22 23 24

11 12 13 14 15

27 28 29 30 31 2020 A.D. Wed Jan. 1 Thu 2 Fri 3 Sat 4 Sun 5

6 6 6 6 6

41.4 41.7 42.0 42.3 42.5

12 12 12 12 12

03.2 03.7 04.1 04.6 05.0

17 17 17 17 17

25.3 25.9 26.6 27.2 27.9

6 7 8 9 S 10

18 21 23 25 27

27.6 00.6 26.8 32.8 07.3

16 17 18 19 20

Mon Tue Wed Thu Fri

6 7 8 9 10

6 6 6 6 6

42.7 42.9 43.1 43.3 43.4

12 12 12 12 12

05.6 06.0 06.4 06.8 07.2

17 17 17 17 17

28.6 29.3 30.0 30.6 31.3

11 12 13 14 S 15

28 28 27 26 24

21 22 23

Sat Sun Mon

11 12 13

6 43.5 6 43.6 6 43.6

12 12 12

07.6 08.0 08.4

17 17 17

32.0 32.8 33.5

K

24

Tue

14

6 43.7

12

08.7

17

34.2

25

Wed

15

6 43.7

12

09.1

17

34.9

K

26 27

Thu Fri

16 17

6 43.7 6 43.6

12 12

09.6 10.0

17 17

35.6 36.3

28 29 30

Sat Sun Mon

18 19 20

6 43.6 6 43.5 6 43.4

12 12 12

10.2 10.5 10.8

17 17 17

37.0 37.8 38.5

6 7 (8 9 K 10 K 11

S

Yoga No. Ending Moment h m

39.6 59.1 41.1 50.1

6 (7 8 9 10 11

8 30 27 25 23 22

39.0 00.6) 34.6 24.5 33.7 05.6

17 18 20 22 25

30.0 43.1 29.7 46.6 27.6

12 13 14 15 16

21 20 20 20 21

02.7 26.4 16.4 30.4 03.8

25 26 26 27 1

28 7 10 12

22.7 19.8 05.4 27.2

17 18 19 20 21

21 22 23 23 23

49.8 39.8 24.1 53.5 59.5

02.5 14.8 44.4 34.7 51.3

2 3 4 5 6

14 15 15 15 14

15.4 23.9 50.8 37.6 48.5

22 23 24 25 26

23 22 21 19 16

37.2 42.1 13.8 13.9 45.8

1 22 2 20 3 17

41.2 12.3 32.6

7 8 9

13 11 9

30.0 49.6 55.3

4 14

49.7

55.2 56.8) 06.8

54.4 45.3 24.6 58.4) 32.6

10.7

7 29 28

13 10 7 27 24

5 12

10 (11 12

27 1 2 (3 4 5

21

12.3

13 14

26 25

30.6 12.6

6 7

18 15

02.1 05.5

15 16 17

24 23 23

15.6 41.2 30.3

8 9 10 (11

12 10 7 30

24.9 02.2 58.0 12.9)

9 7 29 28 26 26

41.8 28.2 33.7) 01.0 51.6 06.2

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

385

INDIAN CALENDAR SAKA ERA 1941 Month of PAUSHA (30 days)

Uttarayana Dakshina Gola

Ayanamsa on 1st : 24° 07/ 53//

(Nirayana) 8 Pausha, 5120 Kali Era to (Nirayana) 7 Magha, 5120 Kali Era

20

10

21 22

11 12

23

13

24

14

25

15

26 27 28 29 30

16 17 18 19 Jan. 20

Festivals

1- Uttarayana day, Saphala Ekadasi. 4- Sayana Vyatipata (20h 56m.8) 5- New Moon (10h 43m.1) 5- Solar Eclipse (visible in India)

4- Birthday of Sadhu T. L.Vaswani (Sindhi),Vakula Amavasya (Odisha). 5- Jor Mela- 3 days (Punjab).

15- Samba Dasami (Odisha). 16- Putrada ekadasi,Vaikuntha Ekadasi (S India).

PA U S H A

6 7 8 9

Phenomena

12- Guru Govind Singh’s Birthday (according to tithi).

21- Enters Uttarashadha nak. (19h 35m.5) 23- Saura Maghadi (29h 20m.3)

C H AA N D R A

16 17 18 19

8- Enters Purvashadha nak. (17h 36m.1)

P A U S HA

11 12 13 14 15

27 28 29 30 31 2020A.D. Jan. 1 2 3 4 5

S A U R A

6 7 8 9 10

MAG HA

26

SAU RA

5

C H AA N D R A M A R G AS H I R S H A

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2019 A.D. 1- Enters Tropical 1 Dec. 22 23 Capricornus 2 24 (9h 49m.4) 3 25 4

30- Enters Tropical Aquarius (20h 24m.6)

18- Jupiter rises in the East (30h 33m) 18- Sayana Vaidhriti (7h 19m.0) 20- Full Moon 20- Arudra Darshanam (24h 51m.3) (Purvarunodaya) (S. India), Paushi Purnima, Pushyabhisheka Yatra.

29- Sayana Vyatipata (29h 19m.3)

23- Lohri (Punjab,J&K), Ganesha Sankashta Chaturthi. 24- Bhogi(S. India), Birthday of Sant Paramanand (Sindhi). 25- Pongal (S. India), Makara Snana,Tila Samkranti, Tai Pongal(Kerala), Tamil New Year’s Day, Magha Bihu (Assam), Makara Samkranti (N.India), Makara Samkranti. 26- Mattu Pongal or Kanuvu(S. India), 27- Birthday of Swami Vivekananda (according to tithi),Ashtaka (Mamashtaka). 30- Sattila Ekadasi.

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Vrischika 2, 11h 52m.7; Dhanus 4, 16h 41m.1; Makara 6, 23h 45m.1; Kumbha 9, 9h 34m.6; Mina 11, 21h 38m.3; Mesha 14, 10h 05m.4; Vrisha 16, 20h 36m.4; Mithuna 18, 27h 49m.1; Karkata 21, 7h 52m.0; Simha 23, 9h 55m.3; Kanya 25, 11h 28m.3; Tula 27, 13h 49m.2; Vrischika 29, 17h 47m.6; Sun enters :- Nirayana Makara 24, 26h 08m.1.

386

INDIAN CALENDAR SAKA ERA 1941

Kumbha : Tapasya Winter (Sisira), 2nd Month

Month of MAGHA (30 days)

(Nirayana) 8 Magha, 5120 Kali Era to (Nirayana) 7 Phalguna, 5120 Kali Era

h

m

Tithi No. Ending Moment h m

11.0 11.4 11.6 11.9 12.1

17 17 17 17 17

39.2 39.9 40.6 41.3 42.0

K 12 13 14 K 30 S 1

12 12 12 12 12

12.4 12.6 12.8 13.0 13.2

17 17 17 17 17

42.7 43.4 44.1 44.8 45.5

S

40.8 40.4 40.0 39.6 39.1

12 12 12 12 12

13.3 13.5 13.6 13.7 13.8

17 17 17 17 17

46.2 46.8 47.5 48.2 48.8

6 7 8 9 S 10

38.7 38.2 37.7 37.2 36.6

12 12 12 12 12

13.9 14.0 14.0 14.1 14.2

17 17 17 17 17

49.5 50.1 50.7 51.3 52.0

11 12 13 14 S 15

10

6 36.1

12

14.2

17

52.6

K

Tue

11

6 35.5

12

14.2

17

53.2

23 24 25

Wed Thu Fri

12 13 14

6 34.9 6 34.3 6 33.7

12 12 12

14.2 14.2 14.2

17 17 17

53.8 54.3 54.9

K

26 27 28 29 30

Sat Sun Mon Tue Wed

15 16 17 18 19

6 6 6 6 6

12 12 12 12 12

14.1 14.1 14.0 13.9 13.9

17 17 17 17 17

55.5 56.1 56.6 57.2 57.7

7 8 9 K 10 K 11

Date Week Gregorian Day Date

h

m

Apparent Noon h m

2020 A.D. Tue Jan. 21 Wed 22 Thu 23 Fri 24 Sat 25

6 6 6 6 6

43.3 43.1 43.0 42.8 42.6

12 12 12 12 12

6 7 8 9 10

Sun Mon Tue Wed Thu

26 27 28 29 30

6 6 6 6 6

42.3 42.1 41.8 41.5 41.1

11 12 13 14 15

Fri Sat Feb. Sun Mon Tue

31 1 2 3 4

6 6 6 6 6

16 17 18 19 20

Wed Thu Fri Sat Sun

5 6 7 8 9

6 6 6 6 6

21

Mon

22

1 2 3 4 5

Sunrise

33.0 32.4 31.7 31.0 30.3

Sunset

Nakshatra No.

Ending Moment h m

Yoga No. Ending Moment h m

25 25 26 27 28

45.3 49.1 17.9 12.0 31.6

18 19 20 21 22

23 24 25 26 28

43.1 19.8 20.6 45.9 35.5

12 13 14 15 16

28 27 26 26 26

46.8 39.8 52.0 23.7 14.7

2 30 3 3 8 4 10 5 13

15.9 22.4 46.3 19.7

23 23 24 25 26

6 9 12 15

48.7 22.9 13.3 12.4

17 18 19 20 21

26 26 27 28 29

24.3 51.3 31.6 21.1 12.9

15 18 20 21 21

52.2 11.2 04.1 19.6 50.0

27 1 2 3 4

18 20 23 24 25

09.8 53.5 11.2 52.3 49.2

22 23 24 25 26

29 30 30 30 29

58.6 29.4 36.5 12.7 12.9

21 20 18 16 13

31.3 23.9 31.9 02.1 03.2

5 6 7 8 9

25 25 24 22 19

58.5 20.9 00.6 05.0 43.2

27 1 2 3 4

27 25 22 19 15

34.9 19.3 29.1 09.8 28.0

1 9 (2 30 3 26

45.2 18.5) 53.3

10

17

05.7

5

11

31.6

11

14

23.2

4 23 5 20 6 18

39.8 46.8 21.5

12 13 14 (15

11 9 7 30

46.3 24.9 27.6 00.9)

6 (7 8 9 10

7 27 23 20 16

28.7 27.7) 36.5 02.1 50.1

29.6 14.2 35.9 33.1 02.6

16 17 18 19 20

29 28 29 30 -

09.0 53.6 13.7 06.4 -

11 12 13 14 15

14 11 10 8 7

04.8 48.4 01.4 42.6 49.5

16 15 14 14 15

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

387

INDIAN CALENDAR SAKA ERA 1941 Month of MAGHA (30 days)

Uttarayana Dakshina Gola

Ayanamsa on 1st : 24° 07/ 58//

(Nirayana) 8 Magha, 5120 Kali Era to (Nirayana) 7 Phalguna, 5120 Kali Era

24

5

25

6 7 8 9

26 27 28 29

10

30

11

31

4- Enters Sravana nak. (21h 51m.4)

4- New Moon (27h 12m.0)

A

2 3 4

16

5

17 18 19 20

6 7 8 9

21 22 23 24 25

10 11 12 13 14

26 27 28 29

15 16 17 18

30

Feb. 19

C H A A N D R A

13 14 15

M A G H A

M

1 S A U R A

Feb.

SAURA PHALGUNA

12

Festivals 1- Martyrdom Day of Hemu Kalani (Sindhi). 2- Meru Trayodasi (Jain). 3- Netaji’s Birthday, Ratanti Kalika Puja. 4- Mauni Amavasya, Tai Amavasya, Makara Vavu (Kerala). 5- Magha Sukladi. 6- Republic Day.

A

4

H

22 23

Phenomena

G

2 3

C H AA N D R A P A US HA

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D. 1 Jan. 21

13- Sayana Vaidhriti (15h 38m.9)

8- Birthday of Lala Lajpat Rai, Varada Chaturthi,Tila Chaturthi, Kunda Chaturthi, Ganesa Puja (Bengal). 10- Martyr’s Day (Mahatma Gandhi Commemoration Day), Vasanta Panchami, Sarasvati Puja, Sri Panchami. 12- Ratha Saptami (Purvarunodaya), Vidhana Saptami, Arogya Saptami. 13- Bhismashtami.

16- Jaya Ekadasi, Bhaimi Ekadasi (Bengal).

17- Enters Dhanishtha nak. (24h 57m.5)

23- Saura Phalgunadi (18h 04m.9)

30- Enters Trop. Pisces (10h 27 m.0) 30- Enters Satabhisaj (29h 29m.7)

20- Full Moon (13h 03m.2)

25- Sayana Vyatipata (14h 22m.7)

17- Bhishma Dvadasi. 18- Desert Festival- 3 days(Jaisalmer). 19- Floating Festival (Tai Poosam). 20- Maghi Purnima, Guru Ravi Das’s Birthday (according to tithi).

26- Vaikkatashtami (Kerala) 27- Ashtaka (Sakashtaka), Janaki Janma. 29- Birthday of Swami Dayananda Saraswati (Founder of Arya Samaj)(according to tithi). 30- Vijaya Ekadasi, Sivaji Jayanti.

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Dhanus 1, 23h 43m.1; Makara 4, 7h 39m.6; Kumbha 6, 17h 39m.3; Mina 8, 29h 29m.5; Mesha 11, 18h 09m.8;Vrisha 13, 29h 40m.3; Mithuna 16, 13h 59m.8; Karkata 18, 18h 24m.3; Simha 20, 19h 43m.2; Kanya 22, 19h 43m.0; Tula 24, 20h 22m.9; Vrischika 26, 23h 18m.7; Dhanus 28, 29h 13m.7; Sun enters :- Nirayana Kumbha 24, 15h 03m.6.

388

INDIAN CALENDAR SAKA ERA 1941

Mina : Madhu Spring (Vasanta), 1st Month

Month of PHALGUNA (30 days)

(Nirayana) 8 Phalguna, 5120 Kali Era to (Nirayana) 7 Chaitra, 5120 Kali Era

h

m

Tithi No. Ending Moment h m

13.8 13.7 13.6 13.4 13.3

17 17 17 17 18

58.2 58.8 59.3 59.8 00.3

K 12 13 14 K 30 S 1

12 12 12 12 12

13.1 13.0 12.8 12.7 12.5

18 18 18 18 18

00.8 01.8 01.8 02.3 02.7

S

21.6 20.7 19.8 19.0 18.1

12 12 12 12 12

12.3 12.1 11.9 11.7 11.4

18 18 18 18 18

03.2 03.7 04.1 04.6 05.0

6 7 8 9 S 10

6

17.2

12

11.2

18

7 8

6 6

16.3 15.3

12 12

11.0 10.7

Mon Tue

9 10

6 6

14.4 13.5

12 12

21

Wed

11

6

12.6

22 23 24

Thu Fri Sat

12 13 14

6 6 6

25

Sun

15

26 27 28 29 30

Mon Tue Wed Thu Fri

16 17 18 19 20

Date Week Gregorian Day Date

h

m

Apparent Noon h m

2020 A.D. Thu Feb. 20 Fri 21 Sat 22 Sun 23 Mon 24

6 6 6 6 6

29.6 28.8 28.1 27.3 26.5

12 12 12 12 12

6 7 8 9 10

Tue Wed Thu Fri Sat

25 26 27 28 29

6 6 6 6 6

25.7 24.9 24.1 23.3 22.4

11 12 13 14 15

Sun Mar. Mon Tue Wed Thu

1 2 3 4 5

6 6 6 6 6

16

Fri

6

17 18

Sat Sun

19 20

1 2 3 4 5

Sunrise

Sunset

Nakshatra No.

Ending Moment h m

Yoga No. Ending Moment h m

16 17 19 21 23

00.1 21.5 03.2 02.0 15.4

20 21 22 23 24

7 9 11 13 16

27.7 13.4 19.4 42.7 20.7

16 17 18 19 20

7 7 7 7 8

18.9 07.7 12.9 32.0 03.2

2 25 3 28 4 4 6 5 9

40.2 12.2 44.9 09.8

25 26 27 1 2

19 22 25 28 -

10.4 08.1 08.2 02.7 -

21 8 22 9 23 10 24 11 25 12

44.5 33.4 26.4 18.9 04.3

11 12 13 14 13

16.3 53.3 50.5 00.4 19.2

2 3 4 5 6

6 8 10 11 11

42.0 55.1 31.6 23.4 25.8

26 27 1 2 3

12 12 12 11 9

35.3 43.8 22.2 24.7 47.7

05.4

11 11

47.4

7

10

38.4

18 18

05.9 06.3

18 18

06.7 07.1

29.2 8 31.7 9 04.2) (10 17.7 11 23.7 12

9 6 28 25 22

04.9 52.2 09.8) 08.8 01.5

30.4 35.1) 06.3 10.9

10.5 10.2

12 9 13 6 (14 27 S 15 23 K 1 19

4 7 (5 28 6 25 7 21 8 16 9 12

57.2 34.3

12

10.0

18

07.5

2 15

33.9

13

18

59.9

11.6 10.7 09.7

12 12 12

09.7 09.4 09.1

18 18 18

07.9 08.3 08.7

16 13 12

08.8

12

08.8

18

09.1

59.5 51.0 17.4 25.7) 19.7

14 15 16

6

3 11 4 8 K 5 6 (6 28 7 27

17

6 6 6 6 6

07.8 06.8 05.9 04.9 03.9

12 12 12 12 12

08.6 08.3 08.0 07.7 07.4

18 18 18 18 18

09.5 09.9 10.3 10.7 11.1

8 9 K 10 11 K 12

00.2 24.3 26.7 59.9 -

18 19 20 21 22

27 27 28 29 -

15.7 59.5 20.0

10 (11 12 13 14

8 27 24 20 17

11.5 58.3) 03.5 34.5 37.3

11

23.4

15 15

15.7

11 11 13 14 17

12.3 46.1 00.7 49.6 05.0

16 17 18 19 20

31.2 22.6 46.6 38.2 51.7

13 12 11 11 11

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

389

INDIAN CALENDAR SAKA ERA 1941 Month of PHALGUNA (30 days)

Uttarayana Dakshina Gola

Ayanamsa on 1st : 240 08/ 02//

(Nirayana) 8 Phalguna, 5120 Kali Era to (Nirayana) 7 Chaitra, 5120 Kali Era

6 7 8 9

20

10

21 22 23 24 25

11 12 13 14 15

26 27 28

16 17 18

1- Maha Sivaratri (Kashmir). 2- Maha Sivaratri, Sivaratri (S. India). 4- New Moon (21h 02m.0)

12- Holashtaka. P H A L G U N A

16 17 18 19

Festivals

8- Sayana Vaidhriti (19h 53m.1)

14-Enters Purva Bhadrapada nak. (11h 42m.6)

19- Full Moon (23h 17m.7) 20- Sayana Vyatipata (29h 49m.8)

A

1 2 3 4 5

Phenomena

6- Birthday of Sri Ramakrishna (according to tithi).

C H A A N D R

Mar.

S A U R A

11 12 13 14 15

25 26 27 28 29

SAU RA C HAIT RA

6 7 8 9 10

P H A L G U N A

CHAANDRA M AG HA

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D. 1 Feb. 20 2 21 3 22 4 23 5 24

23-Saura Chaitradi (14h 36m.0)

27-Enters Uttara Bhadrapada nak. (20h 13m.5) 29-Enters Trop. Aries (9h 19m.6)

16- Amlaki Ekadasi, Govinda Dvadasi. 18- Masi Magham. 19- Holikadahana,Birthday of Sri Chaitanya, Dolyatra. 20- Holi, Hola, Vasantotsava.

23- Ranga Panchami. 24- Bijoy Govindaji Halangkar (Manipur). 26- Varsitaparambha (Jain), Sitalashtami.

29- Papamochani Ekadasi (Smarta). 30- Indian Year Ending day,Vanjuli Mahadvadasi, Mahavishuva day, Ekadasi (Vaishnava & 1942 S.E. Vidhava). Chtr. 1- Indian New Year’s Day, 1 Mar. 21 MahaVaruni (after 19h 40m.0). 0 N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½ E. Long. Moon enters :- Makara 1, 13h 52m.0; Kumbha 3, 24h 29m.1; Mina 6, 12h 27m.1; Mesha 8, 25h 08m.2; Vrisha 11, 13h 18m.2; Mithuna 13, 23h 03m.5; Karkata 15, 28h 54m.9; Simha 18, 6h 52m.2; Kanya 20, 6h 22m.1; Tula 21, 29h 34m.8; Vrischika 24, 6h 41m.0; Dhanus 26, 11h 12m.3; Makara 28, 19h 25m.0; Sun enters: Nirayana Mina 24, 11h 53m.8. 29 30

19 Mar. 20

390

INDIAN CALENDAR SAKA ERA 1942 Month of CHAITRA(31 days)

Mesha : Madhava Spring (Vasanta), 2nd Month

(Nirayana) 7 Chaitra, 5120 Kali Era to (Nirayana) 7 Vaisakha, 5121 Kali Era

Date Week Gregorian Day Date

Sunrise

Nakshatra No.

m

Tithi No. Ending Moment h m

Ending Moment h m

Yoga No. Ending Moment h m

h

m

Apparent Noon h m

Sunset

6 6 6 6 5

03.0 02.0 01.0 00.0 59.1

12 12 12 12 12

07.1 06.8 06.5 06.2 05.9

18 18 18 18 18

11.4 11.8 12.2 12.6 12.9

K 12 13 14 K 30 S 1

7 10 12 14 17

56.2 08.4 30.6 58.2 27.3

23 24 25 26 27

19 22 25 28 -

39.5 26.6 21.1 18.9 -

21 22 23 24 25

12 13 13 14 15

21.5 02.4 50.5 42.6 36.0

2 3 4 5 6

19 22 24 26 27

53.8 12.9 18.2 01.8 15.1

27 1 2 3 4

7 10 12 15 17

16.3 09.2 52.0 17.5 17.7

26 27 1 2 3

16 17 17 18 18

27.9 14.9 52.7 15.3 18.0

7 8 9 S 10 11

27 27 26 24 22

50.2 40.6 43.4 58.7 30.4

5 6 7 8 9

18 19 19 18 17

43.9 29.0 28.3 40.5 08.1

4 5 6 7 8

17 16 15 13 10

53.1 55.5 21.4 09.2 19.9

12 19

25.3

10

14

57.1

52.3 11 01.8 12 05.1 13 13.7) (14 39.2 15

12 9 6 27 24

16.0 15.4 06.9 02.7) 14.9

9 (10 11 12 13

6 27 22 18 14

57.3 07.1) 56.7 35.1 11.6

14

9

55.5

3 21

32.2

16

21

54.7

4 5 6 7

19 17 16 16

02.1 16.2 19.1 11.8

17 18 19 20

20 19 19 19

11.5 12.7 02.3 40.7

15 (16 17 18 19 20

5 26 23 20 19 18

56.0 21.7) 19.3 53.9 07.9 01.3

8 9 K 10 11 12 K 13

16 18 20 22 24 27

51.8 12.0 04.1 17.9 43.4 12.3

21 22 23 24 25 25

21 23 25 28 7

04.1 05.6 35.7 24.6 22.8

21 22 23 24 25 26

17 17 17 18 19 20

31.2 32.5 58.2 41.0 33.8 30.4

h

1 2 3 4 5

Sat Sun Mon Tue Wed

2020 A.D. Mar. 21 22 23 24 25

6 7 8 9 10

Thu Fri Sat Sun Mon

26 27 28 29 30

5 5 5 5 5

58.1 57.1 56.1 55.2 54.2

12 12 12 12 12

05.6 05.3 05.0 04.7 04.4

18 18 18 18 18

13.3 13.7 14.1 14.4 14.8

11 12 13 14 15

Tue Wed Apr. Thu Fri Sat

31 1 2 3 4

5 5 5 5 5

53.2 52.3 51.3 50.3 49.4

12 12 12 12 12

04.1 03.8 03.5 03.2 02.9

18 18 18 18 18

15.2 15.5 15.9 16.3 16.7

16

Sun

5

5

48.4

12

02.6

18

17.0

17 18 19

Mon Tue Wed

6 7 8

5 5 5

47.5 46.6 45.6

12 12 12

02.4 02.1 01.8

18 18 18

17.4 17.8 18.2

20

Thu

9

5

44.7

12

01.5

18

18.5

21

Fri

10

5

43.8

12

01.3

18

18.9

22 23 24 25

Sat Sun Mon Tue

11 12 13 14

5 5 5 5

42.9 42.0 41.1 40.2

12 12 12 12

00.0 00.7 00.5 00.2

18 18 18 18

19.3 19.7 20.1 20.5

26 27 28 29 30 31

Wed Thu Fri Sat Sun Mon

15 16 17 18 19 20

5 39.3 12 5 38.4 11 5 37.6 11 5 36.7 11 5 35.9 11 5 35.1 11

00.0 59.7 59.5 59.3 59.1 58.9

18 18 18 18 18 18

20.9 21.3 21.7 22.1 22.5 22.9

S

13 14 S 15 (K 1 2

K

15 12 8 28 24

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

391

INDIAN CALENDAR SAKA ERA 1942 Month of CHAITRA (31 days)

Uttarayana Uttara Gola

Ayanamsa on 1st : 240 08/ 06//

(Nirayana) 7 Chaitra, 5120 Kali Era to (Nirayana) 7 Vaisakha, 5121 Kali Era

26

7 8 9 10

27 28 29 30

11

31

12 Apr.

1

13 14 15

2 3 4

16

5

17

6

18 19 20

7 8 9

21 22 23

10 11 12

24

13

25

14

26 27 28 29 30 31

15 16 17 18 19 20

Phenomena

3 -SayanaVaidhriti (23h 17m.1) 4- New Moon (14h 58m.2)

9- Jupiter enters Makara (27h 54m.2)

Festivals

1- Indian New Year’s Day, Maha Varuni (after 19h 40m.0 ). 2- Madhukrishna Trayodasi, Varuni (upto 10h 08m.4 ) 5- Chaitra Sukladi (Gudi Padava, Ugadi),Telugu New Year’s Day, Vasanta Navaratrarambha, Cheti Chand (Sindhi New Year’s Day). 7- Gauri Tritiya (Gangaur), Sarhul (Bihar), Andolana Tritiya. 9- Sri (Lakshmi) Panchami. 10- Skanda Shashthi. 11- Vasanti Pujarambha, Oli begins(Jain). 12- Asokashtami,Annapurna Puja, Mela Bahu Fort (Jammu). 13- Rama Navami.

11-Enters Revati nak. (6h 57m.9) C H A I T R A

6

C H A A N D R A

24 25

C H A I T R A

4 5

S A U R A

22 23

S AUR A VAI SAK HA

2 3

CHANDRA PHALGUNA

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D Mar. 21 1

15- Kamada Ekadasi. 16-Sayana Vyatipata (24h 40m.1)

19-Full Moon (8h 05m.1)

23-Saura Vaisakhadi (22h 41m .9) 24-Enters Asvini nak. (20h 23m .0)

28-SayanaVaidhriti (27h 20m.2)

16- Birthday anniversary of Swami Leela Shah (Sindhi). 17- Ananga Trayodasi, Mahavira Jayanti (Jain), Damanaka Chaturdasi. 18- Panguni Uttiram. 19- Chaitri Purnima, Hanumat Jayanti (S. India), Oli ends(Jain), Trivandrum Arat (Kerala).

24- Chaitra Samkranti, Chadaka Puja (Bengal), Cheiraoba (Manipur), Visu (Kerala), Vaisakhi (H.P, Punjab, Haryana,Delhi,Odisha), Mesha Samkranti (Odisha), Rangali Bihu (Assam). 25- Dr. B.R.Ambedkar Jayanti, Bahag Bihu (Assam), Shilhenba (Manipur),Vaisakhadi(Bengal), Mesadi (T.N.), Beginning of Nirayana 5121 KE. 29- Varuthini Ekadasi, Sri Vallabhacharya Jayanti.

30-Enters Trop. Taurus (20h 15m.5) N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Kumbha 1, 6h 20m.4; Mina 3, 18h 37m.0; Mesha 6, 7h 16m.3; Vrisha 8, 19h 30m.3; Mithuna 11, 6h 05m.5; Karkata 13, 13h 32m.9; Simha 15, 17h 08m.1;Kanya 17, 17h 32m.2;Tula 19, 16h 33m.6;Vrischika 21, 16h 26m.6;Dhanus 23, 19h 12m.7;Makara 25, 25h 57m.6;Kumbha 28,12h 17m.7;Mina 30,24h 37m.8;Sun enters :- Nirayana Mesha 24, 20h 23m.0. Apr.

392

INDIAN CALENDAR SAKA ERA 1942 Month of VAISAKHA (31 days)

Vrisha : Sukra Summer (Grishma), 1st Month

(Nirayana) 8 Vaisakha, 5121 Kali Era to (Nirayana) 7 Jyaishtha, 5121 Kali Era

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

5 5 5 5 5

34.2 33.4 32.6 31.9 31.1

11 11 11 11 11

58.7 58.5 58.3 58.1 57.9

Nakshatra

m

Tithi No. Ending Moment h m

18 18 18 18 18

23.3 23.7 24.2 24.6 25.0

K 14 14 5 K 30 7 S 1 10 2 11

38.1 55.8 01.8 52.2

26 27 1 2 3

10 13 16 18 20

22.5 18.0 04.7 39.2 57.6

27 1 2 3 4

21 22 22 23 23

25.9 16.4 59.2 31.5 50.7

3 4 5 6 7

23.3 30.3 08.3 12.6 39.5

4 5 6 7 8

22 24 25 26 25

55.9 29.3 32.7 01.5 52.6

5 6 7 8 9

23 23 22 21 20

53.5 36.4 55.4 47.0 08.5

27.2 36.2 09.7 13.2 54.2) 21.6

9 10 11 12

25 23 21 19

04.8 40.0 42.6 19.3

13

16

38.9

10 11 12 13 (14 15

17 15 12 8 28 24

58.4 17.5 08.3 35.1 44.1) 42.3

13 11 8 6 29 28

51.4 07.4 37.8 33.1 02.4) 13.1

16 17 18 19

20 16 12 9

38.1 39.7 55.6 33.5

20 (21

6 28

40.4 21.7)

Sunset h

No.

Ending Moment h m

Yoga No. Ending Moment h m

1 2 3 4 5

Tue Wed Thu Fri Sat

2020 A.D. Apr. 21 22 23 24 25

6 7 8 9 10

Sun Mon Tue Wed Thu

26 27 28 29 30

5 5 5 5 5

30.3 29.6 28.9 28.2 27.5

11 11 11 11 11

57.8 57.6 57.5 57.3 57.2

18 18 18 18 18

25.4 25.9 26.3 26.8 27.2

11 12 13 14

Fri May Sat Sun Mon

1 2 3 4

5 5 5 5

26.8 26.1 25.4 24.8

11 11 11 11

57.1 57.0 56.9 56.8

18 18 18 18

27.6 28.1 28.5 29.0

15

Tue

5

5

24.2

11

56.7

18

29.5

8 13 9 11 S 10 9 11 6 (12 26 13 23

16 17 18 19

Wed Thu Fri Sat

6 7 8 9

5 5 5 5

23.6 23.0 22.4 21.8

11 11 11 11

56.6 56.5 56.5 56.4

18 18 18 18

29.9 30.4 30.8 31.3

14 S 15 K 1 2

19 16 13 10

45.2 15.3 02.2 15.6

20

Sun

10

5

21.3

11

56.4

18

31.8

3

8

04.4

14 15 16 17 (18 19

21 22 23 24 25

Mon Tue Wed Thu Fri

11 12 13 14 15

5 5 5 5 5

20.8 20.2 19.8 19.3 18.8

11 11 11 11 11

56.4 56.4 56.3 56.3 56.4

18 18 18 18 18

32.2 32.7 33.2 33.7 34.1

4 5 6 7 8

6 5 5 6 8

35.6 53.6 59.8 51.6 22.6

20 21 22 22 23

28 28 6 8

09.9 54.0 22.7 29.7

22 23 24 25 26

26 25 25 25 25

40.6 37.7 11.3 16.8 47.5

26 Sat 16 5 18.4 11 56.4 18 34.6 9 10 23.4 24 27 Sun 17 5 18.0 11 56.4 18 35.1 K 10 12 42.7 25 28 Mon 18 5 17.6 11 56.4 18 35.6 11 15 09.0 26 29 Tue 19 5 17.2 11 56.5 18 36.0 12 17 31.8 27 30 Wed 20 5 16.9 11 56.6 18 36.5 13 19 43.0 1 31 Thu May 21 5 16.5 11 56.6 18 37.0 K 14 21 36.6 2 N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long.

11 13 16 19 22 25

05.3 58.5 57.8 53.4 37.1 03.6

27 26 1 27 2 28 3 3 5 4 6

35.3 31.7 28.9 20.1 00.3

S

K

13 14 15 15 14

Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

393

INDIAN CALENDAR SAKA ERA 1942 Month of VAISAKHA (31 days)

Uttarayana Uttara Gola

Ayanamsa on 1st : 240 08/ 08//

(Nirayana) 8 Vaisakha, 5121 Kali Era to (Nirayana) 7 Jyaishtha, 5121 Kali Era

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D CHANDRA 1 Apr. 21 CHAITRA 2 22 3 23 4 24 5

Phenomena

3- New Moon (7h 55m.8)

25

May

1 2

13

3

14 15

4 5

16 17

6 7

18 19 20

8 9 10

21 22

11 12

23 24 25

13 14 15

26 27 28 29 30 31

16 17 18 19 20 21

11- Sayana Vyatipata (15h 17m.8)

V A I S A K H A

11 12

17-Full Moon (16h 15m.3)

21-Enters Krittika nak. (6h 22m .7) 23-Saura Jyaishthadi (19h 12m .8)

3- Babu Kuer Singh Day (Bihar), Tithi of Sri Deva Damodara (Assam) 5- Parasuram Jayanti 6- Akshaya Tritiya,Varshitapa Samapanna (Jain), Kedar Badri Yatra. 8- Sri Shankaracharya Jayanti, Sri Ramanujacharya Jayanti (S.India) 9- Sri Ramanujacharya Jayanti. 10- Gangotpatti.

7- Enters Bharani nak. (12h 8m .4)

C H A A N D R A

29 30

S A U R A

9 10

SAU RA J YA I S H T H A

7 8

26 27 28

VAI SAK HA

6

Festivals

11- May Day 12- Sita Navami, Trichur Pooram (Kerala). 13- Mohini Ekadasi(Smarta), Birthday Anniversary of Dada Chellaram (Sindhi). 14- Mohini Ekadasi(Vaishnava & Vidhava), Minakshi Kalyanam, Trisprisa Mahadvadasi 16- Nrisimha Chaturdasi. 17- Vaisakhi Purnima, Buddha Purnima. 18- Birthday of Rabindranath Tagore

23-Sayana Vaidhriti (10h 33m.0)

28- Apara Ekadasi, Bhadrakali Ekadasi(Punjab)

30-Enters Trop. 31- Savitri Chaturdasi, Phalaharini Gemini Kalika puja (19h 19m.2) N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Mesha 2, 13h 18m.0;Visha 4, 25h 15m.4; Mithuna 7, 11h 46m.1; Karkata 9, 19h 57m.8; Simha 11, 25h 04m.8; Kanya 13, 27h 08m.9; Tula 15,27h 15m.4; Vrishchika 17, 27h 13m.3; Dhanush 19, 29h 02m.4; Makara 22, 10h 16m.5; Kumbha 24, 19h 22m.0; Mina 27, 7h 14m.2; Mesha 29, 19h 53m.4; Sun enters :- Nirayana Vrisha 24, 17h 16m.2.

394

INDIAN CALENDAR SAKA ERA 1942 Month of JYAISHTHA (31 days)

Mithuna : Suchi Summer (Grishma), 2nd Month

(Nirayana) 8 Jyaishtha, 5121 Kali Era to (Nirayana) 7 Ashadha, 5121 Kali Era

Nakshatra

m

Tithi No. Ending Moment h m

18 18 18 18

37.4 37.9 38.4 38.8

K 30 23 S 1 24 2 25 3 25

08.8 17.5 01.1 18.6

3 4 5 5

27 28 6

09.2 51.7 09.6

57.1

18

39.3

4 25

09.3

6

7

02.1

11 11 11 11

57.2 57.3 57.5 57.6

18 18 18 18

39.7 40.2 40.6 41.1

5 6 7 8

24 23 21 19

32.4 27.7 55.7 57.9

14.2

11

57.7

18

41.5

9 17

37.2

7 8 9 10 (11 12

7 7 6 6 28 27

28.0 26.8 58.1 02.8 42.6) 01.1

5 5 5

14.1 13.9 13.9

11 11 11

57.9 58.1 58.2

18 18 18

41.9 42.4 42.8

S 10 14 11 12 12 9

57.7 05.0 05.5

13 14 15

25 22 20

02.9 54.5 43.0

4

5

13.8

11

58.4

18

43.2

18

5

13.7

11

58.6

18

43.6

06.5 16.1) 42.4

16

5

13 6 (14 27 S 15 24

17

Sat Sun Mon Tue Wed

6 7 8 9 10

5 5 5 5 5

13.7 13.7 13.7 13.7 13.7

11 11 11 11 11

58.7 58.9 59.1 59.3 59.5

18 18 18 18 18

44.0 44.4 44.7 45.1 45.4

K

1 2 3 4 5

22 20 19 19 20

33.4 56.2 56.8 39.4 05.0

21 22 23 24 25

Thu Fri Sat Sun Mon

11 12 13 14 15

5 5 5 5 5

13.8 13.9 14.0 14.1 14.2

11 11 12 12 12

59.7 59.9 00.1 00.3 00.5

18 18 18 18 18

45.8 46.1 46.4 46.7 47.0

6 7 8 9 K 10

21 22 24 27 -

26 27 28 29 30 31

Tue Wed Thu Fri Sat Sun June

16 17 18 19 20 21

5 5 5 5 5 5

14.3 14.5 14.7 14.8 15.0 15.3

12 12 12 12 12 12

00.8 01.0 01.2 01.4 01.6 01.9

18 18 18 18 18 18

47.3 47.6 47.8 48.1 48.3 48.5

10 5 11 7 12 9 13 11 14 11 K 30 12

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

1 2 3 4

2020 A.D. Fri May 22 Sat 23 Sun 24 Mon 25

5 5 5 5

16.2 15.9 15.6 15.4

11 11 11 11

56.7 56.8 56.9 57.0

5

Tue

26

5

15.1

11

6 7 8 9

Wed Thu Fri Sat

27 28 29 30

5 5 5 5

14.9 14.7 14.5 14.3

10

Sun

31

5

11 12 13

Mon June Tue Wed

1 2 3

14

Thu

15

Fri

16 17 18 19 20

Sunset h

S

K

No.

Ending Moment h m

Yoga No. Ending Moment h m 5 6 6 6 7 6 8 5 (9 29 10 27

25.8 34.3 24.2 54.5 04.2) 52.7

11 12 13 14

26 24 22 19

19.2 23.5 05.7 27.0

15 16

29.5

36.5

16 13 17 9 18 6 (19 26 20 23

16.3 51.7 20.9 49.8) 24.9

16

43.5

21 20

12.6

18 19 20 21 22

15 14 13 14 14

12.3 10.7 45.1 00.2 57.5

22 23 24 25 26

17 14 12 11 10

19.3 50.8 52.0 26.2 34.5

11.5 52.8 59.5 19.8 -

23 24 25 26 27

16 18 21 24 27

35.4 48.5 27.7 21.5 17.5

27 1 2 3 4

10 10 11 11 12

16.1 27.2 01.7 51.6 47.8

40.8 50.7 39.9 01.6 52.4 11.4

1 1 2 3 4 5

6 8 10 12 13

03.8 30.6 31.2 01.8 01.4

5 6 7 8 9 10

13 14 14 14 14 13

41.2 23.6 48.7 51.8 30.6 44.4

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

395

INDIAN CALENDAR SAKA ERA 1942 Month of JYAISHTHA (31 days)

Uttarayana Uttara Gola

Ayanamsa on 1st : 240 08/ 12//

(Nirayana) 8 Jyaishtha, 5121 Kali Era to (Nirayana) 7 Ashadha, 5121 Kali Era

1

12 13 14 15

2 3 4 5

16 17

6 7

18 19 20

8 9 10

21 22 23 24 25

11 12 13 14 15

26 27 28 29 30

16 17 18 19 20

31

June 21

1- New Moon (23h 08m.8)

1- Vata Savitri Vrata(Amavasya Paksha).

Enters Rohini nak.(26h 33m.4)

S H T H A

June

Y A I

11

Festivals

10- Venus sets in the East (05h 42m)

J

30 31

Phenomena

5- Sayana Vyatipata (25h 7m.0)

N D R A

9 10

3-

H A

27 28 29

Chandra Vaisakha

C

6 7 8

S A U R A

26

S A U R A A S H AD H A

5

Lunar Transit of the Sun Month

J Y A I S H T H A

Date Gregorian Solar Date Month 2020A.D. 1 May 22 2 23 3 24 4 25

15- Full Moon (24h 42m.4)

4- Rambha Tritiya, Pratap Jayanti (Rajasthan). 5- Guru Arjan Dev’s Martyrdom Day (Sikh). 7- Vindhyavasini Puja, Aranya Shashthi, Jamatri Shashthi (Bengal). 9- Mela Kshir Bhawani (Kashmir) 11- Ganga Dasahara (hasta upto 25h 03m ) 12- Nirjala Ekadasi. 13- Champaka Dvadasi. 15- Vata Savitri Vrata (Purnima Paksha), Deva Snana Purnima. 16- Guru Hargobind’s Birthday(J&K)

17- Sayana 17- Enters Vaidhriti Mrigasiras (23h 11m.8) nak.(24h 28m.3) 18- Venus rises in the West (19h 22m)

23- Saura Ashadhadi (25h 35m.3)

24- Rajas Samkranti (Odisha).

27- Jogini Ekadasi. 30- Enters Trop. Cancer (27h 13m.6) 31- Enters Ardra nak.(23h 28m.0)

31- Sayana Vyatipata (10h 55m.1) 31- Annular Solar Eclipse (visible in India) 31- New Moon (12h 11m.4)

31- Dakshinayana Day, Chudamani Yoga

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Vrisha 1, 7h 37m.1;Mithuna 3,17h 33m.8; Karkata 5, 25h 24m.1; Simha 8, 6h 58m.1; Kanya 10, 10h 19m.0; Tula 12, 11h 59m.6; Vrischika 14, 13h 07m.2; Dhanus 16, 15h 12m.3, Makara 18, 19h 45m.0; Kumbha 20, 27h 41m.6; Mina 23, 14h 46m.0; Mesha 25, 27h 17m.5; Vrisha 28, 15h 03m.4; Mithuna 30, 24h 35m.4;Sun enters :-Nirayana Mithuna 24, 23h 53m.9.

396

INDIAN CALENDAR SAKA ERA 1942 Month of ASHADHA (31 days)

Karkata :Nabhas Rains (Varsa), 1st Month

(Nirayana) 8 Ashadha, 5121 Kali Era to (Nirayana) 7 Sravna, 5121 Kali Era

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

Sunset h

m

Tithi No. Ending Moment h m

Nakshatra No.

Ending Moment h m

1 2 3 4

2020 A.D. Mon June 22 Tue 23 Wed 24 Thu 25

5 5 5 5

15.5 15.7 16.0 16.3

12 12 12 12

02.1 02.3 02.5 02.7

18 18 18 18

48.7 48.9 49.1 49.2

S

1 11 2 11 3 10 4 8

59.7 19.7 14.6 48.0

6 7 8 9

13 13 13 12

30.9 32.8 10.2 26.6

5

Fri

26

5 16.5

12

02.9

18

49.4

S

5 7 (6 29

03.4 04.2)

10

11

25.8

6 7 8 9

Sat Sun Mon Tue

27 28 29 30

5 5 5 5

16.8 17.1 17.4 17.8

12 12 12 12

03.1 03.3 03.5 03.7

18 18 18 18

49.5 49.6 49.7 49.7

7 8 9 S 10

26 24 22 19

54.0 35.9 13.3 50.0

10 8 7 5 28 26

Yoga No. Ending Moment h m 11 12 13 14 (15 16

12 11 9 6 28 25

34.0 01.1 08.0 57.3 31.8) 54.1

11.1 46.1 14.1 38.8 04.0) 34.1

17 18 19 20

23 20 17 14

06.8 12.7 14.3 14.6

21

11

16.6

8 5 27 24 23 21

23.9 40.0 09.0) 55.0 02.1 33.8

10

Wed July

1

5 18.1

12

03.9

18

49.8

11 17

29.9

11 12 13 14 (15 16

11 12

Thu Fri

2 3

5 18.4 5 18.8

12 12

04.1 04.3

18 18

49.8 49.8

12 15 13 13

17.3 17.0

17 18

25 24

13.7 07.9

13 14 15

Sat Sun Mon

4 5 6

5 19.2 5 19.5 5 19.9

12 12 12

04.5 04.7 04.8

18 18 18

49.8 49.7 49.7

14 11 S 15 10 K 1 9

34.3 14.4 22.5

19 20 21

23 23 23

22.2 02.0 12.0

22 23 (24 25 26 27

16 17 18 19 20

Tue Wed Thu Fri Sat

7 8 9 10 11

5 5 5 5 5

20.3 20.7 21.1 21.5 21.9

12 12 12 12 12

05.0 05.1 05.3 05.4 05.6

18 18 18 18 18

49.6 388 49.5 49.4 49.3 K 49.1

03.1 19.2 11.7 38.5 33.8

22 23 24 25 25

23 25 27 5

55.9 15.4 09.3 33.0

1 2 3 4 5

20 20 19 20 20

32.8 00.5 56.2 17.1 57.9

21 22 23 24 25

Sun Mon Tue Wed Thu

12 13 14 15 16

5 5 5 5 5

22.3 22.7 23.1 23.5 24.0

12 12 12 12 12

05.7 05.8 05.9 06.0 06.1

18 18 18 18 18

49.0 48.8 48.6 48.3 48.1

7 8 9 K 10 11

15 18 20 22 23

48.3 09.8 24.7 20.1 45.4

26 27 1 2 3

8 11 14 16 18

18.3 13.9 06.6 43.3 52.9

6 7 8 9 10

21 22 23 24 24

50.8 46.7 35.8 08.7 17.9

26 27 28 29 30 31

Fri Sat Sun Mon Tue Wed

17 18 19 20 21 22

5 5 5 5 5 5

24.4 24.8 25.3 25.7 26.1 26.6

12 12 12 12 12 12

06.2 06.3 06.3 06.4 06.4 06.5

18 18 18 18 18 18

47.8 47.5 47.2 46.9 46.5 46.2

12 13 14 K 30 S 1 S 2

24 24 24 23 21 19

33.6 41.8 10.4 02.9 24.8 22.6

4 5 6 7 8 9

20 21 21 21 20 19

27.6 23.4 40.1 20.6 30.2 15.6

11 12 13 14 15 16

23 23 21 19 17 14

58.1 06.7 43.8 51.5 33.6 55.1

2 9 3 9 4 10 5 11 6 13

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

397

INDIAN CALENDAR SAKA ERA 1942 Month of ASHADHA (31 days)

Dakshinayana Uttara Gola

Ayanamsa on 1st : 240 08/ 18//

(Nirayana) 8 Ashadha, 5121 Kali Era to (Nirayana) 7 Sravana, 5121 Kali Era

Date Gregorian Solar Lunar Date Month Month 2020A.D. 1 June 22

6 7 8

27 28 29

5- Kumara Shashthi (Vrata).

H H

9- Jupiter enters into Dhanus (5h 22m.2)

D

30 1

D

July

7 8 9 10 11

21 22 23 24 25

12 13 14 15 16

26 27 28 29 30 31

17 18 19 20 21 July 22

H

16 17 18 19 20

S

6

A

15

H

5

A S

14

A

2 3 4

6- Vivasvat Saptami. 7- Kharchi Puja (Tripura). 8- Mela Sharik Bhagwati (Kashmir). 9- Punaryatra(Smarta). 10- Harisayani Ekadasi, Ultarath (Odisha), Bahudha Yatra.

14- Enters Punarvasu nak.(23h 03m.6)

12- Sayana Vaidhriti (13h 49m.0) 14- Full Moon (10h 14m.4)

13- Mela Jwalamukhi (Kashmir). 14- Guru Purnima, Vyasa Puja, Ashadhi Purnima.

A R

19- Naga Panchami (Bengal).

A

N

S

D

A

U

R

11 12 13

A

A

9 10

Festivals

1- Manoratha Dvitiya Vrata (Bengal). 2- Rathayatra.

A

23 24 25 26

Phenomena

A

2 3 4 5

Transit of the Sun

SAU RA S RAVANA

C

H

A

22- Martyr’s day (Kashmir). 23- Ker puja(Tripura). 24- Saura Sravanadi (12h 24m.7)

25- Sayana Vyatipata (21h 20m.9)

25- Kamika Ekadasi, Manasa Puja begins

29- Enters Pushya nak. (22h 36m.3) 29- New Moon 29- Chitalagi Amavasya(Odisha), (23h 02m.9) Adi Amavasya(Tamil Nadu), CHANDRA 31Enters Trop. Karkataka Vavu(Kerala). SRAVANA Leo (14h 06m.8) N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters:- Karkata 2, 7h 34m.7; Simha 4, 12h 26m.6; Kanya 6, 15h 50m.7; Tula 8, 18h 26m.6; Vrischika 10, 20h 55m.9; Dhanus 12, 24h 07m.9; Makara 14, 29h 01m.4; Kumbha 17, 12h 31m.2; Mina 19, 22h 54m.7; Mesha 22,11h 13m .9; Vrisha 24,23h 18m.7; Mithuna 27,9h 00m.5; Karkata 29,15h 28m.6; Simha 31, 19h 15m.6; Sun enters:-Nirayana Karkata 25, 10h47m.1;

398

INDIAN CALENDAR SAKA ERA 1942

Simha : Nabhasya Rains (Varsa), 2nd Month

Month of SRAVANA (31 days)

(Nirayana) 8 Sravana, 5121 Kali Era to (Nirayana) 7 Bhadra, 5121 Kali Era

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

Sunset h

m

Tithi No. Ending Moment h m

1 2 3

2019 A.D. Thu Jul. 23 Fri 24 Sat 25

5 5 5

27.0 27.5 27.9

12 12 12

06.5 06.5 06.5

18 18 18

45.8 45.4 44.9

4 5

Sun Mon

26 27

5 5

28.3 28.8

12 12

06.5 06.5

18 18

44.5 44.0

6 7 8 9 10

Tue Wed Thu Fri Sat Aug.

28 29 30 31 1

5 5 5 5 5

29.2 29.6 30.1 30.5 30.9

12 12 12 12 12

06.5 06.5 06.4 06.4 06.3

18 18 18 18 18

43.5 43.0 42.5 42.0 41.4

9 S 10 11 12 13

11 12 13

Sun Mon Tue

2 3 4

5 5 5

31.3 31.8 32.2

12 12 12

06.3 06.2 06.1

18 18 18

14 15

Wed Thu

5 6

5 5

32.6 33.0

12 12

06.0 05.9

16 17 18 19 20

Fri Sat Sun Mon Tue

7 8 9 10 11

5 5 5 5 5

33.4 33.8 34.2 34.6 35.0

12 12 12 12 12

21 22 23 24 25

Wed Thu Fri Sat Sun

12 13 14 15 16

5 5 5 5 5

35.4 35.8 36.2 36.6 37.0

26

Mon

17

5

27

Tue

18

28

Wed

29 30 31

Thu Fri Sat

S

Nakshatra No.

Ending Moment h m

3 17 4 14 5 12

03.6 34.7 02.5

10 11 12

17 16 14

44.0 02.7 18.5

6 9 7 7 (8 28

32.7 10.0 58.2)

13 14

12 11

26 25 23 22 21

59.7 16.6 50.4 42.5 54.8

15 16 17 18 19

40.8 40.3 39.6

14 21 S 15 21 K 1 21

29.4 28.8 55.4

18 18

39.0 38.4

2 22 3 24

05.7 05.6 05.5 05.3 05.2

18 18 18 18 18

37.7 37.0 36.3 35.6 34.9

4 26 5 28 6 6 6 7 9

12 12 12 12 12

05.0 04.8 04.6 04.4 04.2

18 18 18 18 18

34.2 33.4 32.7 31.9 31.1

37.3

12

04.0

18

5

37.7

12

03.8

19

5

38.1

12

20 21 22

5 5 5

38.4 38.8 39.1

12 12 12

Yoga No. Ending Moment h m

37.2 03.7

17 18 19 (20 21 22

12 8 5 26 23 20

01.5 58.3 51.1 44.6) 42.8 49.0

9 8 7 7 6

41.5 33.1 40.5 05.1 48.4

23 24 25 26 27

18 15 13 11 9

05.5 33.9 15.6 11.6 23.1

20 21 22

6 7 8

52.2 18.9 10.9

50.8 15.4

23 24

9 11

30.4 18.2

1 7 2 6 3 5 (4 29 5 29 6 29

51.5 38.4 45.8 15.0) 06.9 21.1

06.7 19.1 43.4 07.3

25 26 27 1 2

13 16 19 22 24

33.4 11.9 06.2 05.6 56.8

7 7 8 9 10

5 6 7 8

55.2 44.5 41.9 38.6

11 12 14 14 13

16.9 58.9 02.4 20.5 50.9

3 4 5 5 6

27 29 6 7

26.4 22.2 35.8 02.9

11 12 13 14 15

9 9 9 9 7

24.6 50.0 46.4 08.0 52.0

30.3

13 12

35.7

7

6

44.0

18

29.5

14 10

40.0

18

28.6

19 21

15.1

18 18 18

27.8 26.9 26.1

11.6 19.6) 13.5 03.2 57.7

43.4 08.1) 07.2

03.3 03.1 02.8

K 30 8 (S 1 29 2 26 3 23 S 4 19

5 28 26

58.7 31.0) 34.2

03.6

8 (9 10

16 5 (17 27 18 24

11 12 13

23 21 19

50.8 28.9 11.2

20 17 21 14 22 10

41.3 00.6 20.6

S

K

8 9 K 10 11 12

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

399

INDIAN CALENDAR SAKA ERA 1942 Month of SRAVANA (31 days)

Dakshinayana Uttara Gola

Ayanamsa on 1st : 240 08/ 23//

(Nirayana) 8 Sravana, 5121 Kali Era to (Nirayana) 7 Bhadra, 5121 Kali Era

31 Aug. 1

11 12

2 3

13 14 15

4 5 6

16

7

17 18 19 20

8 9 10 11

21 22 23 24

12 13 14 15

1- Madhusrava Tritiya (Teej), Adi Puram (S. India). 3- Naga Panchami. 5- Goswami Tulasi Das Jayanti.

8- Pavitra Ekadasi, Jhulana Yatrarambha. 9- Vara Mahalakshmi Vrata (S. India). 10- Tilak Commemoration Day. 11- Enters Aslesha nak. (21h 28m.7) 12- Full Moon (21h 28m.8)

C H A N D R A

S A U R A

Festivals

6- Sayana Vaidhriti (26h 13m.1)

A N A

9 10

S R A V

28 29 30

Phenomena

S

6 7 8

R A V A N A

Date Gergorian Solar Lunar Transit of the Sun Date Month Month 2020A.D. 1 July 23 2 24 3 25 4 26 5 27

12- Raksha Bandhana, Jhulana Yatra Samapanna, Naroli Purnima, Balabhadra Puja(Odisha), Amarnath yatra, Solono (Rakhi Bandhan-Delhi), Avani Avittam (S. India), Jaju Upakarma, Sravani Purnima. 13- Gayatri Japam, Rik Upakarma. 15- Teejri (Sindhi). 16- Bahula Chaturthi (Sankashtha Chaturthi). 17- Raksha Panchami (Odisha).

20- Sayana Vyatipata (5h 37m.7)

20- Janmashtmi(Smarta), Vadi Thadri (Sindhi). 21- Janmashtmi(Vaishnava), Gokulashtami(Nandotsava).

24- Independence Day, Paryushana Parvarambha(Chaturthi Paksha) (Jain), Aja Ekadasi. 25- Paryusana 25 16 Parvarambha(Panchami Paksha) (Jain), Manasa Puja ends(Bengal). 26- Simhadi(Kerala), Aghora 26 17 Chaturdasi., Kailash yatra - 2 days 27- Saptapuri Amavasya(Odisha), 27 18 Pithori. 28- New Moon 28- Kusotpatini, Jain Festival. 28 19 29- Tithi of Sri Sankara Deva (8h 11m.6) 29 20 (Assam). 30- Haritalika Gauri Tritya. 30 21 31- Samaveda Upakarma, Haritalika 31 Aug. 22 Chaturthi, Vinayak 31- EntersTrop. Chaturthi(T.N.),Ganesha Virgo Chaturthi,Samvatsari(Chaturthi (21h 14m.9) Paksha - Jain) N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Kanya 2, 21h 36m.7; Tula 4, 23h 49m.3; Vrischika 6, 26h 48m.1; Dhanus 9, 07h 05m.1; Makara 11, 12h 56m.7; Kumbha 13, 20h 47m.2; Mina 16, 6h 57m.1; Mesha 18, 19h 06m.2; Vrisha 21, 7h 36m.8; Mithuna 23, 18h 05m.0; Karkata 25, 24h 52m.9; Simha 27, 28h 08m.1; Kanya 29, 29h 15m.4:; Sun enters :- Nirayana Simha 25, 19h 11m.4. CHANDRA BHADRAPADA

SAU RA B HAD RAPADA

24- Saura Bhadrapadadi (20h 57m.2) 25- Enters Magha nak. (19h 11m.4)

400

INDIAN CALENDAR SAKA ERA 1942

Kanya: Isha Autumn (Sarat), 1st Month

Month of BHADRA (31 days)

(Nirayana) 8 Bhadra, 5121 Kali Era to (Nirayana) 7 Asvina, 5121 Kali Era

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

h

m

Tithi No. Ending Moment h m S

Sunset

1

2019 A.D. Sun Aug. 23

5 39.5

12

02.6

18

25.2

2 3 4 5

Mon Tue Wed Thu

24 25 26 27

5 5 5 5

39.8 40.2 40.5 40.9

12 12 12 12

02.3 02.0 01.7 01.5

18 18 18 18

24.3 23.4 22.5 21.6

6 7 8 9 10

Fri Sat Sun Mon Tue Sept.

28 29 30 31 1

5 5 5 5 5

41.2 41.5 41.9 42.2 42.5

12 12 12 12 11

01.2 00.9 00.5 00.2 59.9

18 18 18 18 18

20.6 19.7 18.8 17.8 16.8

S 10 11 12 13 14

11 12 13 14 15

Wed Thu Fri Sat Sun

2 3 4 5 6

5 5 5 5 5

42.8 43.1 43.4 43.8 44.1

11 11 11 11 11

59.6 59.3 58.9 58.6 58.3

18 18 18 18 18

16 17 18 19 20

Mon Tue Wed Thu Fri

7 8 9 10 11

5 5 5 5 5

44.4 44.7 45.0 45.3 45.6

11 11 11 11 11

57.9 57.6 57.2 56.9 56.5

21 22 23 24 25

Sat Sun Mon Tue Wed

12 13 14 15 16

5 5 5 5 5

45.9 46.2 46.5 46.8 47.1

11 11 11 11 11

26 27

Thu Fri

17 18

5 47.4 5 47.8

28

Sat

19

29 30

Sun Mon

31

Tue

Nakshatra No.

Ending Moment h m

5 17

05.0

14

17

06.1

6 14 7 12 8 10 9 9

31.6 22.3 39.9 25.6

15 16 17 18

15 13 13 12

8 8 8 8 9

38.7 18.0 21.9 49.2 39.3

19 20 21 22 23

15.9 14.9 13.9 12.9 12.0

S 15 10 K 1 12 2 14 3 16 4 19

52.1 27.4 24.1 39.3 07.3

18 18 18 18 18

11.0 10.0 09.0 07.9 06.9

K

5 6 7 8 9

21 24 26 27 28

56.2 55.8 55.5 55.1 54.8

18 18 18 18 18

05.9 04.9 03.9 02.9 01.9

K 10 11 12 13 14

11 11

54.4 54.0

18 17

5 48.1

11

53.7

20 21

5 48.4 5 48.7

11 11

22

5 49.0

11

Yoga No. Ending Moment h m

20.3 58.8 04.1 37.2

23 24 25 26 27 1

6 27 24 21 19 17

48.3 29.6 29.0 49.3 32.0 37.1

12 13 13 15 16

37.3 02.8 52.0 03.9 37.9

2 3 4 5 6

16 14 13 13 13

03.9 51.1 57.3 21.6 03.6

24 25 26 27 1

18 20 23 26 29

33.7 50.9 28.0 21.1 23.7

7 8 9 10 11

13 13 13 14 15

03.0 19.6 52.4 39.2 36.0

39.2 03.2 06.2 35.3 20.1

2 2 3 4 5

8 11 13 15

25.8 15.3 39.0 25.1

12 13 14 15 16

16 17 18 18 18

36.7 33.2 16.1 35.8 23.9

28 27 25 23 19

14.5 16.8 30.0 00.4 57.0

6 7 8 9 10

16 16 15 14 12

24.7 33.6 52.2 25.2 20.5

17 18 19 20 21 (22

17 16 13 11 7 27

34.1 03.3 51.5 02.0 40.4 54.0)

00.8 59.8

K 30 16 S 1 12

30.2 51.0

51.5 42.0

15

34.5

17 17

57.8 56.8

10.5 39.4) 27.5 42.8

25

53.3 53.0

2 9 (3 29 4 26 S 5 23

48.2 59.7 06.7) 20.5

23 19

58.8

9 6 28 25

23 24

17

11 12 (13 14 15 16

22 20

51.7 48.8

52.6

17

55.7

S

31.5

17

19

18.6

26 27 (1 2

11 7 28 25

37.4 58.2 43.0) 56.0

6 21

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

401

INDIAN CALENDAR SAKA ERA 1942 Month of BHADRA (31 days)

Dakshinayana Uttara Gola

Ayanamsa on 1st : 240 08/ 27//

(Nirayana) 8 Bhadra, 5121 Kali Era to (Nirayana) 7 Asvina, 5121 Kali Era

8 9 10

30 31 Sept. 1

11

2

12 13 14 15

3 4 5 6

16 17 18 19

7 8 9 10

20

11

21 22 23 24

12 13 14 15

25

16

26

17

27 28 29 30 31

18 19 20 21 Sept. 22

B H A D R A P A D

28 29

1- Sayana Vaidhriti (14h 39m.2)

8- Enters PurvaPhalguni nak. (15h 06m.8) 11- Full Moon (10h 52m.1)

C H A A N D R A

6 7

14- Sayana Vyatipata (11h 39m.2)

Festivals

1- Samvatsari (Panchami PakshaJain), Rishi Panchami, Mela Pat-3 days(J&K). 2- Surya Shashthi. 3- Mahalakshmi Vratarambha. Durvashtami. 4- Radhashtami, Durvashtami(Bengal). 7- Dol Gyaras (MP), Heikru Hidongba (Manipur), Parsvaparivartani Ekadasi, Sakrotthana, Vamana Jayanti. 8- First Onam Day. 9- Onam or Thiru Onam Day (Kerala). 10- Indra Purnima,Ananta Chaturdasi, Third Onam Day(Kerala). 11- Fourth Onam Day, Sri Narayana Guru Deva’s Birthday (Kerala), Pitri Paksha Tarpana begins. 12- Keil Muhurth (Coorg).

16- Tithi of Sri Madhava Deva (Assam). 19- Mahalakshmi Vrata Samapanna, Sri Jayanti (Ramanuja), Sri Krishna Jayanti (T.N., Assam & Kerala). 20- Matri Navami.

22- Enters U. Phalguni nak. (9h 03m.0) 24- Saura Asvinadi (21h 11m.2) CH A ANDR A ASVINA MALA

26 27 B H A D R A P A D A

4 5

S A U R A

24 25

SAU RA AS VI NA

2 3

Phenomena

A

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D. 1 Aug. 23

22- Indira Ekadasi. 24- Magha Trayodasi (Magha after 14h 25m). 25- Visvakarma Puja. 26- New Moon (16h 30m.2)

26- Mahalaya Amavasya, Sarvapitri Amavasya (Odisha), Tarpana Layba (Manipur).

27- Sayana Vaidhriti (7h 22m.7) 31- Enters Trop. Libra (19h 01m.7)

30- Samadhi day of Narayana Guru (Kerala).

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters : Tula 1, 6h 06m.5;Vrischika 3, 08h 16m.7;Dhanus 5, 12h 37m.2;Makara 7,19h 12m.9;Kumbha 9, 27h 48m.2;Mina 12, 14h 14m.6; Mesha 14, 26h 21m.2;Vrisha 17,15h 09m.9;Mithuna 19, 26h 37m.4;Karkata 22, 10h 36m.2;Simha 24, 14h 25m.2;Kanya 26, 15h 07m.2; Tula 28, 14h 42m.1; Vrischika 30, 15h 16m.6; Sun enters :-Nirayana Kanya 25, 19h 07m.7.

402

INDIAN CALENDAR SAKA ERA 1942

Tula : Urja Autumn (Sarat), 2nd Month

Month of ASVINA (30 days)

(Nirayana) 8 Asvina, 5121 Kali Era to (Nirayana) 7 Kartika, 5121 Kali Era

Date Week Gregorian Day Date

Sunset

Nakshatra

h

m

2020 A.D. Wed Sep. 23 Thu 24 Fri 25 Sat 26 Sun 27

5 5 5 5 5

49.3 49.6 50.0 50.3 50.6

11 11 11 11 11

52.3 51.9 51.6 51.2 50.9

17 17 17 17 17

54.7 53.7 52.7 51.7 50.7

S

7 8 9 S 10 11

19 19 18 19 19

57.5 02.0 44.0 00.3 46.8

18 19 20 21 22

18 18 18 19 20

25.1 09.6 30.9 25.7 49.6

3 4 5 6 7

23 21 20 19 19

39.5 53.7 37.2 47.4 20.8

6 7 8 9 10

Mon Tue Wed Thu Oct. Fri

28 29 30 1 2

5 5 5 5 5

50.9 51.3 51.6 51.9 52.3

11 11 11 11 11

50.6 50.2 49.9 49.6 49.3

17 17 17 17 17

49.7 48.7 47.7 46.7 45.7

12 13 14 S 15 K 1

20 22 24 26 28

59.2 33.5 26.4 35.3 57.1

23 24 25 26 26

22 24 27 5

38.3 47.8 14.9 56.8

8 9 10 11 12

19 19 19 20 21

14.1 24.2 48.7 25.4 12.4

11 12 13 14 15

Sat Sun Mon Tue Wed

3 4 5 6 7

5 5 5 5 5

52.6 53.0 53.4 53.7 54.1

11 11 11 11 11

48.9 48.6 48.3 48.0 47.7

17 17 17 17 17

44.8 43.8 42.8 41.9 40.9

K

2 2 7 3 10 4 12 5 14

28.1 02.6 32.5 47.8

27 1 2 3 4

8 11 14 17 20

50.6 52.4 56.2 54.0 35.7

13 14 15 16 17

22 23 24 24 25

07.0 05.9 03.8 54.4 30.0

16 17 18 19 20

Thu Fri Sat Sun Mon

8 9 10 11 12

5 5 5 5 5

54.5 54.8 55.2 55.6 56.0

11 11 11 11 11

47.5 47.2 46.9 46.7 46.4

17 17 17 17 17

40.0 39.1 38.2 37.2 36.3

6 7 8 9 K 10

16 17 18 17 16

37.1 49.8 17.0 53.8 39.1

5 6 7 8 9

22 24 25 25 24

50.0 26.7 17.7 18.6 29.5

18 19 20 21 22

25 25 24 22 20

42.2 23.7 28.3 52.7 36.3

21 22 23

Tue Wed Thu

13 14 15

5 5 5

56.4 56.9 57.3

11 11 11

46.2 45.9 45.7

17 17 17

35.5 34.6 33.7

54.4 40.7 58.1

23 17 24 14 25 10

41.7 13.7 19.4

16

5

57.7

11

45.5

17

32.9

36.1 51.3 33.5 53.0) 01.0

22 20 17

Fri

14 11 8 28 25

10 11 12

24

11 12 13 (14 K 30

13

14

57.8

25 26 27

Sat Sun Mon

17 18 19

5 5 5

58.1 58.6 59.0

11 11 11

45.3 45.1 44.9

17 17 17

32.0 31.2 30.4

1 21 2 17 3 14

09.0 28.0 08.4

20 21

5 6

59.5 00.0

11 11

44.7 44.6

17 17

29.6 28.8

S

4 11 5 9

19.3 08.1

51.6 51.3 08.3 52.5) 12.3 13.4

07.0 45.4 24.1 12.1 17.6

Tue Wed

11 8 6 27 26 25

6 25 21 17 13

28 29

14 15 16 (17 18 19

26 27 1 2 3

30

Thu

22

6

00.4

11

44.4

17

28.1

S

6

40.1

20

24

58.6

4 9 5 6 (6 28 7 26

47.9 48.8 24.0) 35.2

h

m

S

7

No.

Ending Moment h m

Yoga No. Ending Moment h m

Apparent Noon h m

1 2 3 4 5

Sunrise

Tithi No. Ending Moment h m

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

403

INDIAN CALENDAR SAKA ERA 1942 Month of ASVINA (30 days)

Dakshinayana Dakshina Gola

Ayanamsa on 1st : 240 08/ 31//

(Nirayana) 8 Asvina, 5121 Kali Era to (Nirayana) 7 Kartika, 5121 Kali Era

26 27 28

18 19 20

29 30

21 Oct. 22

1- Jalavisuva Day.

5- Padmini Ekadasi (Purushottami).

S

M A LA

8- Sayana Vyatipata (16h 51m.8) 9- Full Moon (26h 35m.3)

10- Mahatma Gandhi’s Birthday.

AS V I N A

13 14 15 16 17

C HAAN D RA

21 22 23 24 25

Festivals

A

8 9 10 11 12

A

16 17 18 19 20

R

3 4 5 6 7

Phenomena

U

11 12 13 14 15

A

1 2

S

Oct.

S AU RA K ART I K A

9 10

V

I

28 29 30

C H A A ND R A AS V I NA S U D D HA

6 7 8

N A

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D. 1 Sept. 23 2 24 3 25 4 26 4- Enters Hasta 5 27 nak.(24h 29m.1)

18- Enters Chitra nak. (13h 34m.5)

24- Saura Kartikadi (9h 30m.5)

21- Sayana Vaidhriti (25h 28m.8) 24- New Moon (25h 01m.0)

21- Kamala Ekadasi (Purushottami).

25- Saradiya Navaratrarambha, Kaveri Samkramana Snana, Maharaja Agrasen Jayanti. 28- Upanga LalitaVrata (Lalita Panchami). 29- Saraswati Avahana.

30- Enters Trop. Scorpio (28h 29m.5)

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Dhanus 1, 18h 25m.1; Makara 3, 24h 41m.6; Kumbha 6, 9h 41m.2; Mina 8, 20h 36m.6; Mesha 11, 8h 50m .6; Vrisha 13, 21h 41m.6; Mithuna 16, 9h 46m.9; Karkata 18, 19h 09m.5; Simha 20,24h 29m.5; Kanya 22, 26h 02m.4; Tula 24, 25h 24m.7; Vrischika 26, 24h 46m.9; Dhanus 28, 26h 12m.3; Sun enters :- Nirayana Tula 25, 07h 05m.5.

404

INDIAN CALENDAR SAKA ERA 1942

Vrischika : Sahas Hemanta, 1st Month

Month of KARTIKA (30 days) (Nirayana) 8 Kartika, 5121 Kali Era to (Nirayana) 7 Agrahayana, 5121 Kali Era

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

2020 A.D. Fri Oct. 23 Sat 24 Sun 25 Mon 26 Tue 27

6 6 6 6 6

00.9 01.4 01.9 02.4 02.9

11 11 11 11 11

6 7 8 9 10

Wed Thu Fri Sat Sun Nov.

28 29 30 31 1

6 6 6 6 6

03.4 04.0 04.5 05.1 05.6

11 12 13 14 15

Mon Tue Wed Thu Fri

2 3 4 5 6

6 6 6 6 6

16

Sat

7

17 18

Sun Mon

19 20

Sunset

Tithi No. Ending Moment h m

Nakshatra No.

Ending Moment h m

Yoga No. Ending Moment h m

h

m

44.3 44.2 44.0 43.9 43.8

17 17 17 17 17

27.3 26.6 25.8 25.1 24.4

7 6 8 6 9 7 S 10 9 11 10

57.4 59.3 42.3 00.5 47.0

21 22 23 24 24

25 26 28 6

27.8 37.8 23.0 36.5

8 9 10 11 12

25 24 24 24 25

21.5 40.5 27.9 38.4 06.8

11 11 11 11 11

43.8 43.7 43.6 43.6 43.6

17 17 17 17 17

23.8 23.1 22.5 21.8 21.2

12 13 14 S 15 K 1

12 15 17 20 22

54.4 16.1 46.1 19.2 50.4

25 26 27 1 2

9 11 14 17 20

11.0 59.8 57.1 57.8 57.0

13 14 15 16 17

25 26 27 28 29

47.9 37.3 31.0 25.6 17.4

06.2 06.7 07.3 07.9 08.5

11 11 11 11 11

43.5 43.5 43.6 43.6 43.6

17 17 17 17 17

20.6 20.1 19.5 19.0 18.5

2 25 3 27 4 29 5 5 6

14.3 24.9 15.0 37.0

3 4 5 6 6

23 26 28 6

49.7 29.9 50.7 44.8

18 30 19 19 6 20 6 21 6

02.7 37.0 55.1 51.4

6

09.1

11

43.7

17

18.0

6

7

23.8

7

8

04.9

8 9

6 6

09.7 10.3

11 11

43.7 43.8

17 17

17.6 17.1

8 9

8 8

45.3 42.4

10 11

6 6

10.9 11.6

11 11

43.9 44.0

17 17

16.7 16.3

29.7 51.2 28.2) 23.1 41.3

20.8 18.7) 42.0 30.0

Tue Wed

7 7 8 6 (9 29 K 10 27 11 24

22 6 (23 29 24 27 25 25

10 11 (12

7 6 28

55.9 28.3 25.2)

26 22 27 19

43.7 26.6

21 22 23 l 24 25

Thu Fri Sat

12 13 14

6 6 6

12.2 12.8 13.5

11 11 11

44.2 44.3 44.4

17 17 17

15.9 15.6 15.3

12 21 13 17 14 14

30.4 59.4 18.2

13 14 15

25 23 20

54.5 05.6 09.1

Sun Mon

15 16

6 6

14.1 14.8

11 11

44.6 44.8

17 17

14.9 14.7

K 30 10 S 1 7 (2 27

37.2 06.9 57.3)

16 17

17 14

15.8 36.6

1 2 3 (4 5 6

15 11 7 27 23 19

44.1 42.8 30.4 15.2) 05.6 10.0

26 27 28 29 30

Tue Wed Thu Fri Sat

17 18 19 20 21

6 6 6 6 6

15.5 16.1 16.8 17.5 18.1

11 11 11 11 11

45.0 45.2 45.4 45.7 45.9

17 17 17 17 17

14.4 14.2 14.0 13.8 13.6

3 4 5 6 7

18.0 16.7 59.7 30.3 48.8

18 19 20 21 22

12 10 9 9 9

21.5 39.7 38.4 22.4 53.3

7 15 8 12 9 9 10 8 11 6 (12 30

35.9 29.9 57.2 01.1 42.7 00.6)

1 2 3 4 5

S

K K

S S

25 23 21 21 21

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

405

INDIAN CALENDAR SAKA ERA 1942 Month of KARTIKA (30 days)

Dakshinayan Dakshina Gola

Ayanamsa on 1st : 240 08/ 34//

(Nirayana) 8 Kartika, 5121 Kali Era to (Nirayana) 7 Agrahayana, 5121 Kali Era

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D. 1 Oct. 23 1- Enters Svati nak. (24h 00m.0) 2 24

11 12 13 14 15

1 2 3 4 5 6

16 17 18 19 20

7 8 9 10 11

21 22 23

12 13 14

24

15

25

16

26 27 28

17 18 19

Festivals

9- Full Moon (20h 19m.2)

8- Kojagor(Lakshimndra Puja), Kojagori Lakshmi Puja, Sarat Purnima 9- Kumara Purnima (Odisha), Maharshi Valmiki's Birthday, Oli ends(Jain). 10- Martyrdom day of Bhagat Kanwar Ram (Sindhi).

S U D D H A

3- Sayana Vyatipata (21h 35m.9)

1- Durga Puja begins(Saptami), Oli begins. 2- Saraswati Visarjana, Mahashtami, Maha Navami, Ayudha puja, Trivandrum Arat (Kerala) 3- Mahanavami (Bengal), Dussehara/ Dasahara 4- Vijaya Dasami (Bengal & Kerela), Madhvacharya Jayanti, Bharat Milap 5- Papankusa Ekadasi (Pasaukusa Ekadasi)

N A

Nov.

A S V I

10

13- Karaka Chaturthi, Dasaratha Chaturthi. 15- Enters Visakha nak. (8h 14m.0)

C H A A N D R A

31

9

17- Sayana Vaidhriti (13h 46m.6)

17- Ahoyi Ashtami, Karashtami. 20- Rama Ekadasi.

24- Saura Margasirshadi (9h 37m.4) C H A A N D R A KAR T I K A

28 29 30

6 7 8

S A U R A

27

5

SAU R A MARGASIRSHA

4

K A R T I K A

25 26

3

Phenomena

24- New Moon (10h 37m.2)

21- Govatsa Dvadasi. 22- Dhana Trayodasi, Kali Chaturdasi. 23- Hanumajjanma (N. India)(Purvarunodaya), Naraka Chaturdasi (Purvarunodaya), Kali Puja,Dipavali, Lakshmi Puja, Kaumudi Dipam, Lakshmi Dipam, Kedar Gauri Vrata (S. India), Mahavira Nirvana(Jain), Children’s Day (Nehru’s Birthday). 24- Govardhana Puja, Bali Puja, Annakuta. 25- Kartika Sukladi, Yama Dvitiya, Visvakarma Day, Bhratri Dvitiya (Bengal), Dwat Puja (Bihar), Kartika Puja. 26- Death anniversary of Lala Lajpat Rai. 28- Jnana Panchami (Jain)

28- Sayana 28- Enters Vyatipata Anuradha nak. (28h 18m.3) (14h 12m.3) 29- Jupiter enters 29- Pratihara Shashthi or Surya 20 29 Makara Shashthi (Chhat -Bihar), 30 Nov. 21 30- Enters Tropical (13h 22m.9) Birthday celebration of Prof. Ram Sagittarius Panjwani (Sindhi) (26h 09m.7) N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters : Makara 1,07h 01m.8; Kumbha 3, 15h 26m.3;Mina 5, 26h 30m.8; Mesha 8,14h 57m.1;Vrisha 10, 27h 41m.0; Mithuna 13, 15h 43m.2;Karkata 15, 25h 48m.4;Simha 18, 8h 42m.4;Kanya 20,12h 00m.5;Tula 22,12h 31m.7;Vrischika 24,11h 58m.2;Dhanus 26,12h 21m.5;Makara 28,15h 30m.1;Kumbha 30,22h25m.9;Sun enters :- Nirayana Vrischika 25, 6h 54m.0.

406

INDIAN CALENDAR SAKA ERA 1942

Dhanus : Sahasya Hemanta, 2nd Month

Month of AGRAHAYANA (30 days) (Nirayana) 8 Agrahayana, 5121 Kali Era to (Nirayana) 7 Pausha, 5121 Kali Era

Date Week Gregorian Day Date

No.

Ending Moment h m

Yoga No. Ending Moment h m

h

m

2019 A.D. Sun Nov. 22 Mon 23 Tue 24 Wed 25 Thu 26

6 6 6 6 6

18.8 19.5 20.2 20.9 21.6

11 11 11 11 11

46.2 46.5 46.7 47.0 47.4

17 17 17 17 17

13.5 13.3 13.2 13.2 13.1

S

8 9 S 10 11 12

22 24 26 29 -

51.8 32.8 42.6 10.8 -

23 24 25 26 27

11 13 15 18 21

09.2 04.7 31.7 20.3 20.4

13 14 15 15 16

29 30 6 7

50.6 00.8 44.9 34.1

6 7 8 9 10

Fri Sat Sun Mon Tue Dec.

27 28 29 30 1

6 6 6 6 6

22.2 22.9 23.6 24.3 25.0

11 11 11 11 11

47.7 48.0 48.4 48.7 49.1

17 17 17 17 17

13.1 13.1 13.1 13.2 13.2

12 13 14 S 15 K 1

7 10 12 14 16

47.0 21.9 48.1 59.7 52.3

1 2 3 4 4

24 27 30 8

22.5 18.8 03.1 30.6

17 18 19 20 21

8 9 10 10 11

28.5 21.8 08.6 45.0 07.6

11 12 13 14 15

Wed Thu Fri Sat Sun

2 3 4 5 6

6 6 6 6 6

25.6 26.3 27.0 27.7 28.3

11 11 11 11 11

49.5 49.9 50.3 50.7 51.1

17 17 17 17 17

13.3 13.5 13.6 13.8 14.0

2 3 4 5 6

18 19 20 20 19

22.5 27.3 04.1 10.7 45.4

5 6 7 8 9

10 12 13 14 14

37.7 21.3 38.8 27.6 45.9

22 23 24 25 26 (27

11 11 10 9 8 30

13.8 01.4 28.4 32.8 13.1 28.1)

16 17 18 19 20

Mon Tue Wed Thu Fri

7 8 9 10 11

6 6 6 6 6

29.0 29.6 30.3 30.9 31.5

11 11 11 11 11

51.5 52.0 52.4 52.9 53.3

17 17 17 17 17

14.2 14.4 14.7 15.0 15.3

7 8 9 K 10 11

18 17 15 12 10

47.6 17.7 17.9 51.8 04.5

10 11 12 13 14 (15

14 13 12 10 8 30

32.5 47.5 32.6 51.2 48.2 30.1)

1 2 3 4 5

28 25 22 19 15

17.4 41.9 43.2 24.7 50.4

21

Sat

12

6 32.1

11

53.8

17

15.6

28

04.5

6

12

05.6

Sun

13

6 32.8

11

54.3

17

15.9

02.5 53.2) 45.0

16

22

12 7 (13 27 14 24

17

25

40.1

23 24 25

Mon Tue Wed

14 15 16

6 33.4 6 33.9 6 34.5

11 11 11

54.7 55.2 55.7

17 17 17

16.3 16.7 17.1

K 30 21 S 1 19 2 16

46.6 07.0 54.9

18 19 20

23 21 20

25.9 30.9 04.1

7 (8 9 10 11

8 28 24 21 18

16.6 29.7) 52.3 31.0 32.7

26 27 28 29 30

Thu Fri Sat Sun Mon

17 18 19 20 21

6 6 6 6 6

11 11 11 11 11

56.2 56.7 57.2 57.7 58.2

17 17 17 17 17

17.5 17.9 18.4 18.9 19.4

3 4 5 6 7

18.2 23.4 14.7 53.2 15.6

21 22 23 24 25

19 19 19 21 23

13.1 04.0 40.1 01.2 03.0

12 13 14 15 16

16 14 12 12 11

02.9 06.5 45.9 01.5 51.0

35.1 35.6 36.2 36.7 37.2

Sunset

Nakshatra

Apparent Noon h m

1 2 3 4 5

Sunrise

Tithi No. Ending Moment h m

h

m

K

S S

15 14 14 14 16

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

407

INDIAN CALENDAR SAKA ERA 1942 Month of AGRAHAYANA (30 days)

Dakshinayana Dakshina Gola

Ayanamsa on 1st : 240 08/ 38//

(Nirayana) 8 Agrahayana, 5121 Kali Era to (Nirayana) 7 Pausha, 5121 Kali Era

24 25

15 16

26 27 28

17 18 19

29

20

T I K A A R K

12 13 14

D R A

21 22 23

11- Enters Jyeshtha nak. (18h 33m.6)

12- Sayana Vaidhriti (19h 53m.6)

N

7 8 9 10 11

9- Full Moon (15h 00m.0)

7- Vaikuntha Chaturdasi, Bharani Dipam. 8- Krittika Dipam, Rasayatra (Smarta), Tripurotsava. 9- Rasayatra (Vaishnava), Kartiki Purnima, Rathayatra (Jain), Guru Nanak’s Birthday, Pushkar Fair (Ajmer), Huthri-3 days(Coorg).

16- Kalashtami. 17- Prathamashtami (Odisha), Vaikkatashtami (Kerela).

A

16 17 18 19 20

1- Gopashtami or Gosthashtami. 2- Jagaddhatri Puja, Akshya Navami. 3- Guru Tegh Bahadur’s Martyrdom Day. 4- Deva Probodhani Ekadasi. 5- Tulasi Vivaha, Vanjuli Mahadvadasi.

20- Utpanna Ekadasi.

H

2 3 4 5 6

C

11 12 13 14 15

C H AN D R A MAR GA S I R S H A

30 1

I R

Dec.

G A S

9 10

R

29

M A

8

Festivals

A

27 28

Phenomena

S A U R

6 7

A

25 26

S A U R A P A U S H

4 5

S H A

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D. 1 Nov. 22 2 23 3 24

23- Saura Paushadi (24h 25m.9)

23- New Moon (21h 46m.6) 23- Total Solar Eclipse (not visible in India) 24- Enters Mula nak. 24- Sayana (21h 32m.3) Vyatipata (19h 02m.6)

28- Subrahmanya Shasthi (South India). 29- Guha Shashthi, Champa Shasthi (Maharashtra), Mulukrupini Shashthi. 30- Mitra Saptami, Uttarayana Day.

30- Enters Trop. Capricorn (15h 32m.3) N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Mina 3, 8h 52m.5; Mesha 5, 21h 20m.4; Vrisha 8, 10h 01m.2; Mithuna 10, 21h 36m.9; Karkata 13, 7h 22m.0; Simha 15, 14h 45m.9; Kanya 17, 19h 31m.5;Tula 19, 21h 52m.0; Vrischika 21, 22h 41m.1; Dhanus 23, 23h 25m.9; Makara 25, 25h 47m.7; Kumbha 28,7h 16m.3;Mina 30,16h 29m.1; Sun enters :- Nirayana Dhanus 24, 21h 32m.3. 30

Dec. 21

408

INDIAN CALENDAR SAKA ERA 1942

Makara : Tapas Winter (Sisira), 1st Month

Month of PAUSHA (30 days)

(Nirayana) 8 Pausha, 5121 Kali Era to (Nirayana) 7 Magha, 5121 Kali Era

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

2020 A.D. Tue Dec. 22 Wed 23 Thu 24 Fri 25 Sat 26

6 6 6 6 6

37.7 38.2 38.6 39.1 39.5

11 11 11 12 12

6 7 8 9 10

Sun Mon Tue Wed Thu

27 28 29 30 31

6 6 6 6 6

39.9 40.3 40.7 41.0 41.3

11 12 13 14

2021 A.D. Fri Jan. 1 Sat 2 Sun 3 Mon 4

6 6 6 6

15

Tue

5

16 17 18 19 20

Wed Thu Fri Sat Sun

21

Sunset

Tithi No. Ending Moment h m

Nakshatra No.

Ending Moment h m

Yoga No. Ending Moment h m

h

m

58.7 59.2 59.7 00.2 00.7

17 17 17 17 17

19.9 20.4 21.0 21.5 22.1

S

18 20 23 25 28

14.8 39.9 17.7 54.7 18.8

26 27 1 1 2

25 28 7 10

37.4 32.8 36.3 35.3

17 18 19 20 21

12 12 13 14 15

09.3 48.8 40.7 35.5 24.4

12 12 12 12 12

01.2 01.6 02.1 02.6 03.1

17 17 17 17 17

22.7 23.3 23.9 24.5 25.1

13 30 14 14 7 S 15 8 K 1 9

20.8 54.8 58.2 30.7

3 4 5 6 7

13 15 17 18 19

19.0 39.5 32.1 55.0 48.8

22 23 24 25 26

15 16 16 15 14

59.9 16.7 11.5 42.9 51.0

41.6 41.9 42.2 42.4

12 12 12 12

03.6 04.0 04.5 04.9

17 17 17 17

25.8 26.4 27.1 27.7

20 20 19 19

15.2 16.9 56.6 17.0

12

05.4

17

28.4

33.9 10.4 22.9 14.3 47.3) 04.2

8 9 10 11

6 42.7

2 9 3 9 4 8 5 7 (6 29 7 28

12

18

20.6

27 1 2 3 4 5

13 12 10 8 29 27

36.9 02.5 09.6 00.4 36.6 00.0

6 7 8 9 10

6 6 6 6 6

42.9 43.1 43.2 43.4 43.5

12 12 12 12 12

05.8 06.3 06.7 07.1 07.5

17 17 17 17 17

29.1 29.8 30.5 31.2 31.9

26 23 21 19 16

07.0 58.3 40.6 17.5 53.1

13 14 15 16 17

17 15 14 12 10

09.4 45.8 12.4 32.3 49.6

6 7 8 9 10

24 21 18 15 11

12.2 14.8 10.0 00.3 49.0

Mon

11

6 43.6

12

07.9

17

32.6

13 14

32.9

18

9

09.3

22

Tue

12

6 43.6

12

08.3

17

33.3

14 12

23.0

13 14 15

6 43.7 6 43.7 6 43.7

12 12 12

08.7 09.1 09.4

17 17 17

34.0 34.7 35.4

K 30 10 S 1 9 2 8

30.2 01.9 05.2

37.7 21.5) 28.0 04.4 16.8

39.8 37.5) 47.2

Wed Thu Fri

7 30 29 29 29

8 29 26

23 24 25

19 (20 21 22 23

11 (12 13 14 15 16

24 22 20

14.4 04.5 22.2

26 27 28 29 30

Sat Sun Mon Tue Wed

16 17 18 19 20

6 6 6 6 6

12 12 12 12 12

09.8 10.1 10.4 10.7 11.0

17 17 17 17 17

36.2 36.9 37.6 38.3 39.0

3 7 4 8 5 9 6 10 7 13

46.2 08.9 14.4 59.2 15.5

24 25 25 26 27

30 7 9 12

09.3 43.0 54.6 36.3

17 18 19 20 21

19 18 18 18 19

11.1 32.8 26.2 47.5 29.7

1 2 3 4 5

43.7 43.6 43.5 43.5 43.3

8 9 S 10 11 12

8 9 K 10 11 12

S S

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

409

INDIAN CALENDAR SAKA ERA 1942 Month of PAUSHA (30 days)

Uttarayana Dakshina Gola

Ayanamsa on 1st : 24° 08/ 44//

(Nirayana) 8 Pausha, 5121 Kali Era to (Nirayana) 7 Magha, 5121 Kali Era

6 7 8 9 10

21 22 23

11 12 13

24

14

25

15

26 27 28 29 30

16 17 18 19 Jan. 20

M A R G A S I R S H A

16 17 18 19 20

C H A N D R A

11 12 13 14 15

30 31 2021A.D. Jan. 1 2 3 4 5

PA U S H A

9 10

C H AA N D R A

27 28 29

S A U R A

6 7 8

MAG HA

26

SAU RA

5

P A U S HA

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2020 A.D. 1 Dec. 22 23 2 24 3 25 4

Phenomena

Festivals

4- Mauna Ekadasi (Jain), Gita jayanti, Vaikuntha Ekadasi (S India), Mokshada Ekadasi, Birthday of Sadhu T. L.Vaswani (Sindhi) 5- Akhanda Dvadasi, Jor mela-3days (Punjab) 7- Enters Purvashadha nak. (23h 45m.0)

7- Sayana Vaidhriti (25h 20m.4) 9- Full Moon (8h 58m.2)

8- Shri Dutta Jayanti(Maharashtra), Dutts Treya Jayanti. 9- Margi Purnima, Arudra Darshanam (Purvarunodaya) (S. India)

16- Ashtaka(Pupashtaka) 18- Birthday of Parsvanath (Jain). 19- Saphla Ekadasi. 20- Enters Uttarashadha nak. (25h 45m.4)

20- Sayana Vyatipata (9h 16m.9)

23- Saura Maghadi (11h 08m.0)

23- New Moon (10h 30m.2)

29- Enters Tropical Aquarius (26h 09m.8)

22- Vahula Amavasya (Odisha). 23- Lohri (Punjab,J&K), Bhogi (S. India). 24- Birthday of Sant Paramanand (Sindhi), Magha Bihu (Assam), Makara Samkranti (N.India), Makara Samkranti(Bengal), Pongal (S. India), Makara Snana,Tila Samkranti, Tai Pongal(Kerala), Tamil New Year’s Day. 25- Mattu Pongal or Kanuvu(S. India)

27- Jupiter sets in the East (26h 45m) 30- Guru Govind Singh’s Birthday.

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Mesha 2, 28h 32m.8; Vrisha 5, 17h 18m.0; Mithuna 7, 28h 39m.5; Karkata 10, 13h 38m.0; Simha 12, 20h 16m.9; Kanya 14, 25h 04m.4; Tula 16, 28h 29m.1; Vrischika 19, 6h 57m.7; Dhanus 21, 9h 09m.3; Makara 23, 12h 05m.7; Kumbha 25, 17h 05m.9; Mina 27, 25h 15m.9; Mesha 30, 12h 36m.3; Sun enters :- Nirayana Makara 24, 8h 14m.9.

410

INDIAN CALENDAR SAKA ERA 1942

Kumbha : Tapasya Winter (Sisira), 2nd Month

Month of MAGHA (30 days)

(Nirayana) 8 Magha, 5121 Kali Era to (Nirayana) 7 Phalguna, 5121 Kali Era

Date Week Gregorian Day Date

Sunrise h

m

Apparent Noon h m

2021 A.D. Thu Jan. 21 Fri 22 Sat 23 Sun 24 Mon 25

6 6 6 6 6

43.2 43.0 42.8 42.6 42.4

12 12 12 12 12

6 7 8 9 10

Tue Wed Thu Fri Sat

26 27 28 29 30

6 6 6 6 6

42.1 41.8 41.5 41.2 40.9

11 12 13

Sun Mon Feb. Tue

31 1 2

14 15

Wed Thu

16 17

Sunset

Tithi No. Ending Moment h m

Nakshatra No.

Ending Moment h m

Yoga No. Ending Moment h m

h

m

11.3 11.6 11.8 12.1 12.3

17 17 17 17 17

39.7 40.4 41.2 41.9 42.6

S

8 9 S 10 11 12

15 18 20 22 24

50.7 29.6 56.7 58.4 25.0

1 2 3 4 5

15 18 21 24 25

36.3 40.1 32.5 00.8 55.5

22 23 24 25 26

20 21 22 22 22

23.4 18.0 02.8 28.3 27.8

12 12 12 12 12

12.5 12.7 12.9 13.1 13.3

17 17 17 17 17

43.2 43.9 44.6 45.3 46.0

13 14 S 15 K 1 2

25 25 24 23 22

11.6 17.7 46.2 42.4 13.0

6 7 8 9 10

27 27 27 27 26

11.7 49.1 50.5 21.2 28.0

27 1 2 3 4

21 20 19 17 15

57.2 55.6 24.2 26.7 07.5

6 40.5 6 40.1 6 39.7

12 12 12

13.4 13.6 13.7

17 17 17

46.7 47.3 48.0

3 20 4 18 5 16

25.1 25.3 19.6

11 12 13

25 23 22

17.9 57.4 32.4

3 4

6 39.2 6 38.8

12 12

13.8 13.9

17 17

48.6 49.3

6 14 7 12

12.6 07.9

14 15

21 19

07.3 45.3

5 6 7 (8 9 10

12 9 6 27 25 22

31.8 44.8 51.4 55.5) 00.2 07.8

Fri Sat

5 6

6 38.3 6 37.8

12 12

14.0 14.0

17 17

49.9 50.5

18 17

28.3 17.7

11 12

19 16

19.7 36.7

Sun Mon Tue

7 8 9

6 37.3 6 36.8 6 36.2

12 12 12

14.1 14.1 14.2

17 17 17

51.2 51.8 52.4

07.7 13.5 26.5) 48.0 20.0 05.8

16 17

18 19 20

10 8 30 28 27 26

18 19 20

16 15 14

14.6 20.8 38.6

13 14 15

13 11 9

59.9 30.4 10.1

21

Wed

10

6 35.7

12

14.2

17

53.0

14 25

09.4

21

14

11.9

22 23 24 25

Thu Fri Sat Sun

11 12 13 14

6 6 6 6

35.1 34.5 33.8 33.2

12 12 12 12

14.2 14.2 14.2 14.1

17 17 17 17

53.6 54.2 54.8 55.4

K 30 24 S 1 24 2 24 3 25

35.7 30.0 57.0 59.5

22 23 24 25

14 14 15 16

05.0 23.2 11.3 32.8

16 (17 18 19 20 21

7 29 27 26 25 25

01.3 07.4) 32.1 19.2 31.7 11.4

26 27 28 29 30

Mon Tue Wed Thu Fri

15 16 17 18 19

6 6 6 6 6

32.5 31.9 31.2 30.5 29.7

12 12 12 12 12

14.1 14.0 14.0 13.9 13.8

17 17 17 17 17

55.9 56.5 57.0 57.6 58.1

4 27 5 29 6 6 8 7 10

37.5 46.7 18.2 58.7

26 27 1 2 3

18 20 23 26 29

28.8 56.5 48.8 54.0 57.4

22 23 24 25 26

25 25 26 27 28

18.1 48.8 37.4 35.2 31.3

1 2 3 4 5

K

8 9 (K 10 11 12 13

S

S

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

411

INDIAN CALENDAR SAKA ERA 1942 Month of MAGHA (30 days)

Uttarayana Dakshina Gola

Ayanamsa on 1st : 24° 08/ 48//

(Nirayana) 8 Magha, 5121 Kali Era to (Nirayana) 7 Phalguna, 5121 Kali Era

5 6 7 8

20 21 22

9 10 11

23 24 25

12 13 14

26

15

27 28

16 17

29

18

P AU S H A

16 17 18 19

1- Martyrdom Day of Hemu Kalani (Sindhi). 3- Samba Dasami (Odisha), Netaji’s Birthday. 4- Putrada Ekadasi.

C H AN D R A

31 1 2 3 4

15- Sayana Vyatipata (19h 33m.4)

15- Birthday of Swami Vivekananda (according to tithi), Astaka (Mamashtaka)

6- Republic Day.

M S A U R A

Feb.

S A U R A P H A L G U N A

11 12 13 14 15

2- Sayana Vaidhriti (30h 40m.5)

Festivals

8- Paushi Purnima, Pusyabhisheka Yatra, Floating Festival/Tai Poosam, Birthday of Lala Lajpat Rai. 10- Martyr’s Day (Mahatma Gandhi Commemoration Day) 11- Ganesha Sankastha Chaturthi.

M A G H A

30

Phenomena

8- Full Moon (24h 46m.2)

C H A A N D R A

10

G

26 27 28 29

A

6 7 8 9

H

A

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2021 A.D. Jan. 21 1 22 2 23 3 3- Enters Sravana nak. 24 4 (27h 59m.1) 25 5

17- Enters Dhanishtha nak. (7h 12m.1)

22- Saura Phalgunadi (23h 54m.2)

22- New Moon (24h 35m.7)

18- Sattila Ekadasi (Smarta). 19- Sattila Ekadasi (Vaishnava and Vidhava). 20- Meru Trayodasi (Jain). 21- Ratanti Kalika Puja. 22- Mauni Amavasya, Tai Amavasya, Makara Vavu (Kerala). 23- Magha Sukladi.

24- Jupiter rises in the West (10h 06m)

28- Venus sets in the West (10h 10m) 28- Sayana Vaidhriti (11h 10m.6)

26- Varada Chaturthi,Tila Chaturthi, Kunda Chaturthi, Ganesa Puja (Bengal). 27- Sri Panchami, Saraswati Puja, Vasanta Panchami.

29- Enters Trop. 29- Arogya Saptami, Vidhana Saptami. Pisces (16h 13 m.9) Feb. 19 30 30- Enters 30- Shivaji Jayanti, Ratha Saptami Satabhisaj (Purvarunodaya). nak.(11h 37m.0) N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Moon enters :- Vrisha 2, 25h 24m.8; Mithuna 5, 13h 02m.7; Karkata 7, 21h 43m.3; Simha 9, 27h 21m.2; Kanya 12, 6h 58m.5; Tula 14, 9h 49m.7; Vrischika 16, 12h 47m.0; Dhanus 18, 16h 14m.6; Makara 20, 20h 30m.3; Kumbha 22, 26h 10m.6; Mina 25, 10h 09m.1; Mesha 27, 20h 56m.5; Vrisha 30, 9h 40m.6; Sun enters :- Nirayana Kumbha 23, 21h 12m.4.

412

INDIAN CALENDAR SAKA ERA 1942

Mina : Madhu Spring (Vasanta), 1st Month

Month of PHALGUNA (30 days)

(Nirayana) 8 Phalguna, 5121 Kali Era to (Nirayana) 7 Chaitra, 5121 Kali Era

Date Week Gregorian Day Date

1 2 3 4 5

Sat Sun Mon Tue Wed

h

m

Apparent Noon h m

6 6 6 6 6

29.0 28.3 27.5 26.7 25.9

12 12 12 12 12

25 26 27 28 1

6 6 6 6 6

25.1 24.3 23.5 22.6 21.8

2021 A.D. Feb. 20 21 22 23 24

Sunrise

Sunset

Tithi No. Ending Moment h m

Nakshatra No.

Ending Moment h m

Yoga No. Ending Moment h m

h

m

13.7 13.6 13.5 13.3 13.2

17 17 17 18 18

58.7 59.2 59.7 00.2 00.7

S

8 9 S 10 11 12

13 15 17 18 18

32.2 42.7 16.8 05.7 06.0

4 4 5 6 7

8 10 12 13

43.4 57.8 30.8 17.2

27 1 2 3 4

29 29 29 28 27

14.3 34.0 22.2 34.2 08.6

12 12 12 12 12

13.0 12.9 12.7 12.5 12.3

18 18 18 18 18

01.2 01.7 02.1 02.6 03.1

13 14 S 15 K 1 2 (3

17 15 13 11 8 29

19.1 8 50.2 9 47.3 10 19.4 11 36.1 12 46.7) (13

13 12 11 9 7 29

17.2 35.1 18.2 35.6 36.9 31.8)

5 6 7 8 9

25 22 19 16 12

07.3 34.7 36.9 21.1 54.7

4 26

59.7

14

27

29.0

9 29 26 23 20 18

24.9 58.1) 39.7 33.9 43.1 08.7

6 7 8 9 10

Thu Fri Sat Sun Mon Mar.

11

Tue

2

6

20.9

12

12.1

18

03.5

12 13 14 15

Wed Thu Fri Sat

3 4 5 6

6 6 6 6

20.0 19.2 18.3 17.4

12 12 12 12

11.9 11.7 11.5 11.2

18 18 18 18

04.0 04.4 04.9 05.3

K

5 6 7 8

24 21 19 18

22.1 59.3 54.9 10.8

15 16 17 18

25 23 22 21

35.7 57.4 37.6 38.0

10 (11 12 13 14 15

16 17 18 19 20

Sun Mon Tue Wed Thu

7 8 9 10 11

6 6 6 6 6

16.5 15.6 14.6 13.7 12.8

12 12 12 12 12

11.0 10.8 10.5 10.3 10.0

18 18 18 18 18

05.7 06.2 06.6 07.0 07.4

9 K 10 11 12 13

16 15 15 14 14

47.5 44.9 02.6 40.7 40.3

19 20 21 22 23

20 20 20 21 21

59.0 40.3 41.4 02.7 45.3

16 17 18 19 20

15 13 12 10 9

51.0 49.9 04.9 35.9 23.6

21 22 23 24 25

Fri Sat Sun Mon Tue

12 13 14 15 16

6 6 6 6 6

11.8 10.9 09.9 09.0 08.0

12 12 12 12 12

09.7 09.5 09.2 08.9 08.6

18 18 18 18 18

07.8 08.2 08.6 09.0 09.4

14 15 K 30 15 S 1 17 2 18 3 20

03.0 51.2 06.7 50.0 59.4

24 25 26 27 1

22 24 26 28 -

51.0 21.9 19.5 43.5 -

21 22 23 24 25

8 7 7 7 8

29.1 53.7 39.1 45.7 13.1

26 27 28 29 30

Wed Thu Fri Sat Sun

17 18 19 20 21

6 6 6 6 6

07.1 06.1 05.1 04.1 03.2

12 12 12 12 12

08.3 08.1 07.8 07.5 07.2

18 18 18 18 18

09.8 10.2 10.6 10.9 11.3

4 23 5 26 6 28 7 7 7

29.2 10.0 48.7 10.5

1 2 3 4 5

7 10 13 16 19

30.8 34.5 44.0 45.5 24.5

26 8 27 9 1 10 2 11 3 12

58.3 56.2 58.8 56.6 38.7

S

S

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

413

INDIAN CALENDAR SAKA ERA 1942 Month of PHALGUNA (30 days)

Uttarayana Dakshina Gola

Ayanamsa on 1st : 240 08/ 53//

(Nirayana) 8 Phalguna, 5121 Kali Era to (Nirayana) 7 Chaitra, 5121 Kali Era

2 3 4 5 6

16 17

7 8

18 19

9 10

20 21 22

11 12 13

23 24 25

14 15 16

26 27 28 29 30

17 18 19 20 Mar. 21

M A G H A

11 12 13 14 15

C H A N D R A

25 26 27 28 Mar. 1

Phenomena

1- Bhishmashtami.

4- Jaya Ekadasi, Bhaimi Ekadasi (Bengal). 5- Bhishma Dvadasi.

8- Full Moon (13h 47m.3)

13-Enters Purva Bhadrapada nak. (17h 59m.7)

Festivals

6- Desert Festival - 3 days (Jaislmer). 8- Guru Rabi Das’s Birthday (according to tithi), Maghi Purnima Masi Magham.

11- Sayana Vyatipata (6h 54m.5) 14- Vaikkatashtami (Kerela). 15- Ashtaka (Sakashtak), Janaki Janma. 17- Birthday of Swami Dayananda Saraswati (Founder of Arya Samaj). 18- Vijaya Ekadasi. 19- Maha Sivratri (Kashmir). 20- Maha Sivaratri, Maha Sivaratri (S. India).

PH ALG UN A

6 7 8 9 10

S A U R A

24

SAU RA C HAIT RA

5

P H A L G U N A

Date Gregorian Solar Lunar Transit of the Sun Date Month Month 2021 A.D. 1 Feb. 20 2 21 3 22 4 23

22-Saura Chaitradi (20h 26m.0)

22- New Moon (15h 51m.2) 23- Sayana Vaidhriti (16h 45m.5) 24- Birthday of Sri Ramakrishna (according to tithi).

C H A A NDR A

26-Enters Uttara Bhadrapada nak. (26h 21m.6) 29- Mahavishuva Day. 29-Enters Trop. 30- Indian Year Ending day, Aries Holastaka (15h 07m.4) N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½0 E. Long. Moon enters :- Mithuna 2, 21h 55m.3; Karkata 5, 7h 10m.1; Simha 7, 12h 35m.1; Kanya 9, 15h 07m.0; Tula 11, 16h 29m.7; Vrischika 13, 18h 20m.4; Dhanus 15, 21h 38m.0; Makara 17, 26h 38m.7; Kumbha 20, 9h 21m.2; Mina 22, 17h 56m.7; Mesha 24, 28h 43m.5; Vrisha 27, 17h 21m.9; Mithuna 30, 6h 08m.7; Sun enters: Nirayana Mina 23, 18h 03m.6.

414

PRINCIPAL FESTIVALS AND ANNIVERSARIES FOR HOLIDAYS Festivals Criterion Date National / Nirayana / Gregorian Saka 1941/Kali 5120 /2020 A.D. 77. Guru Gobind Singh’s Birthday Pausha S 7 Pausha 12 / Pausha 19 / Jan 02 78. Vaikuntha Ekadasi (S.India) S 11 of Saura Pausha Pausha 16 / Pausha 23 / Jan 06 79. Bhogi (S.India) Day before Pongal Pausha 24 / Magha 1 / Jan.14 80. Makara Samkranti (Bengal) Saura Maghadi (Midnight Rule) Pausha 25 / Magha 2 / Jan 15 Magha Bihu (Assam) Saura Maghadi (Midnight Rule) Pausha 25 / Magha 2 / Jan. 15 81. Pongal (S.India),Tai Pongal(Kerala) The day of Saura Maghadi Pausha 25 / Magha 2 / Jan. 15 Tamil New Year’s day ,Tila Samkranti, (Sunset Rule) Pausha 25 / Magha 2 / Jan. 15 Makara Samkranti (N.India), Makaradi -doPausha 25 / Magha 2 / Jan. 15 Snana 82. Mattu Pongal or Kanuvu Day after Pongal Pausha 26 / Magha 3 / Jan. 16 83. Netaji’s Birthday Fixed Magha 3 / Magha 10 / Jan. 23 84. Republic Day Fixed Magha 6 / Magha 13 / Jan. 26 85. Sri Panchami, Vasanta Panchami Magha S 5 Magha 10 / Magha 17 / Jan 30 86. Guru Ravidas’s Birthday Magha S 15 Magha 20 / Magha 27 / Feb 9 87. Birth Day of Swami Dayananda Saraswati (Founder of Arya Samaj) Phalguna K 10 (Purnimanta) Magha 29 / Phalguna 6 / Feb 18 88. Sivaji Jayanti Fixed Magha 30 / Phalguna 7 / Feb 19 89. Maha Sivaratri (Kashmir) Magha K 13 Phalguna 1/ Phalguna 8/ Feb 20 90. Maha Sivaratri Magha K 14(Prodosa & Phalguna 2/ Phalguna 9/ Feb 21 Nishithavyapini) 91. Holikadahana Phalguna S 15 (night) Phalguna 19/ Phalguna 26/ March 9 92. Dolyatra Phalguna S 15 Phalguna 19/ Phalguna 26/ March 9 93. Holi Day after Holikadahana Phalguna 20/Phalguna 27/March 10 94. Hola,Vasantotsava Phalguna K 1 Phalguna 20/Phalguna 27/March 10 95. MahaVishuva day Day of Sun’s entry into Trop . Phalguna 30 / Chaitra 6 / March 20 Aries (Midnight rule) Saka 1942/Kali 5120 /2020 A.D. 1. Indian New Year’s Day Fixed Chaitra 1 / Chaitra 7/ Mar. 21 2. Chaitra Shukladi(Gudi Padava, Ugadi), Chaitra S 1 Chaitra 5 / Chaitra 11/ Mar. 25 Cheti Chand (Sindhi New Year's Day), Chaitra S 1 Chaitra 5 / Chaitra 11/ Mar. 25 Vasanta Navaratrarambha, Telugu Chaitra S 1 Chaitra 5 / Chaitra 11/ Mar. 25 New Year's Day Chaitra S 1 Chaitra 5 / Chaitra 11/ Mar. 25 3. Sarhul (Bihar) Chaitra S 3 Chaitra 7 / Chaitra 13/ Mar. 27 4. Oli begins ( Jain) Chaitra S 7 Chaitra 11 / Chaitra 17/ Mar. 31 5. Rama Navami Chaitra S 9 Chaitra 13 / Chaitra 19/ Apr. 2 6. Mahavira Jayanti Chaitra S 13 Chaitra 17 / Chaitra 23/ Apr. 6 7. Oli ends (Jain) Chaitra S 15(Udayvyapini) Chaitra 19 / Chaitra 25 / April 8 8. Vaisakhi (Punjab,Haryana, H.P,Delhi Saura Vaisakhadi(Sunrise Rule) Chaitra 24 / Chaitra 30 / April 13 & Odisha),Visu (Kerala), Saura Vaisakhadi(Sunrise Rule) Chaitra 24 / Chaitra 30 / April 13 Chaitra Samkranti, Saura Vaisakhadi(Midnight Rule) Chaitra 24 / Chaitra 30 / April 13 Chadak Puja(Bengal), Saura Vaisakhadi(Midnight Rule) Chaitra 24 / Chaitra 30 / April 13 Cheiraoba (Manipur), Day of Saura Vaisakhadi Chaitra 24 / Chaitra 30 / April 13 Mesha Samkranti (Odisha), Saura Vaisakhadi (Sunrise Rule) Chaitra 24 / Chaitra 30 / April 13 Rangali Bihu(Assam) Chaitra 24 / Chaitra 30 / April 13 Saka 1942/Kali 5121 /2020 A.D. 9. Vaisakhadi (Bengal) , Bahag Bihu Day Following Saura Vaisakhadi Chaitra 25/ Vaisakha 1 / Apr. 14 (Assam), Shilhenba (Manipur), (Midnight Rule) Chaitra 25/ Vaisakha 1 / Apr. 14 Meshadi (T.N.), Saura Vaisakhadi (Sunset Rule) Chaitra 25/ Vaisakha 1 / Apr. 14 Dr. B. R. Ambedkar Jayanti Fixed Chaitra 25/ Vaisakha 1 / Apr. 14 10. Babu Kuer Singh Day (Bihar), Fixed Vaisakha 3 / Vaisakha 10 /Aprl.23 Tithi of Deva Damodara(Assam) S1 of Saura Vaisakha Vaisakha 3 / Vaisakha 10 /Aprl.23 11. Akshaya Tritiya Vaisakha S 3 Vaisakha 6 / Vaisakha 13 /April 26 12. May Day Fixed Vaisakha 11 / Vaisakha 18 / May 1 13. Buddha Purnima Vaisakha S 15 Vaisakha 17/ Vaisakha 24 / May 7 Festivals numbered 77 to 95 are repetition of the same for Pausha to Phalguna, 1941 S.E., published in the previous year.

415

PRINCIPAL FESTIVALS AND ANNIVERSARIES FOR HOLIDAYS Festivals 14. Birthday of Rabindranath 15. Pratap Jaynati 16.Guru Arjan Dev's Martyrdom Day (Sikh) 17. Rajas Samkranti (Odisha) 18. Rathayatra 19. Kharchi Puja (Tripura) 20. Punaryatra (Smarta) 21. Ultarath, Bahudha Yatra 22. Ker Puja (Tripura) 23. Karkataka Vavu (Kerela) 24. Jhulana Yatrarambha 25. Tilak Commemoration Day 26. Raksha Bandhana , Amar nath yatra, Solono (Rakhi Bandhan), Naroli Purnima, Balabhadra Puja (Odisha), Sravani Purnima, Avani Avittam (S. India), Jaju Upakarma, Jhulana Yatrasamapanna 27. Rik Upakarma 28. Raksha Panchami (Odisha) 29. Janmashtami (Smarta) 30. Janmashtami (Vaishnava), Gokulashtami (Nandotsava ) 31. Independence Day, Paryusana Parvarambha (Chaturthi Paksha –Jain ) 32. Paryusana Parvarambha (Panchami Paksha –Jain ) 33. Vinayak Chaturthi (T.N),Ganesh Chaturthi, Samvatsari(Chaturthi paksha - Jain), Sama Veda Upakarma 34. Samvatsari(Panchami paksha - Jain) 35. Radhashtami 36. First Onam Day 37. Onam or Thiru Onam Day 38. Ananta Chaturdasi Third Onam day 39. Fourth Onam day 40. Tithi of Sri Madhava Deva (Assam) 41. Sri Krishna Jayanti (T.N., Kerala, Assam), Sri Jayanti (Ramanuja). 42. Mahalaya Amavasya ,Sarvapitri Amavasya (Odisha) 43. Mahatma Gandhi’s Birthday 44. Sthapana Navaratrarambha (Saradia) 45. Durga Puja (Saptami ) Oli begins ( Jain) 46. Durga Puja (Maha Astami ), Durga Puja (Maha Navami), Trivandram Arat 47. Ayudha Puja, Mahanavami (Bengal & Kerela), Dussehara or Dasahara

Criterion 25 Vaisakha of Beng. Calendar Jyaishtha S 3 Jyaishtha S 4

Date National / Nirayana / Gregorian Saka 1942/Kali 5121/2020 A.D. Vaisakha 18 / Vaisakha 25 /May 8 Jyaishtha 4/Jyaishtha 11/ May 25 Jyaishtha 5/Jyaishtha 12/ May 26

Saura Ashadhadi (Sunrise Rule) Ashadha S 2 Ashadha S 8 Ashadha S 10 9th day from Rathyatra First Tues. or Sat.day after 14 days from Kharchi Puja not falling on K 10 K 30 of Saura Sravana Sravana S 11 Fixed Sravana S 15 Sravana S 15 Sravana S 15 Sravana S 15 Sravana S 15 Sravana S 15 Sravana nak . of Chandra Sravana Sravana K 5 Sravana K 8 (Nishitha) Sravana K 8 Sravana K 8 Fixed 7 days before Samvatsari (Chaturthi paksha) 7 days before Samvatsari (Panchami paksha) S4 of Saura Bhadra Bhadra S 4 (Udayavyapini)

Jyaishtha 24/Jyaishtha 31/June14 Ashadha 2/ Ashadha 9 / June 23 Ashadha 7/ Ashadha 14/June 28 Ashadha 9/ Ashadha 16/June 30 Ashadha 10/ Ashadha 17/ July1 Ashadha 23/ Ashadha 30/July 14

Hasta in Chandra Bhadra Bhadra S 5 current at Sunset Bhadra S 8 Day before Thiru Onam Day Sravana nak.of Saura Bhadra Bhadra S 14 Day after Thiru Onam day 2 days after Thiru Onam day K 5 of Saura Bhadra K8 of Saura Bhadra

Sravana 31 / Bhadra 7 / Aug.22 Bhadra 1/ Bhadra 8/ Aug 23 Bhadra 4/ Bhadra 11/ Aug 26 Bhadra 8/ Bhadra 15/ Aug 30 Bhadra 9/ Bhadra 16/ Aug 31 Bhadra 10/ Bhadra 17/ Sept 1 Bhadra 10/ Bhadra 17/ Sept 1 Bhadra 11/ Bhadra 18/ Sept 2 Bhadra 16/ Bhadra 23/ Sept 7 Bhadra 19/ Bhadra 26/ Sept 10

Ashadha 29/ Sravana 5/ July 20 Sravana 8 / Sravana 15 / July 30 Sravana 10/ Sravana 17/ Aug 1 Sravana 12 / Sravana 19 / Aug 3 Sravana 12 / Sravana 19 / Aug 3 Sravana 12 / Sravana 19 / Aug 3 Sravana 12 / Sravana 19 / Aug 3 Sravana 12 / Sravana 19 / Aug 3 Sravana 12 / Sravana 19 / Aug 3 Sravana 13 / Sravana 20 / Aug. 4 Sravana 17 / Sravana 24 / Aug.8 Sravana 20 / Sravana 27 / Aug. 11 Sravana 21 / Sravana 28 / Aug.12 Sravana 21 / Sravana 28 / Aug.12 Sravana 24 / Sravana 31 / Aug.15 Sravana 24 / Sravana 31 / Aug.15 Sravana 25 / Bhadra 1 / Aug.16 Sravana 31 / Bhadra 7 / Aug.22 Sravana 31 / Bhadra 7 / Aug.22

Rohini Nakshatra of Saura Bhadra Bhadra 19/ Bhadra 26/ Sept 10 Bhadra 26 / Asvina 2 / Sept 17 Bhadra K 30

Fixed Asvina S1 Asvina S 7 8 days before Oli ends Asvina S 8 Asvina S 9 Sravana Nakshatra of Saura Kartika Day before Vijaya Dasami Day before Vijaya Dasami Asvina S 10 (Aparahnavyapini) with Sravana Nakshatra 48. Vijaya Dasami (Bengal & kerala) Asvina S 10 49. Kojagori Lakshmi Puja (Bengal) Asvina S 15 (Pradosa) 50. Kumara Purnima (Odisha) Asvina S 15 Maharsi Valmiki's Birthday (according Asvina S 15 ( Udayavyapini) to tithi), Oli ends Asvina S 15 ( Udayavyapini)

Asvina 10/ Asvina 17 / Oct 2 Asvina 25 / Kartika 2 /Oct 17 Kartika 1/ Kartika 8 /Oct 23 Kartika 1/ Kartika 8 /Oct 23 Kartika 2/ Kartika 9 /Oct 24 Kartika 2/ Kartika 9 /Oct 24 Kartika 2/ Kartika 9 /Oct 24 Kartika 3/ Kartika 10 /Oct 25 Kartika 3 /Kartika 10 /Oct 25 Kartika 3/ Kartika 10 /Oct 25 Kartika Kartika Kartika Kartika Kartika

4 / Kartika 11 / Oct 26 8 / Kartika 15 / Oct 30 9 / Kartika 16 / Oct 31 9 / Kartika 16 / Oct 31 9 / Kartika 16 / Oct 31

416

PRINCIPAL FESTIVALS AND ANNIVERSARIES FOR HOLIDAYS Festivals Date Criterion National / Nirayana / Gregorian Saka 1942/Kali 5121/2020 A.D. 51. Naraka Chaturdasi (Purvarunodaya) Kartika 23/ Kartika 30 /Nov. 14 Asvina K 14(Purvarunodaya) (S. India) Kali Puja, Asvina K 30( Nisithavyapini ) Kartika 23/ Kartika 30 /Nov. 14 Dipavali Kartika 23/ Kartika 30 /Nov. 14 Asvina K 14 52. Govardhan Puja, Kartika 24 / Agrahn.1 / Nov 15 Kartika S 1 Bali Puja Kartika 24 / Agrahn.1 / Nov 15 Kartika S 1 Annakuta Kartika 24 / Agrahn.1 / Nov 15 Kartika S 1 53. Kartika Sukladi Kartika 25/ Agrahn.2 /Nov 16 Kartika S 1 54. Bhratri Dvitiya, Dwat Puja, Tikka Kartika S 2 (Aparhna) Kartika 25/ Agrahn.2 /Nov 16 Ceremony, Bhai Duj Kartika 25/ Agrahn.2 /Nov 16 Bhratri Dvitiya (Bengal) Kartika 25/ Agrahn.2 /Nov 16 Kartika S 2 (Madhyahna) 55. Pratihar Shasthi or Surya Shashthi, Kartika 29 / Agrahn.6 / Nov 20 Kartika S 6 Chhat-Bihar 56. Goshtashtami or Gopashtami Agrahayana 1 / Agrahn. 8 / Nov22 Kartika S 8 57. Guru Teg Bahadur's Martyrdom Day Fixed Agrahayana 3/Agrahn. 10 / Nov 24 58. Rasayatra ( Smarta) Agrahayana 8/Agrahn. 15 / Nov 29 Kartika S 15 (Nisithavyapini) 59. Rasayatra (Vaishnava) Agrahayana 9/Agrahn. 16 / Nov 30 Kartika S 15 (Udayavyapini) 60. Guru Nanak’s Birthday Agrahayana 9/Agrahn. 16 / Nov 30 Kartika S 15 (Udayavyapini) Ratha Yatra (Jain), Agrahayana 9/Agrahn. 16 / Nov 30 Kartika S 15 (Udayavyapini) Kartiki Purnima, Agrahayana 9/Agrahn. 16 / Nov 30 Kartika S 15 Pushkar Fair Kartika S 15 Agrahayana 9/Agrahn. 16 / Nov 30 Huthri –( 3 days.) Coorg S 15 to K 2 of Saura Margasirsa Agrahayana 9/Agrahn. 16 / Nov 30 61. Prathamashtami (Odisha) Agrahayana 17/Agrahn. 24 / Dec 8 Kartika K 8 62. Vaikuntha Ekadasi (S.India) Pausha 4 / Pausha 11 / Dec 25 S 11 of Saura Pausha 63. Jor Mela-3 days- (Punjab) Pausha 5 / Pausha 12 / Dec 26 Fixed Saka 1942/Kali 5121 /2021 A.D. 64. Bhogi (S. India) Pausha 23 / Pausha 30 / Jan 13 Day before Pongal 65. Makara Samkranti (Bengal) Saura Maghadi (Midnight Rule) Pausha 24 / Magha 1 / Jan.14 Magha Bihu (Assam) Saura Maghadi (Midnight Rule) Pausha 24 / Magha 1 / Jan.14 66. Pongal (S.India),Tai Pongal(Kerala) Pausha 24 / Magha 1 / Jan.14 The day of Saura Maghadi Tamil New Year’s day ,Tila Samkranti, The day of Saura Maghadi Pausha 24 / Magha 1 / Jan.14 Makara Samkranti (N. India) Pausha 24 / Magha 1 / Jan.14 The day of Saura Maghadi Makaradi snana Pausha 24 / Magha 1 / Jan.14 The day of Saura Maghadi 67. Mattu Pongal or Kanuvu Pausha 25 / Magha 2 / Jan.15 Day after Pongal 68. Guru Gobind Singh's Birth Day Pausha 30 / Magha 7 / Jan.20 Pausha S 7 69. Netaji’s Birthday Magha 3/ Magha 10/ Jan.23 Fixed 70. Republic Day Magha 6/ Magha 13/ Jan.26 Fixed 71. Sri Panchami, Vasanta Panchami Magha 27 / Phalguna 4 / Feb 16 Magha S 5 72. Sivaji Jayanti Magha 30 / Phalguna 7 / Feb 19 Fixed 73. Guru Ravidas’s Birthday Phalguna 8 / Phalguna 15 / Feb 27 Magha S 15 74. Birth Day of Swami Dayananda Phalguna 17/ Phalguna 24 / Mar 8 Phalguna K 10 (Purnimanta) Saraswati (Founder of Arya Samaj”) 75. Maha Sivaratri (Kashmir) Phalguna 19/ Phalguna 26/March 10 Magha K 13 76. Maha Sivaratri, Maha Sivaratri (S.India) Magha K 14 (Prodosa & Phalguna 20 /Phalguna 27/March 11 Nishithavyapini) Phalguna 20 /Phalguna 27/March 11 77. MahaVishuva day Day of Sun's entry into Trop. Phalguna 29 / Chaitra 6 / March 20 Aries (Midnight rule) Saka 1943/Kali 5121 /2021 A.D. 78. Indian New Year's Day Fixed Chaitra 1/ Chaitra 8 / March 22 79. Holikadahan, Dolyatra Phalguna S 15 (night) Chaitra 7/ Chaitra 14 / March 28 80. Holi, Hola, Day after Holikadahana, Chaitra 8/ Chaitra 15 / March 29 Vasantotsava Phalguna K 1 Special Festivals for Jammu and Kashmir National / Nirayana / Gregorian Saka 1941/ Kali 5120/ 2020 A.D. Pausha 23/ Pausha 30/ Jan. 13 7. Lohri Day before Saura Maghadi (Sunrise Rule) Saka 1942/ Kali 5120/ 2020 A.D. Chaitra 12 / Chaitra 18 / April 1 1. Mela Bahu Fort Chaitra S 8 Saka 1942 / Kali 5121 / 2020 A.D Jyaishtha 9 / Jyaishtha 16/May 30 2. Mela Kshir Bhawani (2 days) Jyaishtha S 8 Jyaishtha 16 / Jyaishtha 23 / June 6 3. Guru Hargobind's Birthday Jyaishtha K 1 Asadha 22 / Asadha 29 / July 13 4. Martyr's Day Fixed 5. Kailas Yatra Sravana K 13, K 14 Sravana 26 / Bhadra 2 / Aug 17 Bhadra 1 / Bhadra 8 / Aug 23 6. Mela Pat Bhadra S 5 to S 7 Saka 1942/ Kali 5121 / 2021 A.D. Pausha 23 / Pausha 30 / Jan. 13 7. Lohri Day before Saura Maghadi (Sunrise Rule)

. 417

Festivals

1. Sab-e-Miraj * 2. Sab-e-Barat* 3. First day of Ramadan 4. Shahadat-e-Hazrat Ali 5. Sab -e- Qadr *. 6. Jumat Ul Vida 7. Id-ul -Fitr 8. Id-uz -Zuha (Bakrid) 9. Muharram 10. Chelhum

MOSLEM FESTIVALS, 2020-2021 A.D. Criterion

Date National / Nirayana / Gregorian Saka 1942 / Kali 5120 / 2020 A.D 27 Rajab Chaitra 3 / Chaitra 9 / Mar 23 15 Shaban Chaitra 20 / Chaitra 26 / April 9 Saka 1942 / Kali 5121 / 2020 A.D 1 Ramadan Chaitra 24 / Vaisakha 1 / April 14 21 Ramadan Vaisakha 25 / Jyaishtha 1 / May 15 27 Ramadan Vaisakha 31 / Jyaishtha 7/ May 21 Last Friday of Ramadan Jyaishtha 1 / Jyaishtha 8/ May 22 1 Shawwal Jyaishtha 4 / Jyaishtha 11/ May 25 10 Zulhijja Sravana 10 / Sravana 17 / Aug. 1 10 Muharram Bhadra 8 /Bhadra 15 / Aug. 30 Fortieth day from (39 days after) Asvina 16 / Asvina 23 / Oct 8 10 Muharram Last Wednesday of Safar Asvina 22 / Asvina 29 / Oct 14 28 Safar Asvina 24 / Kartika 1 / Oct. 16 12 Rabiu’l awwal Kartika 8 / Kartika 15 / Oct.30

11. Akheri Chahar Shumba 12. Shahadat -e- Iman Hasan 13. Milad-un Nabi or Id-e-Milad(Birth Day of the Prophet), Fateha Dwaz Daham or Bara Wafat 17 Rabiu’l awwal 14. Id-e-Maulad 15. Fateha Yazdadham (Giarhween Sharif) 11 Rabius Sani 16. Hazrat ali’s Birthday 17. Sab-e-Miraj *

13 Rajab 27 Rajab

1. Sab-e-Barat *

15 Shaban

2. First day of Ramadan

1 Ramadan

Kartika 13 / Kartika 20 /Nov. 4 Agrah. 6/ Agrahayana 13 / Nov. 27 Saka 1942 / Kali 5121 / 2021 A.D Phalguna 7 / Phalguna 14 /Feb 26 Phalguna 21 / Phalguna 28 /Mar 12 Saka 1943 / Kali 5121 / 2021 A.D Chaitra 9 / Chaitra 16 / Mar 30 Saka 1943 / Kali 5122 / 2021 A.D Chaitra 24 / Vaisakha 1 / April 14

* The festival is observed in the preceding night THE ISLAMIC CALENDAR 2020-2021 A.D. (Hejira : 1441-1442 A. H.) The beginning dates of the different months of the Islamic Calendar for the year 2020-2021 A.D. determined on the basis of the first visibility of the lunar crescent after the New-Moon day culculated for the Central Station of India are as follows:Jumadu's sani 1441A.H. Jan. 27 2020 (30) Safar 1441A.H. Sept. 19 2020 (30) Rajab " Feb. 26 " (29) Rabiu'l awwal " Oct. 19 " (29) Shaban " Mar. 26 " (30) Rabiu's sani " Nov. 17 " (30) Ramadan " Apr. 25 " (30) Jumadu'l awwal " Dec. 17 " (29) Shawwal " May 25 " (29) Jumadu's sani " Jan. 15 2021 (30) Zu'lqada " June 23 " (30) Rajab " Feb. 14 " (30) Zulhijja " July 23 " (29) Shaban " Mar. 16 " (29) MUHARRAM 1442A.H. Aug. 21 " (29) Ramadan " April 14 " (30) N.B.-Actually the months begin from sunset of the preceding day when the Moon becomes first visible. Fixed Calendar According to the Fixed Calendar the beginning dates of different months are as follows : 2020 - Jan. 27, Feb. 25, Mar. 26, Apr. 24, May 24, June 22, July 22, Aug. 20, Sept. 19, Oct. 18, Nov. 17, Dec. 16 2021 - Jan. 15, Feb. 13, Mar. 15, Apr. 12.

418

THE PARSI (SHAHENSHAHI) CALENDAR, 2020 - 2021 A.D. (As used by the Indian Parsis) Yazdejardi Era : 1389 - 1390 The beginning dates of different months of the Parsi Shahenshahi Calendar are as follows : As regards the Parsi Kadmi Calendar, the months are the same but they begin 30 days earlier. Shahrivar 1389 Jan. 14 2020 (30) Ardibehesht 1390 Sept. 15 Meher " Feb. 13 " (30) Khordad " Oct. 15 Avan " Mar. 14 " (30) Tir " Nov. 14 Adar " Apr. 13 " (30) Amardad " Dec. 14 Dei " May 13 " (30) Shahrivar " Jan. 13 Bahman " June 12 " (30) Meher " Feb. 12 Aspandad " July 12 " (30) Avan " Mar. 14 Gathas(I-V) " Aug. 11 " ( 5) Adar " Apr. 13 FARVARDIN 1390 Aug. 16 " (30) Dei " May 13 Festivals

Zarthost-no-Diso Gatha Gahambar Parsi New Year Eve Parsi New Year's Day Khordad Sal (Birthday of Prophet Zarthost)

Shebat Adar Nisan Iyar Sivan Tammuz Ab Ellul

PARSI FESTIVALS 2020-2021 A.D. Shahenshahi National / Nirayana / Gregorian Saka 1942/ Kali 5121/ 2020 A.D. 11 Dei Jyaishtha 2/ Jyaishtha 9/ May 23 Gatha III Sravana 22/ Sravana 29/ Aug. 13 Gatha V Sravana 24/ Sravana 31/ Aug. 15 1 Farvardin Sravana 25/ Bhadra 1/ Aug. 16 6 Farvardin Shravana 30/ Bhadra 6/ Aug. 21 Criterion

2020 " " " 2021 " " " "

(30) (30) (30) (30) (30) (30) (30) (30) (30)

Kadmi National / Nirayana / Gregorian Saka 1942/ Kali 5121/ 2020 A.D. Vaisakha 3/ Vaisakha 10/ Apr. 23 Ashadha 23/ Ashadha 30/ July 14 Ashadha 25/ Sravana 1/ July 16 Ashadha 26/ Sravana 2/ July 17 Ashadha 31/ Sravana 7/ July 22

N.B.- Jamshedi Naoroj falls on March 21 every year THE JEWISH CALENDAR, 2020 - 2021 A.D. Jewish Era : 5780 - 81 A.M. To beginning dates of different months of the Jewish Calendar are as follows: TISHRI 5781 Sept. 19 2020 5780 Jan. 27 2020 (30) Heshvan " Oct. 19 " " Feb. 26 " (29) Kislev " Nov. 17 " " Mar. 26 " (30) Tebeth " Dec. 16 " " Apr. 25 " (29) Shebat " Jan. 14 2021 " May 24 " (30) Adar Feb. 13 " " June 23 " (29) Nisan " Mar. 14 " " July 22 " (30) Iyar " Apr. 13 " " Aug. 21 " (29)

(30) (29) (29) (29) (30) (29) (30) (29)

JEWISH FESTIVALS 2020-2021 A.D. Festivals

Criterion

First day of Passover (Pesach)

15 Nisan

Feast of Weeks (Shebuoth) Tishabeab Jewish New Year (Rosh Hashanah) Day of Atonement (Yom Kippur) First day of Tabernacles (Succoth) Last day of Succoth (SimhathTorah) Hanukah

6 Sivan 9 Ab 1 Tishri 10 Tishri 15 Tishri 23 Tishri 25 Kislev

Purim

14 Adar

First day of Passover (Pesach)

15 Nisan

Date National / Nirayana / Gregorian Saka 1942/Kali 5120 / 2020 A.D. Chaitra 20 / Chaitra 26 / April 9 Saka 1942/Kali 5121 / 2020 A.D. Jyaishtha 8 / Jyaishtha 15 / May 29 Sravana 8 / Sravana 15 / July 30 Bhadra 28/ Asvina 4 / Sept 19 Asvina 6 / Asvina 13 /Sept 28 Asvina 11/ Asvina 18 / Oct 3 Asvina 19 / Asvina 26 /October 11 Arghayana 20 /Argh. 27 / Dec 11 Saka 1942/Kali 5121 / 2021 A.D. Phalguna 7/ Phalguna 14 / Feb 26 Saka 1943/Kali 5121 / 2021 A.D. Chaitra 7/ Chaitra 14 / March 28

419

CHRISTIAN Festivals

FESTIVALS, 2020-2021 A.D. Criterion

1. Christian (English) New Year's Day 2. Epiphany 3. Septuagesima Sunday 4. Quinquagesima (Shrove) Sunday 5. Ash Wednesday

Fixed Fixed 63 days before Easter Sunday 49 days before Easter Sunday 46 days before Easter Sunday

6. Palm Sunday 7. Good Friday 8. Easter (Holy) Saturday 9. Easter Sunday

7 days before Easter Sunday 2 days before Easter Sunday Day before Easter Sunday First Sunday after the 14th day of the Moon (nearly Full Moon) occurring on or immediately after March 21

10. Low Sunday 11. Rogation Sunday 12. Ascension Day-Holy Thursday 13. Ascension Sunday 14. Whit Sunday-Pentecost 15. Trinity Sunday 16. Corpus Christi (Thursday) 17. First Sunday in Advent

7 days after Easter Sunday 35 days after Easter Sunday 39 days after Easter Sunday 3 days after Ascension day 49 days after Easter Sunday 56 days after Easter Sunday 60 days after Easter Sunday Fourth Sunday before Christmas, i.e.,Sunday nearest to Nov.30. Day before Christmas Fixed Fixed

18. Christmas Eve 19. Christmas Day 20. New Year Eve 1. Christian (English) New Year’s Day 2 Epiphany 3. Septuagesima Sunday 4. Quinquagesima (Shrove) Sunday 5. Ash Wednesday 6. Palm Sunday 7. Good Friday 8. Easter (Holy) Saturday 9. Easter Sunday

10. Low Sunday

Date

National / Nirayana / Gregorian Saka 1941 / Kali 5120/ 2020 A.D. Pausha 11 / Pausha 18 / Jan. 01 Pausha 16 / Pausha 23 / Jan. 06 Magha 20 / Magha 27 / Feb 09 Phalguna 04/Phalguna 11 /Feb 23 Phalguna 07 /Phalguna 14/Feb 26 Saka 1942/ Kali 5120 / 2020 A.D. Chaitra 16/Chaitra 22 / April 05 Chaitra 21/ Chaitra 27/ April 10 Chaitra 22/ Chaitra 28/ April 11 Chaitra 23/ Chaitra 29/ April 12

Saka 1942/ Kali 5121 / 2020 A.D. Chaitra 30/Vaisakha 6/April 19 Vaisakha 27/Jyaishtha 3 / May 17 Vaisakha 31 /Jyaishtha 7 / May 21 Jyaishtha 3/Jyaishtha 10/ May 24 Jyaishtha 10/Jyaishtha 17 /May 31 Jyaishtha 17 / Jyaishtha 24/June 7 Jyaishtha 21/ Jyaishtha 28/June 11 Agrahn. 8 / Agrahn. 15 / Nov 29

Pausha 03 / Pausha 10 / Dec. 24 Pausha 04 / Pausha 11 / Dec. 25 Pausha 10 / Pausha 17 / Dec. 31 Saka 1942/ Kali 5121 / 2021 A.D. Fixed Pausha 11 / Pausha 18 / Jan 01 Fixed Pausha 16 / Pausha 23 / Jan 06 63 days before Easter Sunday Magha 11 / Magha 18 / Jan 31 49 days before Easter Sunday Magh 25/ Phalguna 2 / Feb 14 46 days before Easter Sunday Magh 28/ Phalguna 5 / Feb 17 Saka 1943 / Kali 5121/ 2021 A.D. 7 days before Easter Sunday Chaitra 7/ Chaitra 14 / March 28 2 days before Easter Sunday Chaitra 12/ Chaitra 19 / April 2 Day before Easter Sunday Chaitra 13/ Chaitra 20 / April 3 First Sunday after the 14th day of Chaitra 14 /Chaitra 21 /April 4 the Moon (nearly Full Moon) occurring on or immediately after March 21 Chaitra 21/ Chaitra 28 /April 11 7 days after Easter Sunday

420

THE INDIAN LUNAR CALENDAR TIME OF NEW MOON (IN I.S.T.) MARKING THE COMMENCEMENT OF LUNAR MONTHS 2009 2006 2003 (1930 - 31 S.E.) (1927 - 28 S.E.) (1924 - 25 S.E.) d h d h m m d h m 2 25 53 ----1 16 19 Jan. 29 19 45 Jan. 26 13 25 3 08 05 Feb. 27 30 01 Feb. 25 07 05 1 24 48 Mar. 29 15 45 Mar. 26 21 36 1 17 44 Apr. 27 25 14 Apr. 25 08 53

Pausha Magha Phalguna Chaitra Vaisakha

Jan. Feb. Mar. Apr. May

Jyaishtha Ashadha Sravana Bhadra Asvina

May June July Aug. Sept

31 29 29 27 26

09 24 12 22 08

49 07 21 54 37

May June July Aug. Sept.

27 25 25 23 22

10 21 10 24 17

56 35 01 40 15

May June July Aug. Sept.

24 22 22 20 18

17 25 08 15 24

41 05 05 32 14

Kartika Margasirsha Pausha

Oct. Nov. Dec.

25 23 23

18 28 15

19 28 13

Oct. Nov. Dec.

22 20 20

10 27 19

44 48 31

Oct. Nov. Dec.

18 16 17

11 24 17

03 44 32

2004 (1925 - 26 S.E.) --21 26 35 20 14 48 20 28 11 19 18 51

Pausha Magha Phalguna Chaitra Vaisakha

Jan. Feb. Mar. Apr.

Jyaishtha

May

19

10

22

Ashadha Sravana

June July Aug. Sept. Oct.

17 17 16 14 14

29 16 06 19 08

57 54 54 59 18

Nov. Dec

Bhadra Asvina Kartika Margasirsha Pausha

2007 (1928 - 29 S.E.) --Jan. 19 09 31 Feb. 17 21 44 Mar. 19 08 13 Apr. 17 17 06 May June July Aug.

16 24 57 15 08 43 14 17 34 12 28 33

2010 (1931 - 32 S.E.) --Jan. 15 12 41 Feb. 14 08 21 Mar. 15 26 31 Apr. 14 17 59 May 14 06 34 June 12 16 45 July 11 Aug. 10

25 10 08 38

Sept. 11 Oct. 11

18 14 10 31

Sept. Oct.

8 7

16 00 24 15

12 12

Nov. Dec.

28 33 23 10 ---

Nov. Dec.

6 5

10 22 23 06 ---

Jan. Feb. Mar. Apr. May June

4 3 4 3 3 1

14 08 26 20 12 26

33 01 16 02 21 33

July July Aug. Sept. Oct.

1 30 29 27 26

14 24 08 16 25

24 10 34 39 26

19 57 06 59 --2005 (1926 - 27 S.E.)

9 9

Pausha Magha Phalguna Chaitra Vaisakha Jyaishtha

Jan. Feb. Mar. Apr. May June

10 8 10 8 8 6

17 27 14 26 14 27

33 58 40 02 15 25

2008 (1929 - 30 S.E.) Jan. 8 17 17 Feb. 7 09 14 Mar. 7 22 44 Apr. 6 09 25 May 5 17 48 June 3 24 53

Ashadha Sravana Bhadra Asvina Kartika

July Aug. Sept Oct. Nov.

6 5 3 3 2

17 08 24 15 06

33 35 15 58 55

July 3 Aug. 1 Aug. 30 Sept. 29 Oct. 28

07 15 25 13 28

Margasirsha Pausha

Dec. Dec.

1 31

20 08

31 42

Nov. 27 Dec. 27

22 25 17 52

49 43 28 42 44

2011 (1932 - 33 S.E.)

Nov. 25 Dec. 24

11 40 23 36

N.B.- The figures in the italics show the beginning of the intercalary (mala or adhika) month followed by the normal (suddha or nija) month of the same name.

421

THE INDIAN LUNAR CALENDAR TIME OF NEW MOON (IN I.S.T.) MARKING THE COMMENCEMENT OF LUNAR MONTHS 2012 (1933 - 34 S.E.) d h m --Jan. 23 13 09 Feb. 21 28 05 Mar. 22 20 07 Apr. 21 12 48

2015 (1936 - 37 S.E.) d h m --Jan. 20 18 44 Feb. 18 29 17 Mar. 20 15 06 Apr. 18 24 27

2018 (1939 - 40 S.E) d h --Jan. 17 07 Feb. 15 26 Mar. 17 18 Apr. 16 07

May

20

05 17

May

18

Ashadha

June

19

20 32

Sravana Bhadra

July Aug. Sept. Oct. Nov. Dec.

June July Aug. Sept

16 19 35 16 06 54 14 20 23 13 12 11

May 15 17 18 June 13 25 13 July 13 08 18

Oct. Nov. Dec.

12 11 11

Pausha Magha Phalguna Chaitra Vaisakha Jyaishtha

Pausha Magha Phalguna Chaitra Vaisakha

19 09 54 17 21 24 16 07 41 15 17 33 13 27 38 13 14 12 --2013 (1934 - 35 S.E.) Jan. 11 25 14 Feb. 10 12 50 Mar. 11 25 21 Apr. 10 15 05 May 10 05 58

Jyaishtha

June

8

Ashadha Sravana

July Aug.

Bhadra Asvina Kartika Margasirsha Pausha

Asvina Kartika Margasirsha Pausha

09 43

Aug. 11 Sept. 09

47 35 42 27

15 28 23 32

Oct. Nov. Dec.

09 07 07

01 09 25 54 00

Jan. Feb. Mar. Apr. May

6 4 6 5 4

06 26 21 14 28

29 36 23 17 15 59 --2016 (1937 - 38 S.E.)

m

09 17 21 32 12 50 --2019 (1940 - 41 S.E.)

2021 (1942 - 43 S.E) d h m Jan. Feb. Mar. Apr. May June

13 11 13 12 11 10

10 24 15 08 24 16

July

10

06 47

Aug. 08 Sept. 07

19 20 06 22

Oct. Nov. Dec.

06 04 04

58 34 34 21 16

Jan. Feb. Mar. Apr. Apr.

2 1 2 1 30

24 11 23 11 25

30 36 51 01 30 23

16 35 26 45 13 13 --2022 (1943 - 44 S.E)

Jan. Feb. Mar. Apr. May

10 8 9 7 6

21 26

June

5

08 30

June

3

15 32

May

30

17 00

8 6

12 44 27 21

July Aug.

4 2

16 31 26 15

July Aug.

2 1

24 46 08 42

June July

29 28

08 22 23 25

Sept. Oct.

5 5

17 06 06 05

Sept. 1 Sept. 30

14 33 29 41

Aug. 30 Sept. 28

16 07 23 56

Aug. 27 Sept. 25

13 47 27 25

Nov. Dec.

3 2

18 20 29 52 ---

Oct. Nov. Dec.

Oct. Nov. Dec.

16 19 28 27 15 47

2014 (1935 - 36 S.E.)

07 20 07 16 25

30 23 08 29 17 48 29 12 23 2017 (1938 - 39 S.E.)

Oct. Nov. Dec.

28 09 09 26 20 36 26 10 43 2020 (1941 - 42 S.E.)

Pausha Magha Phalguna Chaitra Vaisakha

Jan. 1 Jan.. 30 Mar. 1 Mar. 30 Apr. 29

16 27 13 24 11

44 09 30 15 44

Jan. Feb. Mar. Apr.

27 26 28 26

--29 20 08 17

37 28 27 46

Jan. Feb. Mar. Apr.

24 23 24 23

Jyaishtha Ashadha Sravana Bhadra Asvina

May June July Aug. Sept.

24 13 28 19 11

10 39 12 43 44

May June July Aug. Sept.

25 24 23 21 20

25 08 15 24 11

14 01 16 00 00

May June July Aug. Sept. Oct. Nov. Dec.

22 21 20 19 17 16 15 14

28 27 26 25 24

Kartika Oct. 23 Margasirsha Nov. 22 Pausha Dec. 22

27 27 18 02 07 06

Oct. 19 Nov. 18 Dec. 18

24 42 17 12 12 00

--27 21 14 07 23 12 23 08 16 25 10 21 ---

25 23 23

04 16 05 54 58

12 02 58 56 09 11 03 12 30 01 37 47

N.B.- The figures in the italics show the beginning of the intercalary (mala or adhika) month followed by the normal (suddha or nija) month of the same name.

422

INDIAN CALENDAR SAKA ERA 1943 Month of CHAITRA (30 days)

Mesha : Madhava Spring (Vasanta), 2nd Month

(Nirayana) 8 Chaitra, 5121 Kali Era to (Nirayana) 7 Vaisakha, 5122 Kali Era

Date Week Gregorian Day Date

Sunrise

Sunset

Tithi No. Ending Moment h m

Nakshatra

h

m

Apparent Noon h m

2021 A.D. Mar. 22 23 24 25 26

6 6 6 5 5

02.2 01.2 00.3 59.3 58.3

12 12 12 12 12

06.9 06.6 06.3 06.0 05.7

18 18 18 18 18

11.7 12.1 12.5 12.8 13.2

S

8 9 9 10 S 10 10 11 9 12 8

00.7 07.6 23.9 47.7 21.6

6 7 8 9 10

21 22 23 22 21

27.7 45.2 12.2 48.7 39.2

4 5 6 7 8 (9

12 12 11 10 7 28

55.0 37.4 40.5 02.6 45.2 52.5)

13 (14 S 15 K 1 2 3

6 27 24 20 17 14

12.0 27.4) 18.1 54.8 27.7 06.6

11

19

51.6

10 25

31.1

12 13 14 15

17 15 12 9

35.6 02.0 21.7 45.2

11 21 12 17 13 13 14 9

48.5 53.4 53.9 58.2

4 11

00.3

5 8 6 5 (7 28 8 27 9 26

15.9 59.0 13.2) 00.0 19.3

16 (17 18 19

7 29 27 26

21.7 15 6 19.2) (16 26 43.6 17 23 38.5 18 20

13.4 45.6) 39.4 57.8

20 21

26 26

05.6 04.8

19 18 20 16

42.3 53.0

h

m

No.

Ending Moment h m

Yoga No. Ending Moment h m

1 2 3 4 5

Mon Tue Wed Thu Fri

6

Sat

27

5

57.3

12

05.4

18

13.6

7 8 9 10

Sun Mon Tue Wed

28 29 30 31

5 5 5 5

56.4 55.4 54.4 53.5

12 12 12 12

05.1 04.8 04.5 04.2

18 18 18 18

14.0 14.3 14.7 15.1

11

Thu Apr.

1

5

52.5

12

03.9

18

15.4

12 13

Fri Sat

2 3

5 5

51.5 50.6

12 12

03.6 03.3

18 18

15.8 16.2

14 15

Sun Mon

4 5

5 5

49.6 48.7

12 12

03.0 02.7

18 18

16.5 16.9

16 17 18 19 20

Tue Wed Thu Fri Sat

6 7 8 9 10

5 5 5 5 5

47.7 46.8 45.8 44.9 44.0

12 12 12 12 12

02.4 02.1 01.8 01.6 01.3

18 18 18 18 18

17.3 17.7 18.1 18.4 18.8

K 10 11 12 13 14

26 26 27 28 -

09.7 29.4 16.2 28.2 -

22 23 24 25 25

26 27 28 6

34.6 32.9 57.4 46.1

21 22 23 24 25

15 14 13 13 13

29.0 28.7 50.4 32.5 33.5

21 22 23 24 25

Sun Mon Tue Wed Thu

11 12 13 14 15

5 5 5 5 5

43.1 42.2 41.3 40.4 39.5

12 12 12 12 12

01.0 00.8 00.5 00.3 00.0

18 18 18 18 18

19.2 19.6 20.0 20.4 20.8

14 6 K 30 8 S 1 10 2 12 3 15

03.7 00.8 17.1 48.2 27.5

26 27 1 2 3

8 11 14 17 20

57.5 29.4 19.3 22.5 32.5

26 27 1 2 3

13 14 15 16 17

52.1 26.7 15.2 14.3 18.9

26 27 28 29 30

Fri Sat Sun Mon Tue

16 17 18 19 20

5 5 5 5 5

38.6 37.8 36.9 36.1 35.3

11 11 11 11 11

59.8 59.6 59.4 59.1 58.9

18 18 18 18 18

21.2 21.6 22.0 22.4 22.8

4 5 6 7 8

06.2 32.9 35.3 02.0 43.8

4 5 6 7 7

23 26 29 6

39.9 33.5 01.5 52.6

4 5 6 7 8

18 19 19 20 19

22.7 17.5 54.5 05.4 42.7

K

S

S

18 20 22 24 24

N.B. - All timings are given in I.S.T. or the local mean time of the meridian of 82½° E. Long. Names of Nakshatras:- 1.Asvini 2.Bharani 3.Krittika 4.Rohini 5.Mrigasiras 6.Ardra 7.Punarvasu 8.Pushya 9.Aslesha 10.Magha 11.Purva Phalguni 12.Uttara Phalguni 13.Hasta 14.Chitra 15.Svati 16.Visakha 17.Anuradha 18.Jyestha 19.Mula 20.Purvasadha 21.Uttarasadha 22.Sravana 23.Dhanistha 24.Satabhisaj 25.Purva Bhadrapada 26.Uttara Bhadrapada 27.Revati Names of Yogas:- 1.Viskumbha 2.Priti 3.Ayusman 4.Saubhagya 5.Sobhana 6.Atiganda 7.Sukarma 8.Dhriti 9.Sula 10.Ganda 11. Vriddhi 12.Dhruva 13.Vyaghata 14.Harshana 15.Vajra 16.Siddhi (Asrik) 17.Vyatipata 18.Variyan 19.Parigha 20.Siva 21.Siddha 22.Sadhya 23.Subha 24.Sukla (Sukra) 25.Brahma 26.Indra 27.Vaidhriti

423

AYANAMSA, 2020-2021 TRUE AYANAMSA FOR 5h 29m.0 I.S.T. Date 2020

Ayanamsa 0

Jan.

/

Date 2020 //

Ayanamsa 0

/

Date 2020 //

Ayanamsa 0

/

Date 2020-21 //

1 24 07 54.8 Apr. 30 24 08 09.5 Aug. 28 24 08 28.1 4 24 07 55.0 May 3 24 08 10.0 31 24 08 28.7 7 24 07 55.5 6 24 08 10.1 Sept. 3 24 08 28.8 10 24 07 56.3 9 24 08 10.5 6 24 08 28.8 13 24 07 57.0 12 24 08 11.3 9 24 08 29.0 16 24 07 57.3 15 24 08 11.8 12 24 08 29.6 19 24 07 57.6 18 24 08 12.0 15 24 08 30.1 22 24 07 58.3 21 24 08 12.2 18 24 08 30.2 25 24 07 59.0 24 24 08 12.8 21 24 08 30.2 28 24 07 59.4 27 24 08 13.6 24 24 08 30.8 31 24 07 59.5 30 24 08 14.1 27 24 08 31.3 Feb. 3 24 07 59.8 June 2 24 08 14.3 30 24 08 31.5 6 24 08 00.4 5 24 08 14.8 Oct. 3 24 08 31.5 9 24 08 01.1 8 24 08 15.7 6 24 08 31.6 12 24 08 01.3 11 24 08 16.3 9 24 08 32.1 15 24 08 01.5 14 24 08 16.6 12 24 08 32.7 18 24 08 02.0 17 24 08 16.9 15 24 08 32.9 21 24 08 02.6 20 24 08 17.4 18 24 08 32.9 24 24 08 02.9 23 24 08 18.3 21 24 08 33.5 27 24 08 02.9 26 24 08 18.9 24 24 08 34.2 Mar. 1 24 08 03.0 29 24 08 19.1 27 24 08 34.4 4 24 08 03.5 July 2 24 08 19.6 30 24 08 34.5 7 24 08 04.1 5 24 08 20.4 Nov. 2 24 08 34.7 10 24 08 04.3 8 24 08 21.1 5 24 08 35.3 13 24 08 04.3 11 24 08 21.4 8 24 08 36.0 16 24 08 04.7 14 24 08 21.6 11 24 08 36.3 19 24 08 05.3 17 24 08 22.1 14 24 08 36.5 22 24 08 05.5 20 24 08 22.9 17 24 08 37.1 25 24 08 05.5 23 24 08 23.5 20 24 08 38.0 28 24 08 05.6 26 24 08 23.7 23 24 08 38.4 31 24 08 06.0 29 24 08 24.0 26 24 08 38.6 Apr. 3 24 08 06.5 Aug. 1 24 08 24.7 29 24 08 39.0 6 24 08 06.8 4 24 08 25.4 Dec. 2 24 08 39.6 9 24 08 06.8 7 24 08 25.6 5 24 08 40.4 12 24 08 07.3 10 24 08 25.7 8 24 08 40.9 15 24 08 07.9 13 24 08 26.0 11 24 08 41.2 18 24 08 08.2 16 24 08 26.7 14 24 08 41.8 21 24 08 08.3 19 24 08 27.2 17 24 08 42.8 24 24 08 08.4 22 24 08 27.4 20 24 08 43.4 27 24 08 08.9 25 24 08 27.5 23 24 08 43.7 Apr. 30 24 08 09.5 Aug.28 24 08 28.1 Dec. 26 24 08 44.0 Mean Ayanamsa = 23 0 + 51’ + 25’’.53 + precession in longitude from 2000.0 to date = 24 0 + 08’ + 11’’.46 + precession in longitude from 2020.0 to date = 24 0 + 09’ + 01’’.72 + precession in longitude from 2021.0 to date True Ayanamsa = Mean Ayanamsa + Nutation in longitude

Dec.26 29 Jan. 1 4 7 10 13 16 19 22 25 28 31 Feb. 3 6 9 12 15 18 21 24 27 Mar. 2 5 8 11 14 17 20 23 26 29 Apr. 1 4 7 10 13 16 19 22 Apr. 25

Ayanamsa 0

/

24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24

08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08 08

//

44.0 44.7 45.5 46.1 46.3 46.8 47.8 48.4 48.6 48.9 49.4 50.2 50.7 50.8 51.2 07.1 07.5 07.9 08.3 08.7 09.1 09.5 09.9 10.4 10.8 11.2 11.6 12.0 12.4 12.8 13.2 13.7 14.1 14.5 14.9 15.3 15.7 16.1 16.6 17.0 17.4

424

LONGITUDE OF SUN, MOON AND PLANETS, 2021 APPARENT GEOCENTRIC LONGITUDE FOR 5h 29m.0 I.S.T. Date

Sun °

Jan.

Moon '

"

°

'

Mercury "

°

'

Venus "

°

'

Mars "

°

'

Jupiter "

°

'

Saturn "

°

'

"

0 279 45 36 109 46 19 286 05 16 259 09 29

26 55 41 302 33 18 301 30 40

1 280 46 44 122 43 29 287 42 50 260 24 37

27 21 27 302 46 58 301 37 29

2 281 47 53 135 54 26 289 20 37 261 39 45

27 47 29 303 00 41 301 44 19

3 282 49 01 149 18 24 290 58 37 262 54 54

28 13 49 303 14 25 301 51 12

4 283 50 10 162 54 25 292 36 49 264 10 04

28 40 24 303 28 12 301 58 05

5 284 51 19 176 41 25 294 15 11 265 25 14

29 07 16 303 42 01 302 05 01

6 285 52 28 190 38 20 295 53 39 266 40 25

29 34 23 303 55 53 302 11 57

7 286 53 37 204 44 03 297 32 11 267 55 36

30 01 45 304 09 46 302 18 55

8 287 54 47 218 57 08 299 10 43 269 10 48

30 29 22 304 23 41 302 25 54

9 288 55 57 233 15 39 300 49 09 270 25 60

30 57 14 304 37 38 302 32 54

10 289 57 07 247 36 55 302 27 23 271 41 13

31 25 20 304 51 37 302 39 55

11 290 58 16 261 57 22 304 05 18 272 56 26

31 53 41 305 05 37 302 46 58

12 291 59 26 276 12 41 305 42 44 274 11 39

32 22 14 305 19 40 302 54 01

13 293 00 36 290 18 09 307 19 31 275 26 52

32 51 02 305 33 43 303 01 06

14 294 01 45 304 09 17 308 55 26 276 42 06

33 20 02 305 47 48 303 08 11

15 295 02 54 317 42 27 310 30 14 277 57 19

33 49 15 306 01 54 303 15 17

16 296 04 02 330 55 21 312 03 37 279 12 33

34 18 40 306 16 02 303 22 23

17 297 05 09 343 47 23 313 35 14 280 27 46

34 48 17 306 30 10 303 29 30

18 298 06 16 356 19 39 315 04 42 281 42 59

35 18 06 306 44 19 303 36 37

19 299 07 21

8 34 45 316 31 34 282 58 12

35 48 06 306 58 30 303 43 45

20 300 08 26

20 36 29 317 55 18 284 13 25

36 18 17 307 12 41 303 50 53

21 301 09 31

32 29 26 319 15 21 285 28 38

36 48 39 307 26 53 303 58 01

22 302 10 34

44 18 44 320 31 02 286 43 50

37 19 11 307 41 05 304 05 10

23 303 11 36

56 09 37 321 41 39 287 59 03

37 49 53 307 55 18 304 12 19

24 304 12 37

68 07 12 322 46 28 289 14 15

38 20 45 308 09 32 304 19 27

25 305 13 38

80 16 05 323 44 37 290 29 27

38 51 46 308 23 46 304 26 35

26 306 14 37

92 40 10 324 35 19 291 44 40

39 22 57 308 38 01 304 33 44

27 307 15 36 105 22 12 325 17 40 292 59 51

39 54 16 308 52 16 304 40 53

28 308 16 33 118 23 34 325 50 53 294 15 03

40 25 44 309 06 31 304 48 02

29 309 17 30 131 44 05 326 14 13 295 30 15

40 57 20 309 20 46 304 55 10

30 310 18 25 145 21 56 326 27 01 296 45 26

41 29 04 309 35 00 305 02 18

31 311 19 20 159 13 58 326 28 49 298 00 37

42 00 56 309 49 16 305 09 25

425

LONGITUDE OF SUN, MOON AND PLANETS, 2021 APPARENT GEOCENTRIC LONGITUDE FOR 5h 29m.0 I.S.T. Date

Sun °

Feb.

Moon '

"

°

'

Mercury "

°

'

Venus "

°

'

Mars "

°

'

Jupiter "

°

'

Saturn "

°

'

"

1 312 20 13 173 16 11 326 19 22 299 15 48

42 32 55 310 03 31 305 16 32

2 313 21 06 187 24 23 325 58 41 300 30 59

43 05 02 310 17 45 305 23 38

3 314 21 58 201 34 50 325 27 08 301 46 10

43 37 16 310 32 00 305 30 44

4 315 22 49 215 44 36 324 45 22 303 01 21

44 09 38 310 46 15 305 37 49

5 316 23 40 229 51 48 323 54 27 304 16 31

44 42 07 311 00 29 305 44 54

6 317 24 29 243 55 16 322 55 46 305 31 42

45 14 43 311 14 42 305 51 57

7 318 25 18 257 54 16 321 50 59 306 46 53

45 47 25 311 28 56 305 59 00

8 319 26 06 271 47 58 320 41 58 308 02 03

46 20 15 311 43 08 306 06 02

9 320 26 53 285 35 08 319 30 43 309 17 13

46 53 11 311 57 20 306 13 04

10 321 27 39 299 13 58 318 19 14 310 32 23

47 26 14 312 11 31 306 20 03

11 322 28 23 312 42 12 317 09 24 311 47 32

47 59 23 312 25 42 306 27 02

12 323 29 06 325 57 30 316 02 54 313 02 41

48 32 37 312 39 51 306 33 60

13 324 29 48 338 57 51 315 01 11 314 17 50

49 05 58 312 53 59 306 40 56

14 325 30 28 351 42 03 314 05 24 315 32 58

49 39 25 313 08 06 306 47 51

15 326 31 07

4 10 06 313 16 25 316 48 05

50 12 57 313 22 12 306 54 44

16 327 31 44

16 23 17 312 34 46 318 03 12

50 46 35 313 36 16 307 01 36

17 328 32 19

28 24 13 312 00 48 319 18 18

51 20 18 313 50 19 307 08 26

18 329 32 53

40 16 35 311 34 36 320 33 23

51 54 07 314 04 20 307 15 14

19 330 33 25

52 05 02 311 16 07 321 48 28

52 27 60 314 18 20 307 22 01

20 331 33 55

63 54 45 311 05 08 323 03 32

53 01 58 314 32 19 307 28 46

21 332 34 23

75 51 16 311 01 23 324 18 36

53 36 01 314 46 15 307 35 30

22 333 34 49

88 00 06 311 04 30 325 33 39

54 10 08 315 00 10 307 42 11

23 334 35 14 100 26 18 311 14 07 326 48 41

54 44 19 315 14 03 307 48 51

24 335 35 37 113 14 01 311 29 50 328 03 42

55 18 35 315 27 54 307 55 28

25 336 35 58 126 25 54 311 51 14 329 18 43

55 52 55 315 41 43 308 02 03

26 337 36 16 140 02 33 312 17 57 330 33 43

56 27 18 315 55 30 308 08 36

27 338 36 34 154 02 08 312 49 35 331 48 42

57 01 46 316 09 15 308 15 07

28 339 36 49 168 20 24 313 25 47 333 03 41

57 36 16 316 22 57 308 21 36

426

LONGITUDE OF SUN, MOON AND PLANETS, 2021 APPARENT GEOCENTRIC LONGITUDE FOR 5h 29m.0 I.S.T. Date

Sun °

Mar

Moon '

"

°

'

Mercury "

°

'

Venus "

°

'

Mars "

°

'

Jupiter "

°

'

Saturn "

°

'

"

1 340 37 02 182 51 08 314 06 14 334 18 38

58 10 51 316 36 37 308 28 02

2 341 37 14 197 27 07 314 50 37 335 33 36

58 45 29 316 50 15 308 34 25

3 342 37 24 212 01 29 315 38 40 336 48 32

59 20 10 317 03 50 308 40 47

4 343 37 33 226 28 39 316 30 06 338 03 28

59 54 55 317 17 23 308 47 06

5 344 37 41 240 44 55 317 24 41 339 18 24

60 29 43 317 30 53 308 53 22

6 345 37 46 254 48 30 318 22 14 340 33 19

61 04 34 317 44 21 308 59 36

7 346 37 51 268 39 04 319 22 31 341 48 14

61 39 29 317 57 46 309 05 47

8 347 37 54 282 17 11 320 25 23 343 03 08

62 14 27 318 11 08 309 11 55

9 348 37 55 295 43 36 321 30 40 344 18 01

62 49 29 318 24 27 309 18 00

10 349 37 54 308 58 57 322 38 13 345 32 53

63 24 33 318 37 43 309 24 03

11 350 37 52 322 03 22 323 47 55 346 47 45

63 59 40 318 50 56 309 30 02

12 351 37 48 334 56 36 324 59 40 348 02 36

64 34 51 319 04 05 309 35 58

13 352 37 42 347 38 10 326 13 20 349 17 26

65 10 04 319 17 11 309 41 51

14 353 37 34

0 07 42 327 28 51 350 32 15

65 45 20 319 30 14 309 47 41

15 354 37 24

12 25 15 328 46 08 351 47 03

66 20 39 319 43 13 309 53 28

16 355 37 12

24 31 38 330 05 07 353 01 50

66 56 01 319 56 09 309 59 11

17 356 36 58

36 28 34 331 25 44 354 16 37

67 31 25 320 09 01 310 04 51

18 357 36 41

48 18 44 332 47 56 355 31 22

68 06 51 320 21 49 310 10 27

19 358 36 23

60 05 46 334 11 40 356 46 06

68 42 20 320 34 34 310 16 00

20 359 36 02

71 54 10 335 36 54 358 00 50

69 17 52 320 47 14 310 21 30

21

0 35 40

83 49 00 337 03 36 359 15 32

69 53 25 320 59 51 310 26 56

22

1 35 14

95 55 44 338 31 44

0 30 13

70 29 01 321 12 23 310 32 18

23

2 34 47 108 19 49 340 01 17

1 44 53

71 04 39 321 24 51 310 37 36

24

3 34 17 121 06 16 341 32 14

2 59 32

71 40 18 321 37 15 310 42 51

25

4 33 45 134 18 57 343 04 34

4 14 09

72 15 60 321 49 35 310 48 01

26

5 33 11 147 59 53 344 38 16

5 28 46

72 51 43 322 01 50 310 53 08

27

6 32 34 162 08 32 346 13 20

6 43 21

73 27 28 322 14 00 310 58 11

28

7 31 56 176 41 17 347 49 46

7 57 55

74 03 14 322 26 06 311 03 10

29

8 31 15 191 31 36 349 27 35

9 12 28

74 39 02 322 38 08 311 08 04

30

9 30 32 206 30 50 351 06 45

10 27 00

75 14 52 322 50 04 311 12 55

31

10 29 47 221 29 42 352 47 18

11 41 31

75 50 43 323 01 56 311 17 41

427

LONGITUDE OF SUN, MOON AND PLANETS, 2021 APPARENT GEOCENTRIC LONGITUDE FOR 5h 29m.0 I.S.T. Date

Sun °

Apr

Moon '

"

°

'

Mercury "

°

'

Venus "

°

'

Mars "

°

'

Jupiter "

°

'

Saturn "

°

'

"

1

11 29 00 236 19 46 354 29 15

12 56 02

76 26 36 323 13 43 311 22 24

2

12 28 12 250 54 44 356 12 35

14 10 31

77 02 31 323 25 25 311 27 02

3

13 27 21 265 10 52 357 57 19

15 24 59

77 38 27 323 37 02 311 31 36

4

14 26 30 279 06 49 359 43 29

16 39 27

78 14 24 323 48 34 311 36 05

5

15 25 36 292 43 01

1 31 04

17 53 53

78 50 24 324 00 00 311 40 30

6

16 24 41 306 00 60

3 20 05

19 08 19

79 26 24 324 11 22 311 44 51

7

17 23 43 319 02 46

5 10 33

20 22 44

80 02 27 324 22 37 311 49 07

8

18 22 44 331 50 18

7 02 27

21 37 07

80 38 30 324 33 47 311 53 18

9

19 21 43 344 25 21

8 55 49

22 51 30

81 14 36 324 44 52 311 57 24

10

20 20 41 356 49 19

10 50 38

24 05 51

81 50 42 324 55 50 312 01 26

11

21 19 36

9 03 23

12 46 54

25 20 12

82 26 50 325 06 43 312 05 23

12

22 18 29

21 08 37

14 44 36

26 34 31

83 02 60 325 17 29 312 09 15

13

23 17 20

33 06 15

16 43 41

27 48 49

83 39 11 325 28 10 312 13 03

14

24 16 10

44 57 54

18 44 09

29 03 06

84 15 23 325 38 44 312 16 45

15

25 14 57

56 45 39

20 45 56

30 17 22

84 51 37 325 49 13 312 20 22

16

26 13 42

68 32 17

22 48 57

31 31 37

85 27 51 325 59 34 312 23 55

17

27 12 25

80 21 13

24 53 08

32 45 51

86 04 07 326 09 50 312 27 22

18

28 11 06

92 16 34

26 58 22

34 00 03

86 40 24 326 19 59 312 30 45

19

29 09 45 104 22 56

29 04 32

35 14 15

87 16 42 326 30 01 312 34 02

20

30 08 22 116 45 12

31 11 26

36 28 24

87 53 01 326 39 56 312 37 14

428

SUN AND MOON, 2021 h m DECLINATION OF SUN, LATITUDE AND DECLINATION OF MOON FOR 5 29 .0 I.S.T. Date Declination Latitude Declination Date Declination Latitude Declination

of Sun ° Jan.

of Moon '

°

0

-23

04.7

+2

1

22

60.0

2

22

54.8

3

22

4 5

'

of Moon °

of Sun

'

°

of Moon '

°

'

of Moon °

'

37.1 +24

34.2 Feb.

1

-17

05.9

+5

04.7

+7

20.0

3

34.3

23

01.5

2

16

48.7

4

49.1

+1

29.3

4

21.2

20

13.1

3

16

31.2

4

15.9

-4

27.2

49.2

4

54.6

16

18.5

4

16

13.4

3

27.0

10

10.7

22

43.1

5

12.0

11

30.7

5

15

55.3

2

25.6

15

21.9

22

36.6

5

11.9

6

05.1

6

15

36.9

1

15.6

19

41.6

6

22

29.6

4

53.5

+0

17.4

7

15

18.3

+0

01.6

22

51.6

7

22

22.2

4

17.4

-5

35.1

8

14

59.4

-1

12.0

24

37.5

8

22

14.3

3

25.3

11

14.2

9

14

40.3

2

20.7

24

51.3

9

22

06.0

2

20.1

16

19.5

10

14

20.9

3

20.3

23

34.5

10

21

57.3

1

06.0

20

29.6

11

14

01.3

4

07.9

20

57.3

11

21

48.1

0

12.2

23

23.7

12

13

41.4

4

41.1

17

16.1

12

21

38.5

1

29.0

24

46.3

13

13

21.3

4

58.9

12

49.2

13

21

28.5

2

39.3

24

31.6

14

13

01.0

5

01.3

7

54.2

14

21

18.1

3

38.8

22

45.4

15

12

40.5

4

49.1

-2

46.0

15

21

07.2

4

24.5

19

43.1

16

12

19.8

4

23.8

+2

22.9

16

20

56.0

4

54.8

15

44.0

17

11

58.9

3

47.1

7

22.0

17

20

44.4

5

09.2

11

07.6

18

11

37.8

3

00.8

12

02.2

18

20

32.3

5

08.2

6

10.3

19

11

16.5

2

07.0

16

14.5

19

20

19.9

4

53.0

-1

05.3

20

10

55.0

1

07.6

19

49.4

20

20

07.1

4

25.1

+3

57.0

21

10

33.4

-0

04.7

22

36.5

21

19

53.9

3

46.1

8

47.7

22

10

11.6

+0

59.4

24

24.7

22

19

40.4

2

57.6

13

18.2

23

9

49.7

2

02.1

25

03.4

23

19

26.5

2

01.4

17

19.4

24

9

27.6

3

00.4

24

24.0

24

19

12.2

-0

59.4

20

40.9

25

9

05.3

3

50.8

22

23.2

25

18

57.6

+0

06.1

23

10.9

26

8

43.0

4

29.8

19

03.7

26

18

42.6

1

12.5

24

37.1

27

8

20.5

4

53.7

14

35.1

27

18

27.3

2

16.7

24

48.9

28

-7

57.8

+5

00.0

+9

12.6

28

18

11.7

3

15.3

23

40.1

29

17

55.7

4

04.6

21

10.8

30

17

39.4

4

41.1

17

28.3

31

-17

22.8

+5

01.8 +12

45.8

429

SUN AND MOON, 2021 h m DECLINATION OF SUN, LATITUDE AND DECLINATION OF MOON FOR 5 29 .0 I.S.T. Date Declination Latitude Declination Date Declination Latitude Declination

of Sun

Mar.

of Moon °

'

of Moon °

of Sun

'

°

of Moon '

°

'

of Moon

°

'

°

'

1

-7

35.1

+4

47.2

+3

15.5 Apr

1

+4

32.5

+1

25.5

-17

56.6

2

7

12.3

4

15.7

-2

54.7

2

4

55.6

+0

08.7

21

56.1

3

6

49.3

3

27.5

8

55.7

3

5

18.6

-1

07.1

24

28.1

4

6

26.3

2

26.2

14

25.6

4

5

41.6

2

17.3

25

24.4

5

6

03.1

1

16.4

19

03.6

5

6

04.4

3

17.9

24

46.6

6

5

39.9

+0

02.9

22

31.4

6

6

27.1

4

06.4

22

44.6

7

5

16.6

-1

09.7

24

35.5

7

6

49.8

4

41.0

19

33.4

8

4

53.2

2

17.1

25

08.7

8

7

12.3

5

00.8

15

29.8

9

4

29.8

3

15.9

24

12.2

9

7

34.6

5

05.6

10

49.6

10

4

06.3

4

03.1

21

54.9

10

7

56.9

4

55.9

-5

47.3

11

3

42.8

4

36.7

18

30.9

11

8

19.0

4

32.7

+0

35.3

12

3

19.2

4

55.7

14

16.7

12

8

41.0

3

57.3

4

34.8

13

2

55.5

4

59.6

9

28.7

13

9

02.9

3

11.8

9

32.4

14

2

31.9

4

48.9

-4

22.0

14

9

24.6

2

18.1

14

07.4

15

2

08.2

4

24.8

+0

50.5

15

9

46.1

1

18.6

18

09.4

16

1

44.4

3

49.0

5

57.0

16

10

07.5

-0

15.7

21

28.0

17

1

20.7

3

03.4

10

47.3

17

10

28.7

+0

48.2

23

53.3

18

0

57.0

2

10.1

15

11.7

18

10

49.7

1

50.7

25

15.8

49.3

25

28.0

41.4 +24

25.4

19

0

33.3

1

11.3

19

00.4

19

11

10.5

2

20

-0

09.5

-0

09.3

22

03.7

20 +11

31.2

+3

21

+0

14.2

+0

53.8

24

11.4

22

0

37.9

1

55.6

25

13.8

23

1

01.6

2

53.4

25

02.8

24

1

25.2

3

44.3

23

33.4

25

1

48.8

4

25.1

20

45.5

26

2

12.4

4

52.4

16

44.2

27

2

35.9

5

03.0

11

40.1

28

2

59.3

4

54.6

5

49.2

29

3

22.7

4

26.4

+0

28.2

30

3

46.1

3

39.7

-6

48.7

31

+4

09.3

+2

37.8

-12

46.6

430

PLANETS, 2021 h

m

GEOCENTRIC LATITUDE AND DECLINATION FOR 5 29 .0 I.S.T. Date

Mercury Latitude

° Jan.

'

Venus

Declination

°

'

Latitude

°

'

Mars

Declination

°

'

Latitude

°

'

Jupiter

Declination

°

'

Latitude

°

'

Saturn

Declination

°

'

Latitude

°

'

Declination

°

'

0 -2 04.6 -24 31.8 +0 42.0 -22 17.8 +0 51.1 +11 10.3 +0 29.3 -20 03.8 +0 23.2 -20 11.9 2 2 07.4 24 08.6 0 37.0

22 33.5 0 53.5 11 31.1 0 29.5 19 57.6 0 23.3 20 09.0

4 2 08.7 23 39.3 0 32.0

22 46.5 0 55.7 11 52.2 0 29.6 19 51.4 0 23.5 20 06.1

6 2 08.1 23 03.8 0 26.9

22 56.8 0 57.8 12 13.3 0 29.7 19 45.0 0 23.6 20 03.1

8 2 05.6 22 22.1 0 21.8

23 04.3 0 59.8 12 34.6 0 29.8 19 38.6 0 23.7 20 00.0

10 2 00.9 21 34.3 0 16.7

23 08.9 1 01.7 12 56.0 0 30.0 19 32.0 0 23.8 19 56.9

12 1 53.8 20 40.8 0 11.5

23 10.7 1 03.6 13 17.4 0 30.1 19 25.3 0 24.0 19 53.8

14 1 44.0 19 41.8 0 06.4

23 09.7 1 05.3 13 38.8 0 30.2 19 18.6 0 24.1 19 50.7

16 1 31.2 18 38.1 0 01.3

23 05.8 1 06.9 14 00.3 0 30.4 19 11.7 0 24.2 19 47.5

18 1 15.3 17 30.6 0 03.8

22 59.0 1 08.4 14 21.8 0 30.5 19 04.8 0 24.4 19 44.4

20 0 55.8 16 20.7 0 08.9

22 49.5 1 09.9 14 43.2 0 30.7 18 57.7 0 24.5 19 41.1

22 0 32.8 15 10.1 0 13.8

22 37.1 1 11.3 15 04.6 0 30.9 18 50.6 0 24.6 19 37.9

24 -0 06.1 14 01.2 0 18.7

22 22.0 1 12.6 15 25.9 0 31.0 18 43.4 0 24.8 19 34.7

26 +0 24.0 12 56.9 0 23.5

22 04.1 1 13.8 15 47.0 0 31.2 18 36.2 0 24.9 19 31.4

28 0 56.9 12 00.6 0 28.2

21 43.6 1 15.0 16 08.1 0 31.3 18 28.8 0 25.1 19 28.1

30 1 31.5 11 15.8 0 32.8

21 20.4 1 16.1 16 28.9 0 31.5 18 21.4 0 25.2 19 24.8

Feb. 1 2 06.3 10 45.6 0 37.3

20 54.7 1 17.2 16 49.6 0 31.7 18 13.9 0 25.4 19 21.5

3 2 39.0 10 32.3 0 41.6

20 26.4 1 18.1 17 10.1 0 31.9 18 06.4 0 25.5 19 18.2

5 3 06.9 10 36.5 0 45.8

19 55.8 1 19.1 17 30.4 0 32.1 17 58.8 0 25.7 19 14.8

7 3 27.6 10 56.7 0 49.9

19 22.8 1 19.9 17 50.4 0 32.2 17 51.1 0 25.8 19 11.5

9 3 39.3 11 29.6 0 53.7

18 47.6 1 20.7 18 10.1 0 32.4 17 43.4 0 26.0 19 08.2

11 3 41.3 12 10.5 +0 57.4

18 10.1 1 21.5 18 29.6 0 32.6 17 35.7 0 26.1 19 04.9

13 3 34.3 12 54.7 -1 00.9

17 30.6 1 22.2 18 48.8 0 32.8 17 27.9 0 26.3 19 01.5

15 3 19.9 13 38.3 1 04.2

16 49.2 1 22.9 19 07.7 0 33.0 17 20.0 0 26.5 18 58.2

17 3 00.1 14 18.3 1 07.3

16 05.8 1 23.5 19 26.2 0 33.3 17 12.2 0 26.7 18 54.9

19 2 36.7 14 52.9 1 10.2

15 20.6 1 24.1 19 44.4 0 33.5 17 04.3 0 26.8 18 51.6

21 2 11.5 15 21.2 1 12.8

14 33.7 1 24.6 20 02.2 0 33.7 16 56.3 0 27.0 18 48.3

23 1 45.6 15 42.7 1 15.3

13 45.2 1 25.1 20 19.7 0 33.9 16 48.4 0 27.2 18 45.1

25 1 19.7 15 57.4 1 17.5

12 55.3 1 25.6 20 36.7 0 34.2 16 40.4 0 27.4 18 41.9

27 +0 54.6 -16 05.2 -1 19.4 -12 03.9 +1 26.0 +20 53.3 +0 34.4 -16 32.4 +0 27.5 -18 38.6

431

PLANETS, 2021 GEOCENTRIC LATITUDE AND DECLINATION FOR 5h 29m.0 I.S.T. Date

Mercury Latitude

°

'

Declination

°

Venus Latitude

°

'

Mars

Declination

°

'

Latitude

°

'

Jupiter

Declination

°

'

Latitude

°

'

Saturn

Declination

°

'

Latitude

°

'

Declination

°

'

Mar. 1 +0 30.5 -16 06.5 -1 21.1 -11 11.3 +1 26.4 +21 09.4 +0 34.6 -16 24.4 +0 27.7 -18 35.5 3 0 07.7 16 01.3 1 22.6

10 17.4 1 26.8 21 25.1 0 34.9 16 16.4 0 27.9 18 32.3

5 +0 13.6 15 49.9 1 23.8

9 22.5 1 27.1 21 40.3 0 35.1 16 08.4 0 28.1 18 29.2

7 -0 33.4 15 32.3 1 24.8

8 26.5 1 27.4 21 55.1 0 35.4 16 00.5 0 28.3 18 26.1

9 0 51.7 15 08.9 1 25.5

7 29.6 1 27.7 22 09.3 0 35.7 15 52.5 0 28.5 18 23.1

11 1 08.3 14 39.7 1 26.0

6 32.0 1 27.9 22 23.1 0 35.9 15 44.5 0 28.7 18 20.1

13 1 23.3 14 04.9 1 26.2

5 33.6 1 28.1 22 36.3 0 36.2 15 36.6 0 28.9 18 17.1

15 1 36.7 13 24.7 1 26.2

4 34.7 1 28.3 22 48.9 0 36.5 15 28.7 0 29.1 18 14.2

17 1 48.3 12 39.1 1 25.9

3 35.2 1 28.5 23 01.1 0 36.8 15 20.8 0 29.3 18 11.3

19 1 58.3 11 48.4 1 25.3

2 35.4 1 28.6 23 12.6 0 37.1 15 13.0 0 29.6 18 08.5

21 2 06.5 10 52.5 1 24.5

1 35.2 1 28.7 23 23.6 0 37.3 15 05.2 0 29.8 18 05.8

23 2 13.0

9 51.7 1 23.4

-0 34.8 1 28.8 23 34.0 0 37.7 14 57.4 0 30.0 18 03.1

25 2 17.7

8 46.1 1 22.1 +0 25.6 1 28.9 23 43.8 0 38.0 14 49.8 0 30.2 18 00.4

27 2 20.6

7 35.7 1 20.6

1 26.1 1 28.9 23 53.0 0 38.3 14 42.1 0 30.4 17 57.9

29 2 21.6

6 20.6 1 18.8

2 26.5 1 28.9 24 01.6 0 38.6 14 34.6 0 30.7 17 55.4

31 2 20.8

5 01.0 1 16.8

3 26.7 1 28.9 24 09.5 0 38.9 14 27.1 0 30.9 17 53.0

Apr. 2 2 18.0

3 37.1 1 14.5

4 26.7 1 28.9 24 16.9 0 39.3 14 19.7 0 31.1 17 50.6

4 2 13.3

2 08.9 1 12.0

5 26.3 1 28.9 24 23.5 0 39.6 14 12.4 0 31.4 17 48.3

6 2 06.6

-0 36.7 1 09.3

6 25.4 1 28.8 24 29.6 0 40.0 14 05.1 0 31.6 17 46.1

8 1 57.9 +0 59.4 1 06.4

7 24.0 1 28.7 24 34.9 0 40.3 13 58.0 0 31.8 17 44.0

10 1 47.1

2 38.9 1 03.3

8 21.9 1 28.6 24 39.7 0 40.7 13 51.0 0 32.1 17 42.0

12 1 34.3

4 21.6 1 00.0

9 19.0 1 28.5 24 43.7 0 41.0 13 44.0 0 32.3 17 40.0

14 1 19.6

6 06.8 0 56.5

10 15.3 1 28.4 24 47.1 0 41.4 13 37.2 0 32.6 17 38.2

16 1 03.0

7 53.8 0 52.9

11 10.7 1 28.3 24 49.8 0 41.8 13 30.5 0 32.8 17 36.4

18 0 44.7

9 41.9 0 49.0

12 04.9 1 28.1 24 51.8 0 42.2 13 24.0 0 33.1 17 34.7

20 -0 25.0 +11 29.8 -0 45.0 +12 58.1 +1 28.0 +24 53.2 +0 42.6 -13 17.5 +0 33.4 -17 33.1

432

URANUS, NEPTUNE AND PLUTO, 2021 h

m

APPARENT GEOCENTRIC LONGITUDE FOR 5 29 .0 I.S.T. Date

Uranus °

Jan.

Feb.

'

Neptune "

°

'

Pluto "

°

'

Date

Uranus

"

°

'

Neptune "

°

'

Pluto "

°

'

"

0

36 48 40 348 27 19 294 09 20 Feb. 25

37 27 30 350 06 17 295 55 29

2

36 47 18 348 29 32 294 13 15

27

37 31 41 350 10 45 295 58 39

4

36 46 07 348 31 53 294 17 11 Mar.

1

37 36 01 350 15 15 296 01 44

6

36 45 08 348 34 20 294 21 08

3

37 40 31 350 19 45 296 04 45

8

36 44 22 348 36 55 294 25 06

5

37 45 10 350 24 17 296 07 41

10

36 43 48 348 39 37 294 29 05

7

37 49 58 350 28 50 296 10 32

12

36 43 27 348 42 26 294 33 05

9

37 54 55 350 33 23 296 13 18

14

36 43 19 348 45 22 294 37 05

11

38 00 00 350 37 57 296 15 58

16

36 43 23 348 48 24 294 41 04

13

38 05 14 350 42 30 296 18 33

18

36 43 39 348 51 32 294 45 04

15

38 10 35 350 47 03 296 21 02

20

36 44 08 348 54 46 294 49 03

17

38 16 04 350 51 36 296 23 25

22

36 44 50 348 58 06 294 53 02

19

38 21 40 350 56 08 296 25 42

24

36 45 45 349 01 31 294 56 59

21

38 27 24 351 00 39 296 27 54

26

36 46 52 349 05 03 295 00 56

23

38 33 14 351 05 09 296 29 59

28

36 48 12 349 08 39 295 04 52

25

38 39 10 351 09 37 296 31 58

30

36 49 44 349 12 21 295 08 46

27

38 45 12 351 14 04 296 33 50

1

36 51 28 349 16 07 295 12 38

29

38 51 20 351 18 28 296 35 36

3

36 53 24 349 19 58 295 16 28

31

38 57 33 351 22 51 296 37 15

5

36 55 32 349 23 53 295 20 15 Apr.

2

39 03 52 351 27 11 296 38 48

7

36 57 53 349 27 52 295 24 01

4

39 10 15 351 31 29 296 40 15

9

37 00 25 349 31 56 295 27 45

6

39 16 43 351 35 44 296 41 34

11

37 03 09 349 36 03 295 31 25

8

39 23 14 351 39 55 296 42 47

13

37 06 05 349 40 14 295 35 02

10

39 29 50 351 44 04 296 43 53

15

37 09 12 349 44 28 295 38 36

12

39 36 28 351 48 08 296 44 51

17

37 12 30 349 48 45 295 42 06

14

39 43 10 351 52 09 296 45 43

19

37 15 59 349 53 04 295 45 32

16

39 49 55 351 56 07 296 46 28

21

37 19 39 349 57 26 295 48 55

18

39 56 43 351 59 60 296 47 05

23

37 23 30 350 01 51 295 52 14

20

40 03 33 352 03 49 296 47 36

25

37 27 30 350 06 17 295 55 29

22

40 10 24 352 07 33 296 48 00

433

EXPLANATION In the following pages, a short explanation of the terms used in this Ephemeris has been given and the scope and limitations of the information furnished have been stated in a concise form. The values of the different constants and other data upon which the tabulated quantities are based have also been given in some cases in order to facilitate the use of this Ephemeris. It is not intended to furnish here any detailed explanation about the compilation of the tabular matter for which the reader is referred to the relevant literature. Many changes have been incorporated in this publication from time to time including several recomendations of IAU at its General Assembly.

THE STANDARD EPOCH AND TIME SCALES There are two classes of time scales used in Astronomy, one based on the Systeme International (SI) - the atomic second, the other based on the rotation of the Earth. Time scales based on the SI second include TAI and TT for practical applications. Time scale based on the rotation of the Earth include mean and apparent sidereal time and UT1. Because of irregularites in the Earth’s rotation and its tidal deceleration, Earth’s rotation based time scales do not advance at a uniform rate, and they increasingly lag behind the SI-second-based time scales. The widely disseminated time scale UTC is a hybrid, it advances by SI seconds but is subjct to one-second corrections (leap seconds) to keep it within 0s.9 of UT1. h

The standard epoch J 2000.0 corresponds to 2000 January 1, 12 TT (JD 245 1545.0 TT). A date may be expressed in years as a Julian epoch or for some purposes as a Besselian epoch. Julian epoch = J [2000.0 + (JD − 245 1545.0)/ 365.25] Where the quantity in the denominator is the Julian year. Besselian epoch= B [1900.0 + (JD − 241 5020.313 52)/ 365.242 198 781] Where the quantity in the denominator is the length of tropical year. Prefixes J and B stand for the Julian and Besselian epochs respectively. Various time systems used in this publication and their inter-relationships are described below : Sidereal time system is derived from the Earth’s rotation with respect to the stars. Local sidereal time is defined as the local hour angle of the vernal equinox. It is 0h at the instant when the vernal equinox is at the upper transit of the local meridian. It is determined from observation of meridian transits of known stars. As the equinox oscillates about its mean position due to the effect of nutation, it gives rise to two kinds of sidereal time : the apparent sidereal time which is the hour angle of the true equinox of date and the mean sidereal time which is the hour angle of the mean equinox of date. The relation between the two is: Apparent sidereal time = Mean sidereal time + Equation of Equinoxes Equation of equinoxes is the total nutation in longitude multiplied by the cosine of the obliquity of the ecliptic. Its value varies within ± 1.2 seconds of time in a period of about 18.6 years. Sidereal time on the geographic meridian of Greenwich is known as Greenwich sidereal time. Local sidereal time is related to Greenwich sidereal time (mean or apparent as appropriate) as follows: Local sidereal time = Greenwich sidereal time + λ, where λ is the observer’s longitude measured positively to the east (from 1985 onwards the sign convention for east terrestrial longitude to be positive has been adopted). International Atomic Time (TAI) is a highly precise time scale given by atomic clocks. It is now being used as a standard in astronomy as it is independent of the Earth’s rotation. Its fundamental unit, the SI second, is

434

EXPLANATION defined as the duration of 9 192 631 770 cycles of the radiation corresponding to the transition between two hyperfine levels of the ground state of the Cesium 133 atom. This time scale results from analysis of data from atomic time standards of many countries carried out at the Bureau International de l , Heure in Paris. Universal Time (UT) is used for civil time keeping. It is an outgrowth of the mean solar time system derived from the Earth’s rotation with respect to the Sun. It has been formally defined through a strict relationship with the Greenwich mean sidereal time and is, therefore, determined from observation of star transits. The universal time directly derived from observation is designated UT . It contains nonuniformities due to variations in the rotation ° of the Earth and is peculiar to the observer’s geographic location because of polar motion. When UT is corrected ° for Earth’s polar motion, it is called UT1. When UT1 is further corrected for seasonal variation in the Earth’s rotation, it is called UT2. Both UT and UT2 are not for general usage. Instead, the national time services provide what ° is known as co-ordinated universal time (UTC). It is a smoothed version of UT2 and differs from TAI by an integral number of seconds. It contains step adjustments of exactly one second (leap seconds) in order to keep it always within 0.90 seconds of UT1. Beginning with 1972, the step adjustments are usually inserted after the 60th second of the last minute of December 31 or June 30. In this publication, UT1 has been used in computations relating to hour angles, etc., unless otherwise stated. Dynamical Time replaces ephemeris time (ET) as argument of ephemerides with effect from 1985 in this publication. The concept of different dynamical times for observers in different frames of reference arises out of general theory of relativity. In this publication, terrestrial time (TT) is the tabular argument of the fundamental geocentric ephemerides and barycentric dynamical time (TDB) is the arguments of ephemerides referred to the barycentre of the solar system. The former corresponds to proper time and the latter to co-ordinate time in terms of the general theory of relativity. Both TT and TDB are independent of the Earth’s rotation. These scales are so defined that the difference between them is purely periodic. Their difference is given by:s

s

TDB = TT + 0 .001 657 sin g + 0 . 000 022 sin (L − LJ ), where higher order terms have been neglected. Here g is the mean anomaly of the Earth in its orbit around the Sun and is given by:g L− LJ

= 357°.53 + 0°.985 600 28 (JD − 245 1545.0 ) = 246°.11 + 0.902 517 92 (JD − 245 1545.0)

Where L− LJ is the difference in the mean longitude of the Sun and Jupiter. Relationship Between universal time and sidereal time Universal time is defined in terms of Greenwich mean sidereal time by: 2

3

GMST at 0h UT1 = 6h 41m 50s .549 377 + 864 018 4s. 704 478 Tu + 0s .092 772 Tu − 2s .93 × 10-8 Tu − 1s .997 × 4 5 10-6 Tu − 2s .5 × 10-9 Tu where Tu is the number of Julian centuries of 36525 days of universal time elapsed since 1 January, 2000,12h UT (JD 245 154 5.0). In other words, Tu = (JD − 245 1545.0)/ 36525 The above expression implies that the ratio of UT1 to GMST at the epoch J2000.0 is 0.997 269 566 329 084 and its inverse is 1.002 737 909 350 795. The following relationship holds during 2020: h

On day of year d at t UT1 GMST = 6h.609 0775 + 0h.065 709 8246 d + 1h.002 737 91 t where day of the year d is tabulated on pages 4 to 12.

435

EXPLANATION In 2020 : 1 mean solar day = 1.002 737 909 35 mean sidereal days h m s = 24 03 56 .555 37 of mean sidereal time 1 mean sidereal day = 0.997 269 566 33 mean solar days h m s = 23 56 04 .090 53 of mean solar time

Conversion of local mean time to local sidereal time h

Calculate local sidereal time at 15

λ = 77° 13' 00" East ( 5

h

08

m

54

m

42

s

L.M.T. on 2020 January 1, for Delhi longitude,

s

52 )

1. 2.

Universal time = Local mean time − λ Greenwich mean sidereal time at 0h U.T. on January 1, 2020 (Page 13 ).

3.

Add equivalent mean sidereal time for 10 45 50 (UT × 1.002 737 9093).

4. 5.

Greenwich mean sidereal time at desired L.M.T. Add equation of equinoxes at UT=0d. 45 (second order interpolation may be used).

6. 7.

Greenwich apparent sidereal time Add longitude (east positive)

8.

Local apparent sidereal time

h 10 6

m 45 40

s 50 29.234

h 10

m 47

s 36.094

—————————— 17 28 5.328285 -1.010 —————————— 17 28 4.318 5 08 52.000 —————————— 22 36 56.318

For local mean sidereal time, the above process may be repeated by neglecting the equation of equinoxes.

Conversion of local sidereal time to local mean time h

m

s

Calculate local mean time at 22 38 51 .206 local apparent sidereal time on 2020 January 1, for h m s Delhi longitude, λ = 77° 13' 00" East ( 5 08 52 ) h m s 1. Local apparent sidereal time 22 36 56.318 2. Subtract longitude (east positive) 5 08 52.000 —————————— 3. Greenwich apparent sidereal time 17 28 4.318 4. Subtract equation of equinox at 0h U.T. -1.009 —————————— 5. Greenwich mean sidereal time (provisional) 17 28 5.327 6. Subtract Greenwich mean sidereal time at 0h U.T. 6 40 29.234 —————————— 7. Mean sidereal time interval (provisional) M.S.T. (P) 10 47 36.093

436

EXPLANATION 7.

Mean sidereal time interval (provisional) M.S.T. (P)

8.

Mean time interval in days corresponding to (7) above = (M.S.T. (P) × 0.997 269 566) = 0d.45 (UT). Subtract the increment to equation of equinoxes for 0d.45 UT (using second order interpolation)

9. 10. 11.

Mean sidereal time Equivalent UT (MST × 0.997 269 566) Local mean time = UT + λ

10

47 36.096

(-) 0.00310 —————————— 10 47 36.096 10 45 50.002 15 54 42.002

The mean time from the local mean sidereal time may be worked out on similar lines as above by neglecting the equation of equinoxes. Notation for time-scales and related quantities Universal time (also UT); counted from 0h (mid night); unit is second of mean solar time, affected by iregularities in the Earth’s rate of rotation. UT0 local approximation to universal time; not corrected for polar motion (rarely used). GMST Greenwich mean sidereal time; GHA of mean equinox of date. GAST Greenwich apparent sidereal time; GHA of true Eqinox of date. TAI international atomic time; unit is the SI second of geoid. UTC coordinated universal time; differs from TAI by an integral number of seconds, and is the basis of most radio time signals and national and/ or legal time systems. ΔUT = UT1 − UTC; increment to be applied to UTC to give UT1 TDB barycentric dynamical time; used as time-scale of ephemerides, referred to the barycentre of the solar system. Teph the independent variable of the equations of motion used by the JPL ephemerides, in particular DE405/LE405. Teph and TDB may be considered to be equivalent. TT terrestrial time; used as time-scale of ephemerides for observations from the Earth’s surface (geoid). TT = TAI + 32s.184. ΔT = TT − UT1; increment to be applied to UT1 to give TT. = TAI + 32s.184 − UT1 ΔAT = TAI −UT1; increment to be applied to UTC to give TAI; an integral number of seconds. ΔTT = TT − UTC = ΔAT + 32s.184; increment to be applied to UTC to give TT. UT1 - UT0 = − (x sin λ + y cosλ ) tanφ/15 where λ and φ are usual geodetic longitude and latitude of the place, and x and y are the co-ordinates of the pole with respect to the geodetic system, in arcseconds. GAST = GMST + εγ /15 , εγ is equation of equinox. h h In order to convert the tabulations for 0 TT to 0 UT, one may interpolate to ΔT δ1/2/ h where h is the tabular interval and δ1/2 is the first difference of the tabular values. UT1

ΔT s 1620.0 + 124 1621 119 1622 115 1623 110 1624 + 106

Year

REDUCTION OF TIME SCALES, 1620-1644 ΔT = ET - UT Year ΔT Year ΔT Year ΔT s s s 1625.0 + 102 1630.0 + 85 1635.0 + 72 1626 98 1631 82 1636 70 1627 95 1632 79 1637 67 1628 91 1633 77 1638 65 1629 + 88 1634 + 74 1639 + 63

Year 1640.0 1641 1642 1643 1644

ΔT s + 62 60 58 57 + 55

437

EXPLANATION

1645.0 1646 1647 1648 1649

s + 54 53 51 50 49

1680.0 1681 1682 1683 1684

REDUCTION OF TIME SCALES, 1645-1819 ΔT = ET - UT ΔT Year ΔT Year ΔT s s s + 16 1715.0 + 10 1750.0 + 13 15 1716 10 1751 14 14 1717 11 1752 14 14 1718 11 1753 14 13 1719 11 1754 14

1650.0 1651 1652 1653 1654

+ 48 47 46 45 44

1685.0 1686 1687 1688 1689

+ 12 12 11 11 10

1720.0 1721 1722 1723 1724

+ 11 11 11 11 11

1755.0 1756 1757 1758 1759

1655.0 1656 1657 1658 1659

+ 43 42 41 40 38

1690.0 1691 1692 1693 1694

+ 10 10 9 9 9

1725.0 1726 1727 1728 1729

+ 11 11 11 11 11

1660.0 1661 1662 1663 1664

+ 37 36 35 34 33

1695.0 1696 1697 1698 1699

+ 9 9 9 9 9

1730.0 1731 1732 1733 1734

1665.0 1666 1667 1668 1669

+ 32 31 30 28 27

1700.0 1701 1702 1703 1704

+ 9 9 9 9 9

1670.0 1671 1672 1673 1674

+ 26 25 24 23 22

1705.0 1706 1707 1708 1709

1675.0 + 21 1676 20 1677 19 1678 18 1679 + 17

1710.0 1711 1712 1713 1714

Year

ΔT

Year

Year

ΔT

1785.0 1786 1787 1788 1789

s + 17 17 17 17 17

+ 14 14 14 15 15

1790.0 1791 1792 1793 1794

+ 17 17 16 16 16

1760.0 1761 1762 1763 1764

+ 15 15 15 15 15

1795.0 1796 1797 1798 1799

+ 16 15 15 14 14

+ 11 11 11 11 12

1765.0 1766 1767 1768 1769

+ 16 16 16 16 16

1800.0 1801 1802 1803 1804

+ 13.7 13.4 13.1 12.9 12.7

1735.0 1736 1737 1738 1739

+ 12 12 12 12 12

1770.0 1771 1772 1773 1774

+ 16 16 16 16 16

1805.0 1806 1807 1808 1809

+ 12.6 12.5 12.5 12.5 12.5

+ 9 9 9 10 10

1740.0 1741 1742 1743 1744

+ 12 12 12 12 13

1775.0 1776 1777 1778 1779

+ 17 17 17 17 17

1810.0 1811 1812 1813 1814

+ 12.5 12.5 12.5 12.5 12.5

+ 10 10 10 10 + 10

1745.0 1746 1747 1748 1749

+ 13 13 13 13 + 13

1780.0 1781 1782 1783 1784

+ 17 17 17 17 + 17

1815.0 1816 1817 1818 1819

+ 12.5 12.5 12.4 12.3 + 12.2

This table is based on an adopted value of – 26"/cy2 for the tidal term ( ) in the mean motion of the Moon from the results of analyses of observations of lunar occultations of stars, eclipses of the Sun and transits of Mercury. (see F.R. Stephenson and L.V. Morrison, 1984 PhD Trans, R, Soc. London, Ser A, 313, 47-70).

1955)2

To calculate the values of ΔT for a different value of the tidal term ( ′), add – 0.000 091 ( ′+ 26) (year − seconds to the tabulated values of ΔT.

438

EXPLANATION REDUCTION OF TIME SCALES FROM 1820 1820 - 1939, Year

ΔT

ΔT =ET− UT. Year

ΔT

From Year

ΔT

Year

1940, 2018,

ΔT = TDT - UT. ΔT = TT - UT.

ΔT

Year

ΔT

1820.0 1821 1822 1823 1824 1825.0 1826 1827 1828 1829

s + 12.0 11.7 11.4 11.1 10.6 10.2 9.6 9.1 8.6 8.0

1860.0 1861 1862 1863 1864 1865.0 1866 1867 1868 1869

s + 7.88 7.82 7.54 6.97 6.40 6.02 5.41 4.10 2.92 1.82

s 1900.0 − 2.72 1901 1.54 1902 − 0.02 1903 + 1.24 1904 2.64 1905.0 3.86 1906 5.37 1907 6.14 1908 7.75 1909 9.13

1940.0 1941 1942 1943 1944 1945.0 1946 1947 1948 1949

s + 24.33 24.83 25.30 25.70 26.24 26.77 27.28 27.78 28.25 28.71

s 1980.0 + 50.54 1981 51.38 1982 52.17 1983 52.96 1984 53.79 1985.0 54.34 1986 54.87 1987 55.32 1988 55.82 1989 56.30

1830.0 1831 1832 1833 1834 1835.0 1836 1837 1838 1839

+ 7.5 7.0 6.6 6.3 6.0 5.8 5.7 5.6 5.6 5.6

1870.0 1871 1872 1873 1874 1875.0 1876 1877 1878 1879

+ 1.61 + 0.10 − 1.02 1.28 2.69 3.24 3.64 4.54 4.71 5.11

1910.0 + 10.46 1911 11.53 1912 13.36 1913 14.65 1914 16.01 1915.0 17.20 1916 18.24 1917 19.06 1918 20.25 1919 20.95

1950.0 1951 1952 1953 1954 1955.0 1956 1957 1958 1959

+ 29.15 29.57 29.97 30.36 30.72 31.07 31.35 31.68 32.18 32.68

1990.0 + 56.86 1991 57.57 1992 58.31 1993 58.12 1994 59.98 1995.0 60.78 1996 61.63 1997 62.29 1998 62.97 1999 63.47

1840.0 1841 1842 1843 1844 1845.0 1846 1847 1848 1849

+ 5.7 5.8 5.9 6.1 6.2 6.3 6.5 6.6 6.8 6.9

1880.0 1881 1882 1883 1884 1885.0 1886 1887 1888 1889

− 5.40

1920.0 + 21.16 1921 22.25 1922 22.41 1923 23.03 1924 23.49 1925.0 23.62 1926 23.86 1927 24.49 1928 24.34 1929 24.08

1960.0 1961 1962 1963 1964 1965.0 1966 1967 1968 1969

+ 33.15 33.59 34.00 34.47 35.03 35.73 36.54 37.43 38.29 39.20

2000.0 + 63.83 2001 64.09 2002 64.30 2003 64.47 2004 64.57 2005 + 64.69 2006 64.85 2007 65.15 2008 65.46 2009 65.78

1850.0 1851 1852 1853 1854 1855.0 1 856 1857 1858 1859

+ 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.7 7.8 7.8

1890.0 1891 1892 1893 1894 1895.0 1896 1897 1898 1899

− 5.87

1930.0 + 24.02 1931 24.00 1932 23.87 1933 23.95 1934 23.86 1935.0 23.93 1936 23.73 1937 23.92 1938 23.96 1939 24.02

1970.0 1971 1972 1973 1974 1975.0 1976 1977 1978 1979

+ 40.18 41.17 42.23 43.37 44.49 45.48 46.46 47.52 48.53 49.59

2010 2011 2012 2013 2014 2015 2016 2017 2018

2019 2020

+ 69.40 + 70

2021 2022

+ 70 + 71

5.42 5.20 5.46 5.46 5.79 5.63 5.64 5.80 5.66

6.01 6.19 6.64 6.44 6.47 6.09 5.76 4.66 3.74

Extrapolated Values 2023 + 71

+ 66.07 66.32 66.60 66.91 67.28 67.64 68.10 68.59 68.97

439

EXPLANATION Difference TAI – UTC = ΔAT Date

Δ AT

Date

s

1972 Jul.1

1979 Jan.1

1973 Jan.1 + 12.00

1990 Jan.1 + 19.00

+ 13.00 + 14.00 1976 Jan.1

+ 28.00

+ 22.00

+ 16.00 1978 Jan.1

+ 29.00

+ 23.00

+ 17.00

+ 30.00 + 31.00 1999 Jan.1

+ 36.00 2017 Jan. 1

1997 Jul.1 + 24.00

1990 Jan.1

+ 35.00 2015 Jul. 1

1996 Jan.1

1988 Jan.1

+ 34.00 2012 Jul. 1

1994 Jul.1

1985 Jul.1

+ 33.00 2009 Jan. 1

+ 27. 00

+ 21.00

+ 15.00 1977 Jan.1

+ 32.00 2006 Jan. 1

1993 Jul.1

1983 Jul.1

s

+ 26.00

+ 20.00

Δ AT

1999 Jan. 1

1992 Jul.1

1982 Jul.1

Date

+ 25.00 1991 Jan.1

1981 Jul.1

1975 Jan.1

Δ AT s

+ 18.00 1980 Jan.1

1974 Jan.1

Date

s

+ 11.00

1979 Jan.1

Δ AT

+ 37.00 In critical cases descend ΔET = ΔAT + 32s.184 ΔTT

From 1990 onwards, ΔT is for Jan. 1 0h UTC. See page 2 for a summary of the notation for time-scales.

Astronomical Reference System and Reference Frames A reference system is the complete specification of how a celestial coordinate system is to be formed. Both the origin and the orientation of the fundamental planes (or axes) are defined. A reference system also incorporates a specification of the fundamental models needed to construct the system; that is, the basis for the algorithms used to transform between observable quantities and reference data in the system. A reference frame, on the other hand, consists of a set of identifiable fiducial points on the sky along with their coordinates, which serves as the practical realization of a reference system. For example, the fundamental plane of an astronomical reference system has conventionally been the extension of the Earth’s equatorial plane, at some date, to infinity. Declination is the angular distance north or south of this plane, and right ascension is the angular distance measured eastward along the equator from some defined reference point. This reference point, the right asscension origin, has traditionally been the Equinox: the point at which the Sun, in its yearly circuit of the celestial sphere, crosses the equatorial plane moving from south to north. The Sun’s apparent yearly motion lies in the ecliptic, the plane of the Earth’s orbit. The equinox, therefore, is a direction in the space along the nodal line defined by the intersection of the ecliptic and equatorial planes; equivalently, on the celestial sphere, the equinox is at one of the two intersections of the great circles representing these planes. Because both of these planes are moving, the coordinate systems that they define must have a date associated with them; such a reference system must therefore be specified as “the equator and equinox of (some date)”. Of course, such a reference system is an idealization, because the theories of motion of the Earth that define how the two planes move are imperfect. In fact, the very definations of these planes are problematic for high precession work. Even if the fundamental planes of a reference system are defined without any reference to the motions of the Earth, there is no way magically to paint them on the celestial sphere at any particular time. Therefore, in practice, we use a specific reference frame - a set of fiducial objects with assigned coordinates - as the practical representation of an astronomical reference system. The scheme is completely analogous to how terrestrial reference systems are established using survey control stations (geodetic reference point) on the Earth’s surface. Most commonly, a reference frame consists of a catalog of precise positions (and motions, if measurable) of stars or extragalactic objects as seen from the solar system barycenter at a specific epoch (now usually “J2000.0”, which is 12h TT on January 2000). Each object’s instantaneous position, expressed as right ascension and declination, indicates the object’s angular distance from the catalog’s equator and origin of right ascension. Any two such objects in the catalog (if they are not coicident or antipodal) therefore uniquely orient a spherical coordinate system on the sky - a reference frame.

440

EXPLANATION A modern astrometric catalog contains data on a large number of objects (N), so the coordinate system is vastly overdetermined. The quality of the reference frame defined by a catalog depends on the extent to which the coordinates of all possible pairs of objects (N2/2) serve to the identical equator and right ascesion origin, within the expected random errors. Typically, every catalog contains systematic errors, that is, errors in position that are similar for objects that are in the same area of the sky, or are of the same magnitude (flux) or color (spectral index). Systematic errors mean that the reference frame is warped, or is effectively different for different classes of objects. Obviously, minimizing systematic errors when a catalog is constructed is at least as important as minimizing the random errors. To be useful, a reference frame must be implemented at the time of actual observations, and this requires the computation of the apparent coordinates of the catalog objects at arbitrary dates and times. The accuracy with which we know the motions of the objects accross the sky is an essential factor in this computation. Astrometric star catalogs list proper motions, which are the projection of each star’s space motion onto the celestial sphere, expressed as an angular rate in right ascension and declination per unit time. Because the tabulated proper motions are never perfect, any celesial reference frame deteriorates with time. Moreover, systematic errors in the proper motions can produce time-dependent warpings and spurious rotations of the frame. Therefore, the accuracy and consistency of the proper motions are critical to the overall quality, utility, and longevity of reference frames defined by stars. Even reference frames defined by extragalactic objects, which are usually considered to have zero proper motion, may deteriorate, because many of these objects show small apparent motions that are artifacts of their emission mechanisms. The position of solar system objects can also be used to define a reference frame. For each solar system body involved, an ephemeris is used, which is simply a table of the celestial coordinates of the body as a funtion of time (or an algorithm that yields such a table). A reference frame defined by the ephemerides of one or more solar system bodies is called a dynamical reference frame. Because the ephemerides used incorporate the motion of the Earth as well as that of the other solar system bodies, dynamical reference frames embody in a very fundamental way the moving equator and ecliptic, hence the equinox. They have therefore been used to correct the orientation of star catalog reference frames (the star positions were systematically adjusted) on the basis of simultaneous observations of star and planets. In a sense, the solar system is used as a gyrocompass. However, dynamical reference frames are not very practical for establishing a coordinate system for day to day astronomical observations. Descriptions of reference frames and reference systems often refer to three coordinate axes, which are simply the set of right-handed cartesian axes that correspond to the usual celestial spherical coordinate system. The xy-plane is the equator, the z-axis points toward the north celestial pole, and the x-axis points toward the origin of right ascension. Although in principal this allows us to specify the position of any celestial object in rectangular coordinates, the distance scale (based on stellar parallaxes) is not established to high precession beyond the solar system. What a reference system actually defines is the way in which the two coventional astronomical angular coordinates, right ascension and declination, overlay real observable points in the sky. The fundamental celestial reference system for astronomical application is now the International Celestial Reference System (ICRS) as provided in resolution B2 of 1997. The “realization” of of the ICRS, called the International Celestial Reference Frame (ICRF), is a set of high accuracy positions of extragalactic radio sources measured by very long baseline interferometry. The IAU Working Group on nomenclature for Fundamental Astronomy has recomended the following definations for ICRS and ICRF: International Celestial Reference System (ICRS): The idealized barycetric co-ordinate system to which celestial positions are referred. It is kinematically non-rotating with respect to the ensemble of distant extragalactic objects. It has no intrinsic orientation but was aligned close to the mean equator and dynamical equinox of J2000.0 for continuity with previous fundamental reference systems. Its orientation is independent of epoch, ecliptic or equator and is realized by a list of adopted coordinates of extragalactic sources. International Celestial Reference Frame (ICRF): A set of extragalactic objects whose adopted positions and uncertainties realize the ICRS axes and give the uncertainties of the axes. It is also the name of radio catalogue whose 212 defining sources are currently the most accurate realization of the ICRS. The orientation of the ICRF catalogue was carried over from earlier IERS radio catalogs and was within the errors of the standard stellar and dynamical frames at the time of adoption. Successive revision of the ICRF are intended to minimize rotation from its original orientation.

441

EXPLANATION Some important reference systems and their designations as per IAU 2000 resolution B1.6, B1.7 and B1.8, and IAU 2006 resolutions 1 and 2 are listed below: (i) Barycentric Celestial Reference System (BCRS): a system of barycentric space-time coordinates for the solar system within the framework of General Relativity. For all practical applications, the BCRS is assumed to be oriented according to the ICRS axes, the directions of which are realized by the International Celestial Reference Frame. The ICRS is not identical to the system defined by the dynamical mean equator and equinox of J2000.0, although the difference in orientation is only about 0".02. (ii) The Geocentric Celestial Reference System (GCRS): is a system of geocentric space-time coordinates within the framework of General Relativity. The directions of the GCRS axes are obtained from those of the BCRS (ICRS) by a relativistic transformation. Positions of stars obtained from ICRS reference data, corrected for proper motion, parallax, light-bending, and aberration (for a geocentric observer) are with respect to the GCRS. The same is true for planetary positions, although the corrections are somewhat different. (iii) The J2000.0 dynamical reference system: mean equator and equinox of J2000.0; a geocentric system where the origin of right ascension is the intersection of the mean ecliptic and equator of J2000.0; the system in which the IAU 2000 precession-nutation is defined. For precise applications a small rotation (frame bias) should be made to GCRS positions before precession and nutation are applied. The J2000.0 system may also be barycentric, for example as the reference system for catalogues. (iv) The true system of date (t); true equator and equinox of date: a geocentric system of date, the pole of which is the celestial intermediate pole (CIP), with the origin of right ascension at the equinox on the true equator of date (intermediate equator). It is a system “between” the GCRS and the Terrestrial Intermediate Reference System that seperates the components labelled precession-nutation and polar motion. (v) The Celestial Intermediate Reference System (i): the IAU recomended geocentric system of date, the pole of which is the celestial intermediate pole (CIP), with the origin of right ascension at the celestial intermediate origin (CIO) which is located on the intermediate equator (true equator of date). It is a system “between” (intermeiate) the GCRS and the Terrestrial Intermediate Reference System that seperates the components labelled precession-nutation and polar motion.

Precession and Nutation

The algorithms for precession were based on the IAU (1976) value for the rate of general precession in ecliptic longitude. Nutation was given by the 1980 IAU Theory of Nutation. However, IAU (1976) rate of precession had been overestimated by approximately 3 milliarcseconds per year. Further observations also revealed periodic errors of a few milliarcseconds in the 1980 IAU Theory of Nutation. As part of the 2000 IAU resolutions, the IAU 2000A precession-nutation model was introduced, based on an updated value for the rate of precession and a completely new nutation theory. As before, the model actually consists of two parts, a precession algorithm describing the smooth secular motion of the celestial pole and a nutation algorithm describing the small periodic variations in the pole’s position. The precession algorithm consists of short polynomial series for the values of certain angles. The sines and cosines of these angles, in combination, then define the elements of a precession matrix, P. The nutation algorithm consists of a rather long series expansion in Fourier terms for the angular offsets, in ecliptic longitude and latitude, of the actual celestial pole (as modeled) from the precession-only pole (true pole - mean pole). The sines and cosines of these offsets, in combination, then define the elements of a nutation matrix, N. The P and N matrices are applied to the coordinates of celestial objects, expressed as 3-vectors, to transform them from the equator and equinox of one epoch to the equator and equinox of another.

442

EXPLANATION A precession transformation is applied to celestial coordinates to convert them from the mean equator and equinox of J2000.0 to the mean equator and equinox of another date, t. Nutation is applied to the resulting coordinates to transform them to the true equator and equinox of t. Generally we will start with celestial coordinates in the GCRS, which are obtained from basic ICRS data by applying the usual algoriths for proper place. Therefore before we apply precession and nutation - we must first apply the frame bias correction to transform the GCRS coordinates to the dynamical mean equator and equinox of J2000.0. Schematically, GCRS => frame bias = mean equator & equinox of J2000.0 = precession => mean equator & equinox of t = nutation => true equator & equinox of t. The reduction from a geocentric position r with respect to the Geocentric Celestial Reference System (GCRS) to a position rt with respect to equator and equinox of date, and vice versa, is given by; rt = M r and r = M-1rt Using the 4-rotation Fukishma-Williams (F-W) method, the rotation matrix M may be witten as M=NPB Since the rotation to orient the GCRS to J2000.0 system are small the following approximate matrix B is called frame bias matrix, accurate to 2"x 10-9 (1 x 10-14 radians), may be used: B =

1 -dα0 ξ0

dα0 1 η0

-ξ0 -η0 1

where dα0 = -14.6 mas, ξ0 = -16.6170 mas, and η0 = -6.8192 mas, all converted to radians (divide by 206 264 806.247).

Precession The time argument T is given by T = (t - 2000.0)/100 = (JDTT - 2451545.0)/36525, which is a function of TT. The Capitine et al. method, the formulation of which seperates precession of the equator from precession of the ecliptic, is via the precession angles χA, ωA, ψA, which are ψA = 5038".481 507 T - 1".079 0069 T2 - 0".001 140 45 T3 + 0".000 132 851 T4 - 9".51 X 10-8 T5 ωA = ε0 - 0".025 754 T + 0".051 2623 T2 - 0".007 725 03 T3 - 0".000 000 467 T4 + 33".37 X 10-8 T5 χA = 10".556 403 T - 2".381 4292 T2 - 0".001 211 97 T3 + 0".000 170 663 T4 - 5".60 X 10-8 T5 The mean obliquity of the ecliptic at J2000.0 ( or the equivalent TDB date) is ε0 = 84381".406 (i) A rotation from the mean equator and equinox of J2000.0 to the mean ecliptic and equinox of J2000.0. This is simply a rotation around the x-axis (the direction toward the mean equinox of J2000.0) by the angle ε0 , the mean obliquity of J2000.0. After the rotation, the fundamental plane is the ecliptic of J2000.0 (ii) A rotation around the new z-axis (the direction toward the ecliptic pole of J2000.0) by the angle -ψA, the amount of precession of the equator from J2000.0 to t. (iii) A rotation around the new x-axis (the direction along the intersection of the mean equator of t with the ecliptic of J2000.0) by the angle - ωA, the obliquity of the mean equator of t with respect to the ecliptic of J2000.0. After the rotation, the fundamental plane is the mean equator of t.

443

EXPLANATION (iv) A rotation around the new z-axis ( the direction toward the mean celestial pole of t) by the angle χA, accounting for the precession of the ecliptic along the mean equator of t. After the rotation, the new x-axis is in the direction of the mean equinox of date.

P =

C4C2 - S2S4C3 -S4C2 - S2C4C3 S2S3 S1 = sin ε0 C1 = cos ε0

where

C4S2C1 + S4C3C2C1 - S1S4S3 -S4S2C1 + C4C3C2C1 - S1C4S3 -S3C2C1 - S1C3

S2 = sin (-ψA ) C2 = cos(-ψA )

S3 = sin (-ωA ) C3 = cos(-ωA )

C4S2S1 + S4C3C2S1 + C1S4S3 -S4S2S1 + C4C3C2S1 + C1C4S3 -S3C2S1 + C3C1

S4 = sin χA C4 = cos χA

Existing applications that use the 3-angle precession formulation of Newcomb and Lieske can be easily modified for the IAU 2000A precession, by replacing the current polynomials for the angles ζA, ZA and θA with the following: ζA = 2".650545 + 2306".083227 T + 0".2988499 T2 + 0".01801828 T3 - 0".000005971 T4 - 0".0000003173 T5 ZA = -2".650545 + 2306".077181 T + 1".0927348 T2 + 0".01826837 T3 - 0".000028596 T4 - 0".0000002904 T5 θA = 2004".191903 T - 0".4294934 T2- 0".04182264 T3- 0".000007089 T4 - 0".0000001274 T5 The centennial (per Julian century) rates of general precession in right ascension and declination are given by : m = 4612".604 08 + 2".783 169 4 T + 0".108 859 95 T² - 0".000 138 268 T3 and n = 2004".191 903 − 0".858 986 8 T − 0".125 467 92 T² - 0".000 028 356 T3 The elements of the matrix P given in terms of

P

=

ζA, ZA, θA are as follows:

cos ζA cos θA cos ZA− sin ζA sin ZA

− sin ζA cos θA cos ΖA − cos ζA sin ΖA

− sin θA cos ZA

cos ζA cos θA sin ZA+ sin ζA cos ZA

− sin ζA cos θA sin ZA + cos ζA cos ZA

− sin θA sin ZA

− sin ζA sin θA

cos θA

cos ζA sin θA

The formula for reduction of precession in right ascension and declination are as follows : sin (α − ZA ) cos δ = sin (αo + ζA ) cos δo. cos (α− ZA ) cos δ = cos (αo+ ζA ) cos θA cos δo − sin θA sin δo sin δ = cos (αo + ζA ) sin θA cos δo + cos θA sin δo sin (αo + ζA ) cosδo = sin (α − ZA ) cos δ cos (αo + ζA ) cos δo = cos (α − ZA ) cos θA cos δ + sin θA sin δ sin δo = − cos ( α− ZA ) sin θA cos δ + cos θA sin δ

444

EXPLANATION Values of the angles ζA, ZA, θA and of the elements of the matrix P for reduction from the standard epoch J 2000.0 to epoch of year are as follows: Epoch J 2020.5

Rotation matrix P for reduction to epoch J 2020.5

ζA = + 475".410 = + 0°.132 058

+ 0.999 987 51

− 0.004 584 14 − 0.001 991 81

ZA = +470".141 = + 0°.130 595 P =

+ 0.004 584 14 + 0.999 989 49

θA = + 410".841 = + 0°.114 122

+ 0.001 991 81

− 0.000 004 54

− 0.000 004 59 + 0.999 998 02

The obliquity of the ecliptic of date (with respect to the mean equator of date) is given by:

ε = ε0 − 46".836 769T − 0".000 183 1 T ² + 0".002 003 4 T ³ - 0".000 000 576 T4 - 0".000 000 043 4 T5 where ε0 = 84381".406 The precessional motion of the ecliptic specified by the inclination (πA) and longitude of the node

( ΠA ) of the ecliptic of date with respect to the ecliptic and equinox of J 2000.0 are given by:

Sin πA sin ΠA = + 4".199 094 T + 0".193 987 T ² − 0".000 224 66 T ³ Sin πA cos ΠA = − 46".811 015 T + 0".051 028 T ² + 0".000 524 13 T ³ For epoch J 2020.5

ε = 23° 26' 11".80 π A = + 9".633 ΠA = 174° 49'.5

23°.436 612 0°.002 675 9 174°.825

= = =

Approximate formulae for the reduction of precession in co-ordinates and orbital elements referred to the mean equinox and equator or ecliptic of date (t) are as follows : Reduction to J 2000.0

αo δo λo βo Ωo io

ωo

= α − M − N sin αm tan δm = δ − N cos αm = λ − a + b cos (λ+c' ) tan βo = β − b sin (λ + c' ) = Ω − a + b sin (Ω + c' ) cot io. = i − b cos ( Ω + c' ) = ω − b sin ( Ω + c' ) cosec io

Reduction from J 2000.0

α δ λ β Ω i

ω

= = = = = = =

αo + M + N sin αm tan δm δo + N cos αm λo + a − b cos (λo + c) tanβ βo + b sin (λo + c) Ωo + a − b sin (Ωo + c) cot i io + b cos ( Ωo + c ) ωo + b sin ( Ωo + c ) cosec i

The precessional constants M, N etc. are given by : M N a b c c'

= = = = = =

1°.281 155 668 9 T + 0°.000 386 551 31 T ² + 0º.000 010 079 T ³ 0º. 556 719 973 1 T − 0º.000 119 303 72 T ² − 0º.000 011 617 4 T ³ 1º. 396 887 83 T + 0º .000 307 065 22 T ² 0º.013 055 270 3 T − 0º.000 009 303 50 T ² 3 5º.125 890 67 + 0º. 818 993 58 T + 0º.000 104 256 09 T ² - 0º.000 104 155 607 T 3 5º.125 890 67 − 0º.577 894 252 T − 0º.000 164 504 28 T ² - 0º.000 104 177 728 T

where T = ( t − 2000.0)/ 100 = ( JD

TT

− 245 1545.0 )/ 36525

445

EXPLANATION Formulae for the reduction from the mean equinox and equator or ecliptic of the middle of year (t1) to date (t) are as follows :

α λ Ω ω

= α1 + τ (m + n sin α1 tan δ1 ) δ = δ 1 + τ n cos α1 = λ1 + τ {p − π cos (λ1+ 6° ) tan β} β = β1 + τ π sin (λ1 + 6°) = Ω1 + τ {ρ − π sin (Ω1 + 6°) cot i } i = i1 + τ π cos (Ω1+ 6°) = ω1 + τ π sin (Ω1+ 6° ) cosec i where τ = t − t1 and π is the annual rate of rotation of the ecliptic. The precessional constants p, m, etc. are as follows : Epoch J 2020.5 Annual general precession p = + 0°.013 970 98 Annual precession in R.A. m = + 0°.012 813 91 Annual precession in Dec. n = + 0°.005 567 04 Annual rate of rotation π = + 0°.000 130 53 Longitude of axis Π = + 175°.0637 γ = 180°− Π = + 4°.9363 Where Π is the longitude of the instantaneous rotation axis of the ecliptic, measured from the mean equinox of date.

Nutation The changes in the amplitudes of the nutation components are also not directly taken from the observations; instead a new nutation theory is developed and fit to observations by allowing a small number of geophysical constants to be free parameters. These parameters are constants in a “transfer function” that modifies the amplitudes of the terms from a rigid- Earth nutation development. Since there are fewer solved-for geophysical constants than the number of terms with observed amplitudes, the fit cannot be perfect. For the IAU 2000A model, 7 geophysical parameters were determined based on the observed amplitudes of 21 nutation terms (prograde and retrograde amplitudes for each) together with the apparent change in the rate of precession in longitude. Note that the number of free parameters in the model are both quite small compared to the 1365 terms in the new, full nutation serirs. Nutation is conventionally expressed as two small angles, Δψ the nutation in longitude, and Δε, the nutation in obliquity. These angles are measured in the Ecliptic system of date, which is developed as a part of precession formulation. The angle Δψ is the small change in the position of the equinox along the ecliptic due to nutation, so effect of nutation on the ecliptic coordinates of a fixed point in the sky is simply to add Δψ to its ecliptic longitude. The angle Δε is the small change in the obliquity of the ecliptic due to nutation. The true obliquity of date is ε′ = ε + Δε. Nutation in obliquity reflects the orientation of the equator in space and does not affect the ecliptic coordinates of a fixed point on the sky.

Formulas for Nutation l l′

is the mean anomaly of the Moon. is the mean anomaly of the Sun (Earth). Ω is the longitude of the ascending node of the Moon’s mean orbit on the ecliptic, measured from the mean equinox of date. D is the mean elongation of the Moon from the Sun. F is the difference L− Ω, where L is the mean longitude of the Moon. ε = ε0 − 46".836 769 T − 0".000 183 1 T ² + 0".002 003 4 T ³ - 0".000 000 576 T4 - 0".000 000 043 4 T5 where ε0 = 84381".406

446

EXPLANATION The fundamental arguments are given by: The five arguments are the same fundamental luni - solar arguments used in previous nutation theories, but with updated expressions. l = 485 868". 249 036 + (1325 r + 715 923". 2178) T + 31". 8792 T² + 0". 051 635 T³ - 0".000 244 70 T4 l′ = 128 7104". 793 04 + (99 r + 129 2581". 048) T– 0". 5532 T² – 0". 000 136 T³ - 0".000 011 49 T4 r F= 335 779". 526 232 + (1342 + 295 262". 8478) T – 12". 7512 T² - 0". 001 037 T³ + 0".000 004 17 T4 r D= 107 2260". 703 69 + (1236 + 110 5601". 209) T – 6". 3706 T² + 0". 006 593 T³ - 0".000 031 69 T4 r Ω = 450 160". 398 036 – (5 + 482 890". 5431) T + 7". 722 T² + 0". 007 702 T³ - 0".000 059 39 T4 where l r = 360º = 129 6000" Reduction for nutation - rigorous formulae Nutation in longitude (Δψ ) and obliquity (Δε ) have been calculated using IAU 2000A series definitions (order of 1 μas) with the following adjustments which are required for use at the highest precession with the IAU 2006 precession, viz: -6 -6 Δψ = Δψ + (0.4697 x 10 - 2.7774 x 10 T) Δψ 2000A

2000A

Δε = Δε 2000A - 2.7774 x 10-6 T Δε 2000A where T is measured in Julian centuries from 245 1545.0 TT. Δψ and Δε together with the true obliquity of the ecliptic (ε ′ ) are tabulated daily at 0h TT, on page 18 to 32. Once the nutation series has been evaluated and the values of Δψ and Δε are available, the nutation matrix can be constructed. A mean place (rm) may be transformed to a true place (rt ) and vice versa, as follows: rt = N rm rm = N-1 rt where N = R1(-ε ′) R3 (-Δψ) R1 (+ε ) ε′ = ε + Δε R and R3 are the standard rotations about the x and z axes respectively. 1

(i) A rotation from the mean equator and equinox of t to the mean ecliptic and equinox of t. This is simply a rotation around the x - axis ( the direction toward the mean equinox of t) by the angle ε , the mean obliquity of t. (ii) A rotation around the new z-axis (the direction toward the ecliptic pole of t) by the angle - Δψ , the amount of nutation in longitude at t. After the rotation, the new x- axis is in the direction of true equinox of t. (iii) A rotation around the new x-axis ( the direction toward true equinox of t by the angle −ε ′, the true oliquity of t. After the rotation, the fundamental plane is the true equator of t, orthogonal to the computed position of the CIP at t. The nutation matrix can be written:

N = where

C2 - S2C3 S2S3

S1 = sin (ε) C1 = cos (ε)

S2C1 C3C2C1 - S1S3 - S3C2C1 - S1C3 S2 = sin (-Δψ) C2 = cos (-Δψ)

S2S1 C3C2S1 + C1S3 - S3C2S1 + C3C1 S3 = sin (−ε −Δε ) C3 = cos (−ε −Δε)

Approximate reduction for nutation for converting mean place to true place can be done with the help of the following formualae : Δα = (cos ε + sin ε sin α tan δ) Δψ – cos α tan δ Δε Δδ = sin ε cos α Δψ + sin α Δε Δλ = Δψ; Δβ = 0

447

EXPLANATION where Δψ and Δε are nutations in longitude and obliquity respectively. Mean rectangular coordinates (x, y, z) can be converted to true rectangular co-ordinates with the help of the following :

Δx = – (y cos ε + z sin ε) Δψ Δy = + x Δψcos ε – z Δε Δz = + x Δψsin ε + y Δε where both Δψ and Δε are in radians. The elements of the corresponding rotation matrix are:

− Δψ cos ε

1 N =

+ Δψ cos ε + Δψ sin ε

− Δψ sin ε − Δε

1 + Δε

1

Daily values of Δψ and Δε during 2020 are tabulated on pages 18 to 32. Approximate reduction for precession and nutation in right ascension and declination from the standard equinox and equator of J 2000.0 to the true equinox and equator of date during 2020 can be done using the following formulae and table : α = αo + f + g sin (G + αo ) tan δo δ = δo + g cos (G + αo ) where the units of the correction to αo and δo are in second of time and minutes of arc respectively. Date f g g G Date f g g G ′ 2020 s s ′ h m 2020 s s ′ h m Jan.

Feb.

Mar.

Apr.

May.

Jun.

- 8* 2 12 22 1*

+ 60.4 + 60.5 + 60.6 + 60.7 + 60.8

26.2 26.3 26.3 26.4 26.4

6.56 6.57 6.58 6.59 6.60

00 00 00 00 00

02 01 01 01 01

11 21 2 12 * 22

+ 60.9 + 61.0 + 61.0 + 61.1 + 61.1

26.5 26.5 26.5 26.5 26.6

6.61 6.62 6.63 6.63 6.64

00 00 00 00 00

01 01 01 01 00

1 11 21 * 1 11

+ 61.2 + 61.2 + 61.3 + 61.4 + 61.5

26.6 26.6 26.6 26.7 26.7

6.65 6.65 6.66 6.67 6.68

00 00 00 00 00

01 01 00 01 01

21 31 * 10 20 30

+ 61.6 + 61.7 + 61.8 + 61.9 + 62.0

26.7 26.8 26.8 26.9 26.9

6.69 6.70 6.71 6.72 6.73

00 00 00 00 00

01 01 01 01 01

* 40 - day date

Jun. Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

30 10 * 20 30 9

+ 62.0 + 62.1 + 62.2 + 62.3 + 62.4

26.9 27.0 27.0 27.1 27.1

6.73 6.75 6.76 6.77 6.78

00 00 00 00 00

01 01 00 00 00

19 * 29 8 18 28 *

+ 62.5 + 62.5 + 62.6 + 62.6 + 62.7

27.1 27.2 27.2 27.2 27.3

6.79 6.79 6.80 6.81 6.81

00 00 00 00 00

00 00 00 00 00

8 18 28 7* 17

+ 62.8 + 62.8 + 62.9 + 63.0 + 63.1

27.3 27.3 27.3 27.4 27.4

6.82 6.82 6.83 6.84 6.85

00 00 00 00 00

00 00 00 00 00

27 7 17 * † 27 37

+ 63.2 + 63.3 + 63.4 + 63.5 + 63.6

27.4 27.5 27.6 27.6 27.6

6.86 6.88 6.89 6.90 6.91

00 00 00 00 00

00 00 00 00 00

† 400 day date for osculation epoch

448

EXPLANATION Differential Precession and Nutation can be applied to obtain the differences in the mean place of an object relative to a comparison star for a standard epoch (J 2000.0) using the following formulae: correction to R.A. : e tan δ Δα – f sec² δ Δδ correction to declination : f Δα where Δα and Δδ are the observed differences in right ascension and declination of the object relative to the comparison star and e = – cos α (n t + sin ε Δψ) – sin α Δε f = + sin α (n t + sin ε Δψ) – cos α Δε ε = 23°.44, sin ε = 0.398 n = 0.000 0972 radian for epoch J 2020.5 t is the time in years from the standard epoch to the time of observation. Δψ, Δε are nutations in longitude and obliquity at the time of observation expressed in radians, (1" = 0.000 004 8481 rad).

Aberration Aberration is the displacement of the position of a celestial object due to finite speed of light. The actual velocity of light in space c is the vectorial sum of its velocity relative to the observer cr and the velocity V of the observer. Although the special theory of relativity has no provision of breaking up aberration of light into components, total effects of aberration in astronomy are broken into stellar, annual, elliptic, secular and planetary aberration for convenience of computation. In case of stars, all that can be determined is the displacement in their positions caused by the motion of the observer alone. It is calculated on the basis of the actual instantaneous motion of the Earth round the barycentre of the solar system. Earlier, the practice was to resolve the stellar aberration into two components; one contributed by the circular motion of the Earth moving with a constant mean velocity round the Sun, and the other, a nearly constant displacement perpendicular to the major axis of the orbit arising due to ellipticity of the orbit of the Earth. The latter, known as the E-terms of aberration was included in the mean position of the stars as given in star catalogues and was omitted in the computation of day numbers. As a result, the mean places of stars differed from the catalogue mean places. This procedure was adopted to minimise the computation work for the user of star catalogues. However, this practice has caused much confusion lately because the accurate total velocity of the Earth referred to the barycentre of the solar system could not be used in computing stellar aberration. In accordance with a decision of the IAU in 1976, this occasion has been used to simplify this procedure by removing the E terms of aberration from the mean places and to include them in the reduction from mean to apparent place so that the apparent places remain unchanged. Thus, the mean places of FK5 are free from E terms. In other words, they will be the positions of the stars at epoch J 2000.0 as viewed from the barycentre of the solar system, in the co-ordinate system defined by the Earth’s mean equator and equinox of J 2000.0. The conversion of 1950.0 star catalogue positions (α,δ ) to actual mean places (α+Δα, δ+Δδ ) can be accomplished by : h Δα = 0s. 0227 sin (α + 11 . 25) sec δ h Δδ = 0".341 cos (α + 11 . 25) sin δ + 0".029 cos δ For solar system objects, the displacement of the light source during the time (Δt) taken by light to travel from it to the Earth combined with the effect of relative motion of the Earth and the light is known as planetary aberration. Its computation requires a knowledge of the distance and motion of the light source and can be accomplished as follows. First, the barycentric position of the body at time t- Δt is combined with the barycentric position of the Earth at time t and then the correction for annual aberration is applied. Planetary aberration may also be

449

EXPLANATION computed by interpolating the geometric (geocentric) ephemeris of the body to the time t - Δt. The light time Δt is given by: Δ t (in days) = 0.005 7755 x distance in a.u. Annual aberration for reduction from a geometric place (α0, δ ) to an apparent geocentric place (α, δ) is ° given by :

α = α0 + (− sin α0 + cos α0) / (c cos δ0 ) δ = δ0+ ( − cos α0 sin δ0 − sin α0 sin δ0 + cos δ0 )/ c, where c = 173.14 a.u./day and , , are the velocity components of the Earth (pages 256 to 270 ). The reduction of observations of the radial velocity to a common origin at the barycentre is given by adding the component of the Earth’s velocity in the direction (α0, δ0) of the object : cos α0 cos δ0 +

sin α0 cos δ0 +

sin δ0

Differential annual aberration corrections to be added to the observed differences of right ascension and declination (in the sense moving object minus star) to give true differences are: (R.A.) a Δα + b Δδ (in units of 0s. 001) ; (declination) c Δα + d Δδ (in units of 0".01) Here Δα is to be taken in units of 1m and Δδ in units of 1'. The coefficients a, b, c and d are defined by: a = − 5.701 cos (H+α) sec δ b = − 0.380 sin (H +α) sec δ tan δ c = + 8.552 sin (H+α) sin δ d = − 0.570 cos (H+α) cos δ Hh = 23.4 − (day of year/15.2) (The day of year is tabulated on pages 4 to 12 ) Annual parallax correction can be calculated approximately for reduction from the catalogue place ( α0,δ0) to the geocentric place (α,δ) using the following formulae; α = α0 + (π / 15 cos δ0) (X sin α0−Υ cos α0) and δ = δ0 + π(X cos α0 sin δ0 + Y sin α0 sin δ0− Z cosδ0) where π is the annual parallax and X, Y, Z, are the coordinates of the Earth as given on pages 256 to 270. Deflection of light in the gravitational field of the Sun may significantly affect the apparent direction of a star or of a body in the solar system. The elongation (E) from the centre of the Sun is increased by an amount that, for a star, depends on the elongation in the following manner:

E

ΔE

ΔE = 0".004 07/ tan (E/2) 0°.25 0°.5 1° 1".866

0".933

0".466

2° 0".233

5° 0".093

10° 0".047

20° 0".023

50° 0".009

90° 0".004

The body disappears behind the Sun when E is less than the limmiting grazing value of about 8°.25. The effects in right ascension and declination may be calculated approximately from; cos E = sin δ sin δ0 + cos δ cos δ0 cos (α − α0) Δα = 0s. 000 271 cosδ0 sin (α−α0)/ (1−cos E) cos δ Δδ = 0".004 07 [(sin δ cos δ0 cos (α−α0) − cos δ sin δ0 ]/ (1− cos E) where α, δ refer to the star, and α0, δ0 to the Sun.

450

EXPLANATION TABULAR DATA PART-I -TIME SCALES AND EPHEMERIDES Dates of year beginning in 2020 of various Indian and important foreign chronological eras are listed on page 3 followed by Gregorian calendar for the current year (pages 4 to 12 ). The calendar contains, besides the usual information, a count of Julian Day (JD) number for each date. The system of Julian day numbers maintains a continuous count of astronomical days, beginning with JD = 0 on 1 January 4713 B.C., Julian proleptic calendar. Julian Day numbers for other years can be found from the table on page 359. Various time scales used in this publication, their inter -relationships (as given on page 2 ) and the basis for computation of sidereal time as tabulated on pages 13 to 16; have been discussed above under the section on time scales. The concept of equation of time defined as the difference between local apparent solar time and local mean solar time (in the sense apparent minus mean ) is no longer used in astronomy and therefore, it is no more tabulated in this publication. It can, however, be obtained to a precision of about 1 second using the following relation : h h Equation of time at 12 U.T. = 12 − tabulated value of TT of Sun’s ephemeris transit (pages 19 to 33 ). In this publication, the ephemeridies of the Sun and planets were reported earlier based on computation jointly made by USNO and JPL by simultaneous numerical integration designated as DE 200/ LE 200. A more recent JPL ephemeris, DE 405/ LE 405 has now come into widespread use, provide barycentric equatorial rectangular coordinates for the period 1600 to 2201. The reference frame for basic ephemerides is the ICRF; the alignment onto this frame has an estimated accuracy of 1 - 2 arcseconds. The JPL DE 405/ LE 405 ephemerides have been developed in a barycentric reference system using a barycentric coordinate time scale Teph.. The present edition use the DE 405/ LE 405 ephemeridies data on the positions of the Sun, Moon and planets. The value of some astronomical constants based on previously used DE200/ LE200 ephemeridies and currently used DE 405/ LE 405 ephemerides are given below. Constant Light-time for unit distance,τA Geocentric gravitational constant, GE Heliocentric gravitational constant, GS Ratio of mass of Sun to that of Earth, (GS)/ (GE) Ratio of mass of Moon to that of Earth, μ Obliquity of the ecliptic at J2000.0, ε Unit distance, A Ratio of mass of Sun to that of Earth + Moon Ratio of mass of Sun to mass of each planet : Jupiter Saturn Uranus Pluto Pallas Vesta

DE 405 Value 499.004 783 84 s

DE 200/ LE 200 Value 499.004 7837………..s

3.986 004 418 x 1014m3s-2

3.986 004 48……x 1014 m3s-2

20

1.327 124 42 099 x 10 m3s-2 1.327 124 40……x 1020 m3s-2 332 946.0 487

332 946.038……….

0.012 300 0371 23° 26′ 21″.406 1.495 978 707 x 1011 m

0.012 300 034 23° 26′ 21″.4119…. 1.495 978 7066 x 1011 m

328 900.5596

328 900.55

1047.348 644 3497.9018 229 02.98 1.365 66 x 10 8 9.709 x 10 9 7.407 x 10 9

1047.350 3498.0 229 60 1.3 x 10 8 9.247 x 10 9 7.253 x 10 9

451

EXPLANATION The Sun Mean elements of the orbit of the Sun can be calculated with the help of the following expressions for use during 2020 only : Geometric mean longitude : L = 279°.141 941 + 0.985 647 36 d Mean longitude of perigee : Γ = 283°.281 180 + 0.000 047 08 d Mean anomaly : g = 355°.860 761 + 0.985 600 28 d Eccentricity : e = 0°.016 701 22 − 0. 000 000 0012 d Obliquity of the ecliptic w.r.t. mean equator of date : ε = 23°.436 678 − 0.000 000 36 d where d is the interval in days from 2018 January 0 at 0h TT and is given by d = JD − 245 7387.5 = day of the year ( pages 4 to 12) + fraction of day from 0h TT. The above angular elements are referred to the mean equinox and ecliptic of date. The position of ecliptic of date with respect to the ecliptic of the standard epoch J 2000.0 is given by the formulae given under Precession. The length of the principal years at 2020.0 as derived from the Sun’s mean motion are given on page 2. Geometric longitude of the Sun with respect to the mean equinox of date is tabulated on even numbered pages 18 to 32. Apparent longitude and latitude are with respect to the true equinox and ecliptic of date respectively. The two longitudes are related as follows : Apparent longitude = Geometric longitude + nutation in longitude − 20".4955/ R. Aberration has been computed by dividing 20".4955 by the true distance to the Sun. Precession in longitude is the total precessional displacement of a point along the ecliptic since the epoch J 2020.5. Revised value of the annual general precession p = 0°. 013 970 98 (for J 2020.5) has been used to compute this quantity. Components of nutation are the results of summation of the revised series of nutation. The sum of the terms with period shorter than 35 days is separately tabulated under Besselian Day numbers (pages 244 to 251 ). Apparent Right Ascension and true distance (radius vector), declination (tabulated on odd numbered pages 19 to 33) of the Sun have been computed from the original barycentric rectangular co-ordinates. Although the apparent right ascension and declination have been corrected for light time, the radius vector or the true geocentric distance in astronomical units is the geometric distance at the tabular time. The Semidiameter is based on a value of 16′ 01″.18 at unit distance being inclusive of an allowance for irradiation of 1″.55. The tabular value is obtained by dividing 16′ 01″.18 by the radius vector. Ephemeris Transit is the TT of the transit of the Sun over the ephemeris meridian which according to its definition, is 1.002 7379 ΔT east of the Greenwich meridian. Here ΔT is the difference TT − UT. This transit time. This transit time can be interpolated to other meridians with an interpolating factor p, as follows: p = − λ/ 360 + 1.002 7379

× ΔT/ 86400

where λ is the longitude (east positive). The interpolated TT can be converted into UT by subtracting

ΔT from TT.

Equatorial rectangular co-ordinates (geocentric) of the Sun, referred to the ICRS axes, are given in a.u. on pages 34 to 41. The direction of these axes have been defined by the IAU and realized in practice by the coordinates of several hundred extra galactic radio sources.

452

EXPLANATION Horizontal parallax ( page 17 ) of the Sun is the angle subtended at the Sun by the equatorial radius of the Earth. The new value of the Solar parallax Π = 8".794 148 has been used to compute the horizontal parallax. ° Mean longitude and mean anomaly (page 17 ) of the Sun have been computed using revised expressions for the mean motion of the Earth around the Sun as given on page 447. h

Heliographic co-ordinates given on pages 42 to 45 for 0 UT include the position angle P of the northern extremity of the axis of rotation measured eastward from the north point of the disc and the heliographic latitude B ° and longitude L of the central point of the disc. ° The observed angular distance ρ1 from the centre of the disc of the Sun of a feature on the Sun’s surface, as seen from the Earth, can be converted into its heliocentric angular distance ρ from the centreof the Sun’s disc as follows : sin ( ρ + ρ1 ) = ρ1 /S, where S is the semi diameter of the Sun. The observed position (ρ, θ) of a feature (Sunspot, etc.) with respect to the centre of Sun’s disc can be converted into heliographic co-ordinates (L, B) as follows : sin B = sin B cos ρ + cos B sin ρ cos ( P − θ ) ° ° cos B sin (L− L ) = sin ρ sin ( P − θ ) ° cos B cos (L− L ) = cos ρ cos B – sin B sin ρ cos ( P − θ ) ° ° ° The physical ephemeris of the Sun has been calculated from the elements determined by R. C. Carrington (observation of the spots on the Sun, 1863). The Synodic rotation numbers are given below according to R. C. Carrington’s Greenwich photoheliographic series which commenced on 9 November, 1853 with number 1. The standard solar meridian from which heliographic longitudes on the surface of the Sun are measured (positive towards the west) is that which passes through the ascending node of the solar equator on the ecliptic on 1854 January 1, Greenwich mean noon. The beginning of each synodic rotation is the instant at which the standard solar meridian passes through the central point of the apparent disc of the Sun, i.e., when the heliographic longitude L of this central point is zero. ° SYNODIC ROTATION NUMBERS, 2020 Date of Number Commencement 2225 2019 Dec. 10.05 2226 2020 Jan. 6.38 2227 Feb. 2.72 2228 Mar. 1.06 2229 Mar. 28.37

Number 2230 2231 2232 2233 2234

Date of Commencement Apr. 24.64 May. 21.87 June. 18.07 2020 July. 15.27 Aug. 11.49

Number 2235 2236 2237 2238 2239 2240

Date of Commencement Sept. 7.74 Oct. 5.01 Nov. 1.30 Nov. 28.61 2020 Dec. 25.93 2021 Jan. 22.27

At the date of commencement of each synodic rotation period, the value of L is zero ; that is, the prime ° meridian passes through the central point of the disk. The mean rotational elements of the Sun during 2020 are as follows : Longitude of the ascending node of the solar equator on the ecliptic of date is 76°.01, and on the mean equator of date 16°.16. Inclination of the solar equator on the ecliptic of date is 7°.25, and on the mean equator of date 26°.10. The mean position of the pole on the solar equator is at right ascension 286°.16 and declination 63°.90. Sidereal period of rotation of the prime meridian is 14°.18 44 per day and its mean synodic period of rotation is 27.2753 days.

453

EXPLANATION The Moon The ephemerides of the Moon reported in this publication are based on the fundamental arguments developed by Simon et. al (1994). The angular elements are referred to the mean equinox and ecliptic of date. Mean elements of the mean equator and of the orbit of the Moon (page 47) can be computed during 2020 with the help of the following expressions :The inclination i of the mean equator of the Moon to the true equator of the Earth is given by : i = 23°.705 7− 0.001 409 d − 0.000 000 027 d The arc of the mean equator of the Moon from its ascending node on the true equator of the Earth to its ascending node on the ecliptic of date : 2

Δ = 281°.774 6− 0.052 264 d − 0.000 001 502 d2 The arc of the true equator of the Earth from the true equinox of date to the ascending node of the mean equator of the Moon :

Ω′ = - 3°.799 1 − 0.000 734 d + 0.000 001 643 d2 The inclination ( I ) of the mean equator of the Moon to the ecliptic = 1° 32′ 33″.6. The ascending node of the mean lunar equator on the ecliptic is at the descending node of the mean lunar orbit on the ecliptic that is at longitude Ω + 180°. The above expressions give the mean elements with respect to the true equator of the Earth to a precision of about 0°.001. The following expressions for the mean elements of the orbit of the Moon Γ′, Ω mean longitude of the Moon L′ and elongation D are referred to the mean equinox and ecliptic of date. Mean longitude of the Moon, measured along the ecliptic to the mean ascending node and then along the mean orbit : L′ = 332°.128 231 + 13.176 396 46 d Mean longitude of the Moon’s perigee measured in the same way as L′ :

Γ′ = 176°.988 452 + 0.111 403 41 d Mean longitude of the mean ascending node of the lunar orbit on the ecliptic : Ω = 98°.296 816 − 0.052 953 74 d Mean elongation of the Moon from the Sun : D = L′ − L = 52°.986 290 + 12.190 749 10 d Mean inclination of the lunar orbit to the ecliptic = 5°.156 689 8 The above expressions are valid for use in 2020 only. h In all the above expressions, the time argument d is the interval in days since 0 TT January 0, 2020 and is given by d = JD − 245 8118.5 The length of the principal mean months at 2020.0 as derived from the above mean orbital elements of the Moon are given on page 2. The apparent geocentric longitude and latitude of the Moon (pages 48 to 63) are referred to the true equinox and ecliptic of date. The true distance between the centres of the Earth and the Moon is given in a.u. Semi-diameter is derived from the horizontal parallax by S = Sin−1 (k sinπ) where k = 0.272 5076. The semi-diameter at mean distance is taken to be 15′ 32″.58 without making any correction for irradiation.

454

EXPLANATION The right ascension and declination given on pages 64 to 79 for 0 hour & 12 hour of TT are referred to the true equator and equinox of date. Horizontal parallax is tabulated at twelve hourly intervals on pages 64 to 79. It is derived from sin−1 (1/r) where r is the true distance in units of the Earth’s equatorial radius. The tabulated R.A. and declination have been corrected for light time while the horizontal parallax is the geometric value for the tabular time. The times of New Moon, First Quarter, Full Moon and Last Quarter are the moments at which the excess of the Moon’s apparent longitude over that of the Sun is 0°, 90°, 180° and 270° respectively. Moon at Apogee and Perigee are the times when the Moon is at the greatest and least distance from the Earth. The timings are given in U.T. The corresponding timings in U.T. of the phases of the Moon are also given in the calendar portion on pages 4 to 12. For more precise values of the moments of New Moon and Full Moon, a reference may be made to Part VI - Indian Calendar where the times are given in I.S.T. Moon’s Age, given for 0h TT, is the number of days elapsed since the preceding New Moon (conjunction). The times of Moon’s upper and lower transit are given in TT for the ephemeris meridian. Interpolation to any other meridian by means of differences given and with the help of the ephemeris longitude will yield the local mean time of transit. The apparent geocentric declination given for the time of ephemeris transit can also be similarly interpolated. Physical ephemeris of the Moon (pages 88 to 95) has been computed using the formulae and constants of D. Eckhardt (The Moon and the Planets, 25 3, 1981; High precision Earth Rotation and Earth-Moon Dynamics, ed. O. Calame, pages 193-198, 1982) with inclination I as given above ( IAU value). In case of the Moon, selenographic longitudes are measured for a point on the surface of the Moon from the lunar meridian that passes through the mean central point of the visible disc positive towards the west towards Mare Crisium. Selenographic latitudes are reckoned positive towards the north limb. The mean central point of the disc is defined as the point on the lunar surface intersected by the radius of the Moon directed towards the Earth, when the Moon is simultaneously at the ascending node and coincident with the mean longitude. The Moon presents roughly the same hemisphere to the Earth. However, due to non uniformity of the revolution of the Moon around the Earth (optical libration) and an oscillation of the actual rotational motion of the Moon about its mean rotation (physical libration), about 59% of the Moon’s surface can be seen from the Earth. The contribution to the Earth’s selenographic longitude and latitude due to physical libration has been tabulated separately. These are geocentric values. The tabular selenographic longitude and latitude of the Earth are the selenographic co-ordinates of the apparent central point of the Moon from which point the Earth is in selenographic zenith. These co-ordinates are the total librations (sums of optical and physical librations) in longitude and latitude respectively. When the libration in longitude, i.e. the selenographic longitude of the Earth, is positive, the mean central point of the disc is displaced eastward exposing to view a region on the west limb. When the libration in latitude, i.e. the selenographic latitude of the Earth, is positive, a region on the north limb is exposed to view. The selenographic co-ordinates of the point on the lunar surface where the Sun is in the Zenith are the selenographic co-ordinates of the Sun. The selenographic co-longitude of the Sun tabulated in the ephemeris is obtained by subtracting the selenographic longitude of the Sun from 90° or 450° ; it is approximately 270°, 0°, 90° and 180° at new-moon, first quarter, full-moon and last quarter respectively. The position angle of the axis is the angle that the lunar meridian through the apparent central point of the disc towards the north lunar pole forms with the declination circle through the central point, reckoned counter clockwise from the north point of the disc.

455

EXPLANATION The position angle of the bright limb is the position angle of the mid point of the illuminated limb, reckoned eastward from the north point of the disc. The position angle of the two cusps may be obtained by adding ± 90° to that of the bright limb. The expression for calculating the selenographic altitude (a) of the Sun (above the lunar horizon ) at a point at selenographic longitude l and latitude b is as follows :

the time.

sin a = sin b sin b °

+ cos b° cos b sin (c° + l), where (c°, b°) are the Sun’s co-longitude and latitude at

The following expressions can be used to compute the differential corrections to be applied to the tabular geocentric librations to form the topocentric librations :

Δl = – π′ sin (Q – C) sec b Δb = + π′ cos (Q – C) ΔC = + sin (b + Δb) Δl – π′ sin Q tan δ, where Q is the geocentric parallactic angle of the Moon and π′ is the topocentric horizontal parallax. The latter is obtained from the geocentric horizontal parallax (π) (pages 64 to 79) by using :

π′ = π (sin z + 0.0084 sin 2 z) where z is the geocentric zenith distance of the Moon. The values of z and Q may be calculated from the geocentric R.A. (α ) and declination (δ ) of the Moon by using : sin z sin Q = cos φ sin h sin z cos Q = cos δ sin φ − sin δ cos φ cos h cos z = sin δ sin φ + cos δ cos φ cos h where φ is the geocentric latitude of the observer and h is the local hour angle of the Moon given by : h = local apparent sidereal time − α Second differences in the tabular values of the geocentric librations must be taken into account in interpolation for the time of observation.

Major Planets The heliocentric and geocentric positions of the major planets given on pages 96 to 197 have been derived directly from the numerical integration mentioned on page 446. The heliocentric longitude and latitude are referred to the mean equinox and ecliptic of date. The tabular argument of heliocentric ephemeris is barycentric dynamical time (TDB). The apparent geocentric longitude and latitude are referred to the true equinox and ecliptic of date and are planetary aberration. The apparent right ascension and declination are also corrected for planetary aberration and referred to the true equinox and equator of date. The tabular argument for both the terrestrial dynamical time (TDT). The TDT of transit over the ephemeris meridian has been furnished, which may be interpolated to any other meridian to obtain the LMT of transit. As regards Pluto, in addition to the usual data, figures have been furnished for reduction of the apparent right ascension and apparent declination to the corresponding astrometric places referred to the mean equinox and equator of J 2000.0. The astrometric ephemeris is obtained by first adding the usual planetary aberration to the

456

EXPLANATION planet’s true geocentric places referred to the standard equinox J 2000.0 and then subtracting the stellar aberration pertinent to the position occupied by the planet. The astrometric place is thus affected by the amount of the terms in the aberration dependent on the longitude of the Earth’s perihelion as are the catalogue mean places of stars in the neighbourhood. The astrometric ephemeris is, therefore, rigorously comparable with photographic observations that are referred to catalogue mean places J 2000.0 of neighbouring stars, it being only necessary to correct the observations for geocentric parallax in case of the planets and proper motion in case of the stars. The tabular true distance from the Earth is the actual geocentric distance at the tabulated time and not at the instant when the light left the planet. The horizontal parallax of planets is 8".794 143 divided by the geocentric distance. As regards the semidiameter, the tabulated value is the value at unit distance divided by the geocentric distance. The semi-diameters at unit distance are as follows : Mercury 3".36, Venus 8".34, Mars 4".68, Jupiter 98".57 (Equatorial) and 92".12 (Polar), Saturn 83".13 (Equatorial) and 74".96 (Polar), Uranus 35".24, Neptune 34".14 and Pluto 2".07. The heliocentric osculating elements of the orbits of the major planets, including Pluto, are given at intervals of 40 days on pages 200 to 201. The osculating elements are the elements of the instantaneous ecliptic orbit of the planet around the Sun determined by its actual position and velocity components for the instant, and as such the elements are affected by the attractions of other planets. The true place of a planet deduced from these elements is thus inclusive of the planetary perturbations, which need not, therefore, be considered separately in such a deduction. The osculating elements for the Earth refer to the Earth/Moon barycentre. The correction in ecliptic rectangular co-ordinates in conversion from the Earth/Moon barycentre to the Earth’s centre is given by : Earth’s Centre = ( Earth / Moon barycentre ) − ( 0.000 0312 cos L, 0.000 2865 sin L, 0.0000124 sinL, -0.00000718 sinL,0.00000657 cosL, 0.00000285 cosL) where L = 218° + 481 268° T, with T measured in Julian centuries from JD 245 1545.0 to 5 decimals; the co-ordinates are in a.u. with reference to mean equinox and ecliptic of date.

PART II - STARS The mean places of 482 stars, apparent places of 68 stars at 10-day intervals. daily apparent place of Polaris and tables for finding latitude of place from altitude of polaris and azimuth of polaris are given in this section. The ecliptic co-ordinates (mean longitude and latitude) of 451 stars have also been given. To facilitate reduction from mean to apparent place of a star, Besselian Day Numbers as well as the barycentric position and velocity components of the Earth alongwith rotation matrix elements for precession and nutation have been tabulated.

Mean Places of Stars (pages 215 to 226) Beginning with the issue for 1988, calculation of the mean and apparent places are based directly on the basic-FK5 compiled by the A.R.I., Heidelberg. The table for mean places of stars includes all stars of magnitude upto 3.9 as well as the component stars of the different lunar asterisms of the Hindus, Chinese and Arabian even when those are fainter than magnitude 3.9. In case double or multiple stars, m denotes the mean position of the centre of gravity (c.g.) of the system; p the preceding component having less right ascension, f the following component and A the brighter component of the system. The magnitude of the binary stars is the integrated value for the two components.

457

EXPLANATION The mean longitude and latitude of 451 important stars have been computed using the conversion from equatorial mean positions to ecliptic co-ordinates. Similarly, annual variations in longitude and latitude, etc., are the differentials of the conversion formulae. All quantities relate to the middle of the current Julian year.

Apparent Places of Stars ( pages 227 to 243) The apparent places of 68 selected stars are reported under this section. These positions are completely based on the FK5 beginning with the issue for 1988. Smaller aberration has been computed from the total velocity of the Earth referred to the barycentre of the solar system. The E-terms of aberration are no longer included in the mean places in the FK5, but rather in the reduction from mean to apparent places. Reductions to apparent places have been computed rigorously and directly without the intermediary of the mean place for the begining of the year. The rigorous computation also includes effects of relativistic light deflection. Because of this, the apparent places of a star when approaching very closely the Sun cannot be interpolated by the user, but these cases are of no practical interest in normal applications. Apparent places of 68 bright stars with annual variation and annual proper motion at 10-day interval have been given on pages 227 to 243. The number, name, are taken generally from the FK5, magnitude and spectrum are taken from SIMBAD data base. Corrections for parallax have been applied where appreciable. The right ascension and declination are referred to the true equator and equinox of date but with the omission of the short period terms of nutation. After interpolating the given apparent places to date and longitude of the station, the following corrections for the effect of short period terms of nutation are to be applied :

Δα Δδ

= =

a dψ + b dε a′ dψ + b′ dε

seconds of time seconds of arc

where dψ and dε are short period terms of nutation as tabulated on pages 244 to 251. The values of a, b, a′and b′ are given for each star under the apparent place. The Apparent places of Polaris for each day of the year ( pages 272 to 274 ) have been computed rigorously.

Besselian Day Numbers (pages 244 to 251) All stellar data tabulations are now for the standard epoch at the middle of the current Julian year rather than the beginning of the Besselian year and accordingly the Besselian Day Numbers and second order day numbers are referred to the mean equator and equinox of the epoch, J 2020.5. Although for full precision the reduction to the apparent place has to be computed rigorously as described below, Besselian Day Numbers can still be used for less precision. In the tabulated data, τ is the fraction of the Julian year since the standard epoch J 2020.5 A, B and E are Besselian Day Numbers designed to incorporate corrections to the position of a star on account of precession and nutation. In this case, the correction due to precession is measured from the middle of the year, and this is secured by incorporating in A the value of the precision corresponding to τ.The terms of short-period in nutation are included in A and B, which are also shown separately on pages 244 to 251. The Besselian Day Numbers C and D, designed to include the effect of aberration, are now computed based on the total velocity of the Earth. Second order day numbers, needed only for high declination stars for high accuracy, have been tabulated on pages 252 to 255.

458

EXPLANATION The barycentric position and velocity components of the Earth and rotation matrix elements for rigorous reduction of precesision and nutation have been tabulated on pages 256 to 270. Use of these data with examples is discussed below :-

Apparent place reduction with full precision (rigorous method) Conversion of the barycentric co-ordinates of a star for the standard equinox and equator of J 2000.0 (TDB) to its apparent geocentric co-ordinates referred to the true equinox and equator of date ( TT ) can be done rigorously as follows: The geocentric vector P of the star at the required epoch (ignoring the distinction between TDB and TT for the stellar case) is given be by: P = q + Tm − πEB ……….(1) Here q is the barycentric direction of the star at epoch J 2000.0 referred to the standard equinox and equator of J2000.0 and is given by :q = (cos α0 cos δ 0 , sin α0 cos δ0 , sin δ0 ) where

α0 and δ0 are the right ascension and declination for the equator, equinox and epoch of J 2000.0. The space motion vector m = (mx, my, mz ) of the star in equation (1), expressed in radians/century, is given

by : mx = my = mz =

− μα cos δ 0 sin α0 − μδ sin δ 0 cos α0 + νπ cos δ0 cos α0 μα cosδ 0 cosα0 − μδ sin δ 0 sin α0 + νπ cos δ0 sin α0 μδ cos δ 0 + νπ sin δ 0

where these expressions take into account the radial velocity (v ) in au/century (1 km/s = 21.094 952 75 a.u./ century), measured positively away from the Earth as well as proper motion( μα, μδ ) in right ascension and declination in radian/century and π is the parallax in radians. T is the interval in Julian centuries from J2000.0, given by T = ( JD − 245 1545.0 )/ 36525; EB and in a.u. per day are Earth’s barycentric position and velocity vectors at co-ordinate time t = TDB referred to the equator and equinox of J 2000.0 (pages 256 to 270). The heliocentric position of the Earth E is given by E = EB − SB

…………………(2)

Where SB is the barycentric position of the Sun at time t. This can be obtained from the heliocentric position of the barycentre tabulated on page 202 by reversing the sign of the respective x, y, and z. The geocentric direction p of the star and the unit vector e can be computed from p = P/ |P| and e = E/ |E| The geocentric direction p1 of the star after applying the correction for light deflection in the natural frame is obtained as follows: p1 = p + ( 2 μ/c2 E ) (e − (p. e) p)/ (1+ p. e)…………..(3)

459

EXPLANATION Where μ/c2 = 9.87 X 10− 9 a.u and E = | E |, the vector p1 is a unit vector to the order of μ/c2 and dot (. ) indicates scalar product. The proper direction p2 in the geocentric inertial frame, that is moving with the instantaneous velocity V of the Earth relative to the natural frame, is given by: p2 = ( β− p1 + (1 + p1.V )/ (1+ β− ))V ) / (1+ p1.V )……………(4) 1

1

Where V = and β = ( 1− V )− ; the velocity V expressed in units of velocity of light and is /c = 0.0057755 equal to the Earth’s velocity in the barycentric frame to the order of V2. 2

1/2

The apparent geocentric direction p3 is obtained by applying precession and nutation to the proper direction p2 by multiplying it row by column with the rotation matrix M=NPB ( given on pages 257 to 271 ) as follows: p3 = M p2 ………………….. (5) The above direction p3 is in rectangular co- ordinates (ξ , η, ζ ). It can be converted into spherical co- ordinates (α, δ) using :

α = tan − l (η/ξ) and δ = tan − l (ζ/β) ………………(6) Where β =(ξ +η ) where the quadrant of α can be determined by the signs of 2

2 1/2

ξ and η.

Correction for polar motion : The apparent geocentric direction p3, given by equation (5) above, is for the true equator and equinox with the z axis pointing towards the celestial ephemeris pole. A further correction for polar motion may be applied to p3 to obtain p4 i.e. the direction relative to the conventional terrestrial reference system in which the z-axis is in the direction of the adopted mean position of the pole, as follows : p4= R2 (− x ) R1 (− y ) R3 ( GAST ) p3 where GAST is the Greenwich apparent sidereal time at the corresponding instant of UT and

R1 (θ)

=

R3 (θ)

=

1 0 0

0 cos θ − sin θ

cos θ − sin θ 0

sin θ cos θ 0

0 sin θ cos θ

R2 (θ) =

cos θ 0 sin θ

0 1 0

− sin θ 0 cos θ

0 0 1

are the standard matrices that produce rotations through an angle θ about the x, y and z - axes respectively. Polar motion is described by x and y, the co- ordinates of the celestial ephemeris pole with respect to the adopted origin; x and y are measured in seconds of arc from the origin along the meridians at longitudes 0° and 270°. Current values for the reduction of observations are published by the International Polar Motion Service and the Bureau International de l’ Heure.

460

EXPLANATION Example of stellar reduction : h

Calculation of apparent position of a fictitious star on 2020, January 1 at 0 TT from the catalogue data, mean right ascension (α0 ) , declination (δ0 ), centennial proper motion (μα , μδ ) in right ascension and declination, parallax (π) and radial velocity (ν) of a fictitious star for the standard equinox and equator of J 2000.0 (TDB) as given below:

α0 = 14

h

m

39

μα = − 49.486 s/ century = − 0.003 598 7 rad/century

s

36 .087

μδ = + 69 ″.60 s/ century

δ0 = − 60° 50′ 07″.14

= + 0.000 337 4 rad/ century

π = 0″.752

ν = − 22.2 km/ s ν π = − 0.001 707 4 rad/ century

= 3.646 X 10-6 rad

The barycentric position vector of the Sun and the position and velocity vectors of the Earth referred to h

J2000.0 on 2020 January 1, 0 TDB (pages 202, 256 to 270) are : Vector

EB SB

Julian date

245 8849.5 245 8849.5 245 8849.5

Barycentric Rectangular Components x − 0.170 144 389 − 0.017 247 546 + 0.003 798 625

y + 0.895 983 831 − 0.002 737 580 + 0.006 816 842

z + 0.388 436 660 − 0.001 186 171 + 0.002 980 565

In order to calculate the geocentric vector P of the star at J 2000.0, using equation (1), the vectors q and m may be computed using positional data of the star. q = (− 0.373 854 098, − 0.312 594 565, m = ( + 0.000 712 684, + 0.001 690 102, T = ( 245 8849.5 − 245 1545.0)/ 36525 =

− 0.873 222 624 ) + 0.001 655 340 ) + 0.199 986 311

The geocentric vector P may be computed from equation (1) by substituting the vectors q, m and EB and time T. P

= (− 0.373 996 005,

− 0.312 256 567, − 0.872 891 579 ) and | P | = 0.999 658 384

The heliocentric position vector E of earth may be obtained using equation (2) E

= (− 0.166 345 764,

+ 0.889 166 989,

+ 0.385 456 095 ) and | E | = 0.983 293 063

The unit vectors p and e in the direction of P and E respectively are as follows : p

= (− 0.374 123 812,

e

= (− 0.169 172 112,

− 0.312 363 276, + 0.904 274 648,

− 0.873 189 875) + 0.392 005 303 )

The scalar product p. e = − 0.561 465 937 and 2μ/c2 = 1.974 X 10−8 a. u. The second term in the equation (3) represents the correction for the light deflection in the natural frame, and is given by the following vector : ( 2μ/c2 E ) ( e − ( p. e ) p )/ ( 1+ p. e ) = ( − 0.000 000 017, + 0.000 000 032,

− 0.000 000 004 )

461

EXPLANATION Addition of the above correction to the unit vector p gives geocentric direction p1 of the star :

− 0.312 363 243, − 0.873 189 879) The velocity vector V = 0.005 7755 and β−l = (1− V 2 )1/2 are as follows: = ( − 0.374 123 829,

p1

= ( − 0.000 099 613,

V

β− = 0.999 999 995

− 0.000 015 811,

− 0.000 068 507)

l

The scalar product p1. V = + 0.000 048 188 Now substituting quantities computed above in the equation (4), the proper direction is obtained as: p2

= (− 0.374 205 410, − 0.312 364 000, − 0.873 154 650)

The precession and nutation matrix (M) from page 257 is as follows:

M =

+ 0.999 988 499

− 0.004 398 726

− 0.001 911 210

+ 0.004 398 742

+ 0.999 990 325

+ 0.000 004 106

+ 0.001 911 174

− 0.000 012 513

+ 0.999 998 174

Finally the apparent geocentric direction p3 is obtained by multiplying the proper direction p2 to the precession and nutation matrix as given by the equation (5). Thus p3 = (− 0.371 158 321, − 0.314 010 597, − 0.873 864 318 ) and the apparent right ascension and declination: h m s α = tan−l (η/ξ) = 14 40 55 .723 ; δ = tan − l (ζ/β) = −60° 54″ 39′ .066

462

EXPLANATION PART III - Tables of Sunrise, Sunset, Twilight and Moonrise, Moonset The times of Sunrise, Sunset and Twilight, which can be obtained immediately from the given tables by simple interpolation for the desired latitude within the scope of the tables, are in local mean time of the place. Strictly speaking, the timings of these events are for places on the meridian of Greenwich. By simple interpolation for longitude, the correct time (L.M.T.) for the station can be obtained, which can thereafter be reduced to the zonal standard time by applying correction of time pertinent to the place. At the given times of Sunrise and Sunset, the upper limb of the Sun is on the horizon; the true zenith distance of the Sun's center is then taken as 90 50, allowing 16 for semi- diameter and 34 for horizontal refraction. The timings of the beginning of morning twilight and ending of evening twilight relate to the instants when the center of the Sun is 18 below the horizon. This is now known as astronomical twilight. The period of twilight has been divided into three parts  Civil when the Sun is 6 below the horizon, Nautical when 12 and Astronomical when 18 and their duration have been given. The timings of rising and setting in U.T. of a body with right ascension , declination  and zenith distance z at latitude  and east longitude  may be computed from UT = 0.99727 [    cosl {(cos z  sin  sin  )/ ( cos  cos  )} GAST at 0h UT], where each term is expressed in time measure and GAST at 0h UT as tabulated on page 13. The negative sign in the expression corresponds to rising and positive sign to setting. If the quantity {(cos z - sin sin)/ (cos cos) is numerically greater than one, there is no phenomenon. However, the tabulated timings of Moonrise and Moonset have been computed by inverse by interpolation for the zenith distance at z = 90 34.001- 0.72755 , where  is the horizontal parallax of the Moon at the time of phenomena. The above value includes semidiameter and the effect of refraction. The Sunrise and Sunset times for certain stations in India (Kolkata, Varanasi, Chennai, Delhi, Mumbai) have been separately computed and given in Indian Standard Time. In these calculations the amount of horizontal refraction has been taken as 31, the value derived from consideration of the atmospheric conditions in India, and consequently the zenith distance of the Sun's center is 90 47 at the times given. In the section on Indian Calendar, the Sunrise and Sunset times which have been given for latitude 23 11 North and Central Meridian of India, also relates to the times when upper limb of the Sun is on the horizon as in the general tables. The Moonrise and Moonset times given for certain latitudes relate to the local mean time calculated for the Central Meridian of India. By simple interpolation with the help of a table given on page 313, the local mean time for any other latitude can easily be obtained. At the time given, the Moon's upper limb is on the horizon and so the true geocentric zenith distance of the Moon's center is 90 34 plus semi- diameter of the Moon minus the horizontal parallax, where 34 has been allowed for horizontal refraction. Taking the mean values of the semidiameter and the parallax, the zenith distance of the Moon at the moment is about 89 52, which varies from 89 55 to 89 49 as the parallax increases from 53.6 to 61'.9. The times of Moonrise and Moonset for certain stations in India (Kolkata, Chennai, Delhi and Mumbai) are separately calculated and given in I.S.T. The times of Sunrise, Sunset and Moonrise, Moonset given are for an observer on the surface of the Earth considered to be a flat surface around that point without any obstruction in the directions of rising or setting. For an observer stationed at some elevation above the surface, the rising will be further accelerated and the setting retarded according to the height of the observer. The additional arc of depression to be considered on this account is 2.10h where h is the height of the observer in meters above the ground level. The dip of the sensible horizon is however 1.77 h. The effect of atmospheric refraction is included in the above results, without which both the terms would have got reduced to the same value of 1.93 h.

463

EXPLANATION The values of the arc of depression according to height of the observer are given below: Height

Depression

Height

Depression

Height

Depression

Height

Depression

Meters 0 2 5 10 20 30 40

 0.0 3.0 4.7 6.6 9.4 11.5 13.3

Meters 40 50 75 100 150 200 300

 13.3 14.8 18.2 21.0 25.7 29.7 36.4

Meters 300 400 500 750 1000 1500 2000

 36 42 47 58 66 81 94

Meters 2000 3000 4000 5000 6000 7000 8000

 94 115 133 148 163 176 188

The correction to the rising and setting times due to the above height of the observer may be obtained by multiplying the arc of depression given in the table by the figures from the table below: Latitude of Station Decli. of Sun

0

  0 5 10 15 20 23 27

m .067 .067 .068 .069 .071 .073

10

20

30

35

40

45

50

52

54

56

58

60

m .068 .068 .069 .070 .072 .074

m .071 .071 .072 .074 .076 .078

m .077 .077 .079 .081 .084 .087

m .082 .082 .083 .086 .090 .093

m .087 .088 .089 .093 .097 .102

m .094 .095 .097 .101 .108 .114

m .104 .105 .108 .113 .123 .132

m .108 .109 .113 .119 .130 .142

m .113 .115 .119 .127 .139 .155

m .119 .121 .126 .134 .151 .171

m .126 .127 .133 .144 .165 .192

m .133 .135 .142 .156 .183 .223

The deviation of the rising or the setting point on the horizon (i.e., amplitude) on account of the above arc of depression h (obtained after adding to it the normal depression at rising or setting) may be found as h tan  sec A, deviation being towards the north in the northern hemisphere and south in the southern hemisphere. Here A, the amplitude of the rising of setting point measured from the east or west point of the horizon, is obtained from sin A  sin sec. The values of the amplitude for certain latitudes and declinations are given in a table on page 369.

PART IV  ECLIPSES AND OCCULTATIONS Eclipses and Occultations have been calculated on the basis of the tabulated positions of the Sun and the Moon. The semi-diameters of the Sun and the Moon used in these calculations exclude irradiation. The Sun's tabular semi-diameter which includes irradiation is diminished by 1."55 for this purpose. The semi-diameter of the Moon given by sin s = k sin , where  is the Moon's horizontal parallax is based on the adopted constant k = 0.272 5076 to account for the irregularities of the lunar limb. It corresponds to the mean radius of Watt's datum as determined by observations of occultations and to the adopted radius of the Earth, introduced in 1982 and is consistent with the IAU system of Astronomical constants (1976). It is used with effect from 1986 in this publication. Refraction is neglected in calculation of eclipses of both the Sun and the Moon.

464

EXPLANATION The circumstances of the phenomena are given provisionally in Universal Time, using T (A) = + 69s.0 and the points on the Earth's surface are also expressed in terms of geographic longitude measured positively to the east.

Lunar Eclipses In the calculation of lunar eclipses, the semi-diameter of the shadow -cone has been increased by onefiftieth to take account of the influence of the atmosphere in absorbing Sun's rays passing through it . In the calculation of rising and setting limits, the time when the centre of the Moon becomes visible on the horizon has been considered as rising or setting. Elsewhere in this book the upper limb visible on the horizon is taken as the criterion for rising or setting. The horizontal refraction used in these calculations of rising and setting is 31. The method of computation of a lunar eclipse is detailed below : Let ,  be the right ascension and declination of the Moon at an instant T0 at or very near to the moment of opposition, and let ,  be the corresponding co-ordinates of the centre of the Earth's shadow ( = R. A. of Sun + 12h,  = Sun's declination ). Let , s be parallax and semi-diameter of the Moon and , s be parallax and semi-diameter of the Sun. As the Earth is not a perfect sphere, its shadow will differ slightly from a cone. It would however, be sufficient for our purpose if we use a mean radius for the Earth, which is equivalent to submitting for  a parallax 1, reduced to latitude 45º , so that 1 = 0.9983 33 . The radius of the shadow-cone at Moon's distance is 1.02 ( 1 + – s ) for umbra, and 1.02 ( 1 +  + s ) for penumbra. Let L be the angle between the centre of the Moon and that of the shadow-cone at the desired circumstance of the eclipse, so that L1 = 1.02 ( 1 + – s ) + s . . . . . . for first and last contacts L2 = 1.02 ( 1 + – s ) – s

. . .

. . .

for second and third contacts

For the penumbral eclipse, L' = 1.02 ( 1 +  + s ) + s

. .

. . .

.

for first and last contacts

The Besselian elements x, y may be computed with sufficient accuracy with the following : x = (  –  ) cos  y = (  –  )

x = hourly variation of (  –  ) cos  y = hourly variation of (  –  )

Let m sin M = x, and m cos M = y, so that tan M = x/y, and m 2 = x 2 + y 2. The quantity m, taken always positive at all times, represents the angular distance between the centre of the Moon and of the shadow cone. The angle M may take any value from 0º to 360º. Again, let n sin N = x, and n cos N = y, so that n 2 = x 2 + y 2, and tan N = x / y. The angle N lies in the first or the second quadrant according as y is positive or negative. The value of n is positive. The time of greatest obscuration or middle of the eclipse is given by T0 – 1/n { m cos ( M – N ) } or T0 – ( x x + y y  ) / n 2

( hours )

465

EXPLANATION The auxiliary angle ψ is given by : sin ψ = { m sin ( M – N ) }/ L = ( x y – y x )/ nL. The value of either L1, L2 or L' should be used or L according to the circumstances of the eclipse under consideration. Then, time of the beginning or ending = time of middle + (1/n) ( L cos ψ ). The value of ψ should be so taken that cos ψ may be negative for the beginning and positive for the ending of the phase. In other words, when sin ψ is positive, i.e., when ( M – N ) falls in the 1st or the 2nd quadrant, ψ would be in the second quadrant for the beginning and in the first quadrant for the ending; and when sin ψ is negative, i.e., when ( M – N ) is in the 3rd or the 4th quadrant, ψ would be in the third quadrant for the beginning and fourth quadrant for the ending. If greater accuracy is desired, the computations may be repeated using the times obtained above as initial times. The magnitude of the eclipse, the Moon’s diameter being unity, is ( L1 –  )/ 2 s, where  = m sin ( M – N ) is taken positive. When the computations are repeated for greater accuracy, the average values of L1,  and s for the first and last umbral contacts or those corresponding to the time of greatest obscurations should be used. When  becomes less than L2, the eclipse is a total one. The computations of the beginning and ending of the total phase may be done in the same way as above using the value of L2. The position angle of contact P on the Moon’s limb, measured from the north point in the direction N.E.S.W. is 180◦ + N + ψ for the first and last contacts both with umbra and penumbra as the case may be, and is N + ψ for the second and third contacts in case of a total eclipse. When M is calculated for the exact time of the phenomena, i.e., beginning or ending, then P may be obtained by considering N + ψ = M, i.e., P = M + 180◦ or P = M as the case may be.

Solar Eclipses Computation of the elements and circumstances of solar eclipses has been done following the method of Bessel. The geometric position of the shadow of the Moon relative to the Earth is described by the Besselian elements in a system of geocentric rectangular co-ordinates. In this system, the geocentric plane perpendicular to the axis of the shadow is taken as the xy plane and called the fundamental plane. The x-axis is the intersection of the fundamental plane with the plane of equator and is positive towards east. The y-axis is positive towards the north. The z-axis is parallel to the axis of the shadow and is positive towards the Moon. The tabular values of x and y are the co-ordinates of the axis of the shadow on the fundamental plane in units of the Earth’s equatorial radius. The quantities d and μ specify the declination and hour angle of the point on the celestial sphere towards which the axis of the shadow is directed. The elements l1 and l2 are the radii of the penumbral and umbral cones on the fundamental plane. The elements l2 is regarded as positive for an annular eclipse and negative for a total eclipse. The elements f 1 and f 2 are the angles between the axis of the shadow and the generators of the penumbral and umbral cones respectively. The Besselian elements x, y, sin d, cos d, μ, l1 and l2 are computed and tabulated at an interval of 10 minutes to facilitate the accurate computation of the circumstances of the eclipse. The given eclipse maps show the path of the eclipse, beginning and ending times of the eclipse, the area of visibility and rising and setting limits of the eclipse.

466

EXPLANATION The method of computation of the local circumstances of the solar eclipse is given below : The approximate time (U.T.) of the beginning and ending of a solar eclipse may be obtained from the corresponding eclipse map and used as estimated initial time. To obtain the geocentric rectangular co-ordinates, ,, , ζ of the observer located on the surface of the Earth in geographic longitude  (measured east positive) and latitude  in terms of the Besselian elements, we have;

   cos  sin H    sin  cos d   cos  sin d cos H ζ   sin  sin d +  cos  cos d cos H and their variations per minute as :

 ' = μ cos  cos H ' = μ  sin d - d where H = μ +  and μ is variation per minute in hour angle. In most of the cases, the variation ζ' is not needed and may be neglected. The values of  cos  and  sin  used above may be found for the observer’s latitude  using Table – XI. The eclipse begins or ends at the station when ( x   )2 + ( y   )2 = ( l1  ζ tan f1 )2. Now let m sin M = x  , m cos M = y   so that tan M = (x  ,) ( y   ) and m2 = (x   )2 + (y ) . The angle M may have any value from 0° to 360° and m is always positive. 2

Again let n sin N = x  , n cos N = y   so that tan N = (x   ) ( y   ) and n2 = (x   )2 + (y   )2. The angle N is in the first two quadrants and n is positive. 

The radius of the shadow at a height ζ above the fundamental plane may be determined by L1 = l1  ζ tan f1 or L2 = l2  ζ tan f2 as the case may be. Now the required time of the event will be obtained by applying a correction  to the adopted initial time concerned, given by  =  {m cos ( M  N )}/n + ( L cos  )/n (in minutes), where sin  = {m sin ( M  N )}/L The value of  for which cos  is negative should be taken for the beginning of the eclipse for the beginning of the annular phase or the end of the total phase, and the value of  for which cos  is positive is to be taken for the end of the eclipse, for the end of the annular phase or the beginning of the total phase. When M  N falls within 0º to 180º,  is in the 2nd or the 1st quadrant according to the required phase of the eclipse, for the other half it is in the 3rd or the 4th quadrant according to the phase. If the correction  obtained above exceeds 3 or 4 minutes and greater accuracy is desired, the computation should be repeated using the new times now obtained as initial times. For finding the time of greatest phase , the calculations should be started adopting a new assumed time midway between the beginning and ending times. The correction to this adopted time is given by: 

=  {m cos ( M  N )}/n (in minutes).

467

EXPLANATION The magnitude of greatest partial eclipse is the fraction of the Sun’s diameter obscured by the Moon at the time of greatest phase, and is given by : M1 = ( L1   ) / ( 2 L1  0.5459) where , the minimum distance between the centres of the two bodies, is given by m sin ( M  N ) and is to be taken positive. The magnitude of the central phase, in the same units, is M2 = ( 0.5459 ) / ( 2 L1  0.5459). The position angle of the point of contact measured from the north point of the Sun in the direction N. E. S. W. (i.e. clockwise direction) may be obtained from P = N +  or if, measured from the vertex, from V = P  C where C, the parallactic angle, is given by tan C = ( / ).

Occultations The occultations of visible planets and certain bright stars (Aldebaran , Regulas, Spica and Antares) by the Moon are given whenever they occur, together with the time, area of visibility and the Besselian elements. The area of visibility includes also the regions from which the occultations is visible even during day light hours. The two times given in the first table for the occultations are the times of first and last contact of the shadow cylinder with the Earth and as such the occultation may be expected to be visible only within the period between these times. The elements are similar to those for solar eclipses and are given for T0, the instant of conjunction in R.A. when x = 0. The common geocentric hour angle of the bodies, or more precisely of the line passing through the center of the Earth parallel to the line joining the center of the two bodies for the Greenwich meridians is H 0 and its hourly variation is about 60m.16 or 15º.04. Y is the value of y for the instant of conjunction and x', y' are the hourly variations of x and y. For a place where an occultation is visible, the times of immersion and emersion can be computed with the help of these elements by a method similar to that used in computing the local circumstances of a solar eclipse as explained below: Let  and  be respectively the latitude and longitude of the place. The longitude of place is to be taken in hours and minutes and as usual measured positively towards east of Greenwich. For night visibility of an occultation, the necessary conditions are as follows: (1)

The Sun must not be much more than an hour above the horizon at the local mean time T0 +  (and it must be below the horizon at time T0 +  + t).

(2)

The Moon must be above the horizon by an appreciable amount, i.e., the quantity H 0 + , taken without regard to sign for this purpose, must be less than the semidiurnal are of the star of planet by at least one hour.

For prediction of an occultation, find the approximate time (U.T.) of local apparent connection by applying to the given T0 a correction t (in hours) taken from the following table*: H 0+   0 10 20 30 40 50 60

h m 0-00 h 0.00 0.00 0.00 0.00 0.00 0.00 0.00

h m 0-30 h 0.41 0.40 0.37 0.32 0.26 0.20 0.15

h m 1-00 h 0.77 0.75 0.70 0.62 0.51 0.40 0.29

h m 1-30 h 1.08 1.06 0.99 0.87 0.73 0.58 0.42

h m 2-00 h 1.32 1.29 1.21 1.08 0.92 0.73 0.53

h m 2-30 h 1.50 1.47 1.38 1.24 1.07 0.86 0.63

h m 3-00 h 1.62 1.59 1.51 1.36 1.18 0.96 0.72

h m 3-30 h 1.69 1.66 1.58 1.44 1.26 1.03 0.78

h m 4-00 h 1.72 1.70 1.62 1.49 1.30 1.08 0.83

h m 4-30 h 1.73 1.70 1.63 1.50 1.32 1.11 0.85

h m 5-00 h 1.71 1.69 1.61 1.50 1.32 1.11 0.87

h m 5-30 h 1.65 1.63 1.56 1.45 1.30 1.10 0.86

h m 6-00 h 1.58 1.56 1.50 1.40 1.26 1.07 0.85

*The value of t has the same sign as that of sin ( H0 +  ). The Besselian elements x and y at the time of local conjunctions T0 + t may be calculated as follows : x = x' t, and y = Y + y' t.

468

EXPLANATION Occultations for which y -  for the time local conjunction is not within  0.35 will not be visible at the place. In order to decide this, an estimated value of  may be used as an approximation for which the following tables are given indicating the minimum and maximum values of . Limiting value of  (when on meridian i.e., when H0 +  = 0 )  - d ………  ………

0 0.00

10 0.17

20 0.34

30 0.50

40 0.64

50 0.76

60 0.86

The values of  has the same sign as that of  - d. (* The table has been constructed taking x' = 0.5773 ; for other values of x' the figures will vary inversely. For this purpose the figures of the table may be multiplied by 1.15 for x' = 0.50, by 1.05 for x' = 0.55, by 0.95 or x' = 0.60 and by 0.89 for x' = 0.65) Limiting value of  (when rising or setting i.e. when H0 + λ + t = S.D. arc) Latitude (  ) d

0

10

20

30

40

50

60

0.00

0.17

0.34

0.50

0.64

0.76

0.86

 9

0.00

0.17

0.34

0.50

0.65

0.77

0.87

 18

0.00

0.18

0.36

0.52

0.67

0.80

0.91

 27

0.00

0.19

0.38

0.56

0.72

0.86

0.97

0

The value of  has the same sign that of  For the instant T0 + t , compute the following quantities in addition to x and y : Let H = ( H +  ) + a t (converted into arc). The value of a has been given for planets under elements; it is 1.027 for stars. The observer’s position on the fundamental plane is given by:  =  cos ' sin H and  =  sin ' cos d –  cos ' sin d cos H and the hourly variations ;  ' = 0.2618 a  cos ' cos H, ' = 0.2618 a  sin d. The value of the co-efficient 0.2618 a is 0.2625 for stars. Let u = x– , v = y – , u' = x' –  ' , v' = y' – ' so that n2 = u' 2 + v' 2 . Now sin  = (uv' – vu' ) / nl, where l = 0.2725, for stars, and for planets, it will be found under elements. The correction  to the time of immersion and emersion is given by :  = – (60/ n²) ( uu + vv) Ŧ (60 l / n) cos  The negative sign in the second term is to be taken for immersion or the first contact and the positive sign for emersion or the last contact. Instant of immersion or emersion = T0 + t +  . If greater accuracy is desired, a second set of calculations may be done in the following way using the new times now obtained as initial times. For the revised time of immersion or emersion T , compute H = (H +  + at) + a, x, y,  , ,  ,  ; u, v, u, v and D = uu + vv. The second correction t is given by : t = (30/D)x [l² - (u² + v²)] in mins. of time. The final time of immersion or emersion = T + t . The angles of contact on the Moon’s limb:

469

EXPLANATION P = M + 180, where tan M = (u + ut) /( v + vt) , V = P – C, where tan C =(  +  t) /(  +  t ), where t is to be taken in hours.

PART V – Miscellaneous Tables Phenomena The stellar magnitudes of planets together with their elongations from the Sun have been given under ‘phenomena’ at suitable intervals of days. The computation in the next portion of the phenomena has been based on longitude and that in the Astronomical Diary mainly on right ascension, with the exception that the conjunctions, squares and oppositions of planets with the Sun included in the latter have been calculated on the basis of longitudes. In the case of conjunctions in right ascension, the differences in declination between the planets or the Moon and the planet have also been given. The dates of heliacal visibility of planets ( Mercury to Saturn) have also been given and these are based on the method given on page 467.

Interpolation Interpolation Coefficients have been given on pages 355 to 358 according to the formula of both Bessel and Everett, for each hundredth part of the time-interval. Let the tabular value of a function given at equal intervals be represented by f and the first and second differences by  with relevant dashes and subscripts as shown below. It is required to determine the value of the function at some intermediate point. Function f –1 f0 f1 f2

First difference

Second difference

 '-½ 

' ½

 '1½

0 1

The epochs for which the values of the function are to be taken should be so chosen that the time for which the value of the function is required may fall within the interval f0 and f2 and let n be the time interval from f0 up to the moment for which the value of the function is required. It is expressed as a fraction of the interval at which the given values of the function are tabulated. Let fn be the value of the function for the desired time which is now required to be determined. The two formulae for interpolation which are generally used for the purpose are as follows : fn = f0 + n ½ + B (0 + 1)…………………Bessel fn = f0 + n ½ + E0 0 + E11………………Everett in which f0 + n½ may be replaced by (1 n) f0 + nf1 , if necessary, and where B = n (n – 1)/ 4, E0 =  n (n1) (n2)/ 6 and E1 = n (n+1) (n1)/ 6 It will be noted that in Bessel’s formula the value of 0 + 1 is the same as '1½ – '-½ . The value of the coefficients B", E0" and E1", all of which are negative within the range f0 to f1 , will be obtained from the table on page 355 to 358 for the given value of n.

470

EXPLANATION Bessel’s method of interpolation is more simple, but greater accuracy is yielded by Everett’s formula on account of the fact that it includes the effect of third differences also. The more complete formula of Bessel is as follows : fn = f0 + n½ + {n(n – 1) (0 + 1)}/4 + { n(n -1)(n - ½ ) ½ }/6 +        The rate of variation of the function at a point, i.e., the instantaneous motion per unit of time interval may be obtained by the following formula : Motion = '½ + C0" + D1", when n = ½ ,

where C =  (3n²  6n + 2)/6 and D = (3n²  1)/6

When n = 0, the motion f0' = {('-½ + '½)/2} – (1" 0")/6, f 1' = {('½ + '1½ )/2} – (1" 0")/6 f '½ = '½ – {(1" 0")/24} and when n = 1,

The stationary point (i.e., when f ' = 0 ) occurs when n = ½  ('½ /"1) or ½  ('-½ /"0). Geocentric Co-ordinates and other Constants The tables given on pages 363 and 364 are for computing the geocentric co-ordinates of a place for which the geodetic, i.e., geographic or common latitude  is known. From the first table, the values of  sin  and  cos  can be directly obtained, while the second table gives the values of the geocentric latitude  and the radius of the Earth  separately The constants used for these tables and the others given below are the 1976 I.A.U. astronomical constants introduced in this publication with effect from the 1985 issue.

System of

Equatorial radius (a) = 637 8140 m = 3963.20 miles. Polar radius (b) = 635 6755 m = 3949.91 miles. Flattening of the Earth (f) = (a-b)/a = 1/298.257 = 0.003 353 64. Ellipticity or eccentricity (e) = 0.081 8192, e² = 0.006 694 39. The following expressions are obtained from the above values of flattening and radius of the Earth. S = 0.994 9743 – 0.001 6708 cos 2  + 0.000 0021 cos 4  C = 1.001 6799 – 0.001 6820 cos 2  + 0.000 0021 cos 4   = 0.998 3271 + 0.001 6764 cos 2  - 0.000 0035 cos 4   =  - 11 32.726 sin 2  + 1.163 sin 4  - 0.003 sin 6  One degree of longitude (in km.) = 111.4133 cos  - 0.0935 cos 3  One degree of latitude (in km.) = 111.1334 – 0.5598 cos 2  + 0.0012 cos 4  g (cm/sec²) = 978.031 + 5.1859 sin²  - 0.0057 sin² 2  - 0.000 308H. where H is the elevation in meters above sea level. Period of Earth satellite of negligible mass = 84.489 09 d3/2 mins., where d is the mean distance of the satellite from the Earth’s center measured in units of 6378140 m (Earth’s equatorial radius). Invariable plane of the solar system;  = 106°35 01 + 3452T, I = 1° 34 59 - 18T Pole of galactic plane (1950);  = 12h 49m.0,  = +27° 24 Solar apex (1950)..  = 18h 06m,  = +30° Solar motion

= 20.0 km. or 12.4 miles per sec.

Speed of the Earth moving around the Sun = 29.79 km. or 18.51 miles per sec.

471

EXPLANATION Heliacal Rising and Setting of Planets The planets Mercury to Saturn (as well as the Moon) remain invisible to the naked eyes for some days at the time of conjunction with the Sun. This phenomenon of planet's invisibility due to its proximity to the Sun is known as combust or heliacal setting of the planets, and it plays an important part in Indian Calendar. The dates of heliacal setting and rising of the planets marking the period or invisibility have been calculated assuming that the phenomenon occurs when, at the given station, the Sun attains a Zenith distance of 90+h at the time when the zenith distance of the planet is 90. The values of h for different planets adopted for the purpose are as follows : Mercury 10 (Direct) and 11 (Retrograde) Venus 6, Mars 14, Jupiter 8.5 , and Saturn 12 The day of the first visibility of the lunar crescent after a new-moon day has also been determined in a somewhat similar way on the basis of the following values of the limiting altitude of the Moon above the horizon corresponding to its azimuth difference from the Sun, when the zenith distance of the Sun is 90. Azimuth difference Altitude

0 10.4

5 10.0

10 9.3

15 8.0

20 6.2

When the altitude of the Moon at sunset exceeds the above limit, the Moon is likely to be visible in that evening and when the excess is more than a degree, the Moon is sure to be visible. The beginning dates of the months of the Islamic Calendar have been determined on the basis of the above calculations and indicated on the date following that of the first visibility of the Moon. In the above calculations, the atmospheric refraction and the horizontal parallax of the Moon are neglected. The computations of heliacal rising and setting of planets and determination of the dates of first visibility of the Moon have been done for the central station of India.

ASTRONOMICAL CONSTANTS* Units : The units meter (m), kilogram (kg.) and second (s) are the units of length, mass and time in the International System of Unit (SI). The astronomical unit of time is a time interval of one (D) of 86400 seconds. An interval of 36525 days is one Julian century. The astronomical unit of mass is the mass of the Sun (S). The astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value of 0.01720209895 when the units of measurement are the astronomical unit of length, mass and time. The dimensions of k2 are those of the constant of gravitational (G), i.e. L3M1T2. The term "unit distance" is also used for the length A. Defining Constants : 1. Gaussian gravitational constant 2. Speed of light

k = 0.017 202 098 95 c = 299 792 458 ms-1

472

EXPLANATION Primary Constants : 3. 4. 5. 6. 7. 8. 9. 10.

Light-time for unit distance Equatorial radius for Earth [IUGG value Dynamical form-factor for Earth Geocentric gravitational constant Constant of Gravitation Ratio of mass of Moon to that of Earth General precession in longitude, per Julian century, at standard epoch J 2000.0 Obliquity of the ecliptic, at standard epoch J2000.0

A = 499.004 78384 s ae = 637 8136.6 m ae = 637 8137 m] J2 = 0.001 082 6359 GE = 3.986 004 418 X 1014 m3 s-2 G = 6.674 28 X 10-11 m3 kg-1 s -2  = 0.012 300 0371 P = 5028".796195  = 23º 26' 21".406

Derived Constants 11. Constant of nutation at standard epoch J2000.0 12. Unit distance

N = 9".2052 331 cA= A =1.495 978 707 x 1011m

13. Solar parallax arc sin (ae/A) = ⊙ = 8".794143 14. Constant of aberration for standard Epoch J2000.0 k = 20".49551 15. Flattening factor for the Earth f = 0.003 352 82 = 1/298.25642 16. Heliocentric gravitational constant A3 k2/D2 = GS = 1.327 124 42099 x 1020 m3 s -2 17. Ratio of mass of Sun to that of the Earth (GS)/(GE) = S/E = 332 946.0487 18. Ratio of mass of Sun to that of Earth + Moon (S/E)/(1+) = 328 900.5596 19. Mass of the Sun (GS)/G = S = 1.9884 x 1030 kg 20. System of planetary masses : (Ratios of mass of Sun to those of the planets etc.) Mercury Venus Earth + Moon Mars

6023600 408523.719 328900.5596 3098703.59

Jupiter Saturn Uranus Neptune Pluto

1047.348644 3497.9018 22902.98 19412.26 136566000

Other quantities for use in the preparation of ephemerides : It is recommended that the values given in the following list should normally be used in the preparation of new ephemerides. 21. Masses of minor planets in unit of the solar mass : (1) Ceres (2) Pallas (3) Vesta

4.72 x 10-10 1.03 x 10-10 1.35 x 10-10

-----------------------------------------------------------------------------*See page 446 also for some of the constants actually used in preparation of the ephemerides reported in the publication.

473

EXPLANATION 22. Masses of satellites in unit of the planet's mass : Jupiter

Io Europa Ganymede Callisto Titan Triton

Saturn Neptune

4.704 x 10-5 2.528 x 10-5 7.805 x 10-5 5.667 x 10-5 2.366 x 10-4 2.089 x 10-4

23. Equatorial radii in km. Mercury Venus Earth Mars

2439.7 6051.8 6378.1366 3396.19

Jupiter Saturn Uranus Neptune

71492 60268 25559 24764

Pluto

1195

Moon Sun

1737.4 696000

24. Gravity fields of the planets.

Earth Mars Jupiter Saturn Uranus Neptune

J2

J3

+ 1.08263 x 10-3 + 1.964 x 10-3 + 14.75 x 10-3 + 16.45 x 10-3 + 12 x10-3 + 4 x10-3

 2.54 x 10-6 + 36 x 10-6

J4  1.61 x 10-6  580 x 10-6  1000 x 10-6

25. Gravity field of the Moon.  = (BA)/C = 0.000 2278  = (CB)/B = 0.000 6313 C20 =  0.000 2027 C30 =  0.000 006 C31 = + 0.000 029 C22 = + 0.000 0223 S31 = + 0.000 004

C/MR2 = 0".392 I = 5552".7 = 1º 32' 32.7" C32 = + 0.000 0048 S32 = + 0.000 0017 C33 = + 0.000 0018 S33 =  0.000 001

474

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Anderson, J. D. 1974. EOS Trans. of AGU 55.

2.

Anderson, J. D. 1975 Review of Geophysics and Space Physics 13.

3.

Anderson, J. D., Null, G. W., Wong, S. K. 1974. J. Geophys. Res. 79, 3661.

4.

Aoki, S., Guinot, B., Kaplan, G. H., Kinoshita, H., McCarthy, D. D., Seidelmann, P. K. 1982. Astron. Astrophys., 105, 359.

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Aoki, S., Soma. M., Kinoshita, H., Inoue, K. 1983. Astron. Astrophys. 128, 263-267.

6.

Capitaine, N., P. T. Wallace, J. Chapront, 2003. Astronomy and Astrophysics 412, 567-586

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Capitaine, N., P. T. Wallace, J. Chapront, 2005. Astronomy and Astrophysics 432, 355-367

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Clemence, G. M., Szebehely, V. 1967. Astron. J. 72, 1324.

9.

Davies, M. E., Abalakin, V. K., Cross, C. A., Duncombe, R. L., Masursky, H., Morando, B., Owen, T. C., Seidelmann, P. K., Sinclair, A. T., Wilkins, G. A., Tjuflin, Y. S. 1980 Celest. Mech. 22, 205.

10. Duncombe, R. L., Klepczynski, W.J., Seidelmann, P. K. 1973, Fundamentals of Cosmic Physics 1, 119. 11. Duncombe, R. L., Seidelmann, P. K., Janiczek, P. M. 1974. Highlights of Astronomy 3, 223 12. Eckhardt, D. H. 1973. The Moon 6, 127. 13. Explanatory Supplement to the Ephemeris, 1974. Her Majesty’s Stationery Office, London, 48 and 144. 14. Explanatory Supplement to the Astronomical Almanac, 1992. Nautical Almanac Office, U. S. Naval Observatory 15. Fricke, W. 1967. Astron. J. 72, 1368. 16. Fricke, W. 1971. Astron. Astrophys. 13, 298. 17. Fricke, W. 1977. Astron. Astrophys. 54, 363. 18. Fricke, W. 1981. in Reference Co-ordinate System for Earth Dynamics, E. M. Gaposchkin and B. 19. Kolaczek, eds., D. Reidel Publishing Company, 331. 20. Fricke, W. 1982. Astron. And Astrophys. 107. L13-L16. 21. Harrington, R. S., Christy, J. W. 1980. Astron, J. 85, 168. 22. Hertz, H. G. 1968. Science 160, 299. 23. Howard, H. T., Tyler, G. L., Esposito, P. B., Anderson, J. D., Reasenberg, R. D., Shapiro, I. I., Fjeldbo, 24. G., Kliore, A. J., et al. 1974. Science 185, 179. 25. IAG Geodetic Reference System 1967. 1971. IAG Spec. Pub. No. 3 Bulletin Geodesique. 26. IAG Sixteenth General Assembly (1975) proceedings, 1975. Bulletin Geodesique 118. 365. 27. IAU Twelfth General Assembly (1964) proceedings, 1966. Trans. IAU XII B, 116. 28. IAU Fifteenth General Assembly (1973) proceedings, 1974. Trans IAU XV B, 108. 29. IAU Sixteenth General Assembly (1976) proceedings, 1977. Trans. IAU XVI B, 58. 30. IAU Seventeenth General Assembly (1979) proceedings, 1980. Trans. IAU XVII B, 69. 31. IAU Eighteenth General Assembly (1982) proceedings, 1983. Trans. IAU XVIII B. 32. IAU Twenty-first General Assembly (1991) proceedings, 1992. Trans. IAU XXI B. 33. IAU Twenty-third General Assembly (1997) proceedings, 1999. Trans. IAU XXIII B. 34. IAU Twenty-fourth General Assembly (2000) proceedings, 2001. Trans. IAU XXIV B. 35. IAU Twenty-sixth General Assembly (2006) proceedings, 2006. Trans. IAU XXVI B. 36. IERS Technical Note 32, 2004.

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REFERENCES 37. IERS Technical Note 35, 2009. 38. IERS Technical Note 36, 2010. 39. Kaplan, G. H. 1981. U. S. Naval Observatory Circular No. 163. 40. Kaplan, G. H. 2005. U. S. Naval Observatory Circular No. 179. 41. Kinoshita, H. 1977. Celest. Mech. 15, 277. 42. Lieske, J. H. 1979. Astron. Astrophys. 73, 282. 43. Lieske, J. H., Lederle, T., Fricke, W., Morando, B. 1977. Astron. Astrophys. 58, 1 . 44. Liu, A. A., Laing. P. A. 1971. Science 173, 1017. 45. Misner, C. W., Thorne, K. S., Wheeler, J. A.1973. Gravitation, W. H. Freeman and Company, 184 and 1101. 46. Moritz, H. 1980. Bulletin Geodesique 54, 395. 47. Moyer, T. 1981. Celest. Mech. 23, 33 & 57. 48. Null, G. W., Anderson, J. D., Wong, S. K. 1975. Science 188, 476. 49. Schubart, J. 1974. Astron. Astrophys. 30, 289. 50. Schubart, J. 1975. Astron. Astrophys. 39, 147. 51. Scott, F. P. 1964. Astron. J. 69, 372. 52. Scott, F. P., Hughes, J. A. 1964. Astron. J. 69, 368. 53. Seidelmann, P. K. 1982, (1980). Celest. Mech. 27, 79-106. 54. Seidelmann, P. K., Kaplan, G. H., Van Flandern, T. C. 1981. In Reference Co-ordinate system for 55. Earth Dynamics, E. M. Gaposchkin and B. Kolaczek, eds., D. Reida Publishing Company, 305. 56. Sjogren, W. L. 1971. J. Geophys. Res. 76, 7021. 57. Van Flandern, T. C. 1971. Celest. Mech. 4, 182. 58. Van Flandern, T. C. 1981. Preprint, submitted to Astron. J. 59. Wade, C. M. 1976. VLA Scientific Memorandum 122. 60. Wahr, J. 1979. Ph. D. Thesis, University of Colorado. 61. Wahr, J. 1981. Geophys. J. Roy. Astr. Soc. 64, 705. 62. Williams, J. 1975. EOS Trans. Of AGU 56, 236. 63. Winkler, G. M. R., Van Flandern, T. C. 1977. Astron. J. 82, 84. 64. Standish, E. M. 1982. Astron. Astrophys. 115, 20-22.

476

INDEX Page A berration

18, 448

Page F estivals --- contd. C hristian

419

Amplitude of Rising and Setting

373

Jewish, Parsi

418

Arc, Conversion to Time, Table III

353

M oslem

417

Augmentation of Moon's Semi-diameter Astronomical Constants

373 450,472

Geocentric co-ordinates of a place, Table XI Heliacal rising and setting of planets

Astronomical, reference frame

439

I.A.U. System of Astronomical Constants

A tomic time

433

Interpolation co-efficients, Table VII, VIII

Ayanamsa, values of True M ean

423

Julian Day Number, Table IX

423

Jupiter

367 344, 383,471 471 359, 361 363

Barycentric dynamical time (TDB)

434

Distance from the Earth

Barycentre

202

E longations and Magnitudes

343

E phemeris transit

146 146

Calendar

4

146

Indian

380

H orizontal parallax

Islamic

417

Longitude and latitude, geocentric apparent

142

J ewish, Parsi

418

Longitude and latitude, heliocentric

140

R adius vector

140

202

Right ascension and declination, apparent

146

Semi-diameter

146

Latitude and longitude of places

369

Centre of Mass of Solar System E quatorial rect. Co-ord. of Barycentre C hronological Table

3

Conversion of hours, minutes and seconds to decimals of a day, Table V

355

Latitude of Moon for the period

358

Latitude, geocentric of planets for the period

368

Latitude of a place from an observed altitude

Conversion of minutes and seconds to decimals of a degree, Table VI

Jan. 0 to Apr. 20, 2021

Co-ordinates, Conversion of geographic to geocentric, Table XII

J an. 0 to Apr. 20, 2021

Day

of Polaris L ength of

2, 435

of week

4

of year

4

Day Numbers, Besselian

275

Jan. 0 to Apr. 20, 2021

424

Distance from the Earth

132

E longations and Magnitudes

343

Mars

244, 457 428

Declination of planets for the period Jan. 0 to Apr. 20, 2021

430

Longitudes of Sun, Moon and planets for the period

Declination of Sun and Moon for the period Jan. 0 to Apr. 20, 2021

428

E phemeris transit

132

H orizontal parallax

132

430

Longitude and latitude, geocentric apparent

128

∆T, definition

436

Longitude and latitude, heliocentric

126

Table

436-439

R adius vector

126

D ynamical Time (D. T.)

434

R ight ascension and declination, apparent

132

Diary, Astronomical

347

Semi-diameter

132

Earth, barycentric co-ordinates

256

Eclipses

319

Mercury Distance from the Earth

104

B esselian Elements

322, 332

E longations and Magnitudes

342

Elements

320, 330

E phemeris transit

104

Circumstances

320, 330

H orizontal parallax

104

Longitude and latitude, geocentric apparent

100

Maps

321, 325,331

of the Moon

334-337

Longitude and latitude, heliocentric

of the Sun

320-333

R adius vector

Ephemeris Time

434

Epoch J-2000.0

433

E quinoxes

441

E q uation of Equinoxes F estivals

13 414

96 96

R ight ascension and declination, apparent

104

Semi-diameter

104

Month, lengths of

2

Moon Age

80, 454

477

INDEX Page Moon --- contd.

Page Occultations

Apogee and perigee

46, 347

Area of visibility Elements

E phemeris transit, upper and lower

80

Geocentric declination, at upper and lower transits

80

Inclination of orbit

453

M ethod of calculation

338 339-340 467

O sculating elements of planet

200

P henomena

342

Physical ephemeris of observations

Longitude and latitude at 0h and 12h TT

48

of M oon

Longitude, mean

47

of Sun

Mean elongation

47

Orbit of, Perigee and Node

47

Astrometric ephemeris

Parallax, horizontal

64

Distance from the Earth

198

Phases of the Moon

4, 46, 317

Elongations

343

P hysical ephemeris of observations E arth's Selenographic Long., Lat.

88, 454 42

Pluto

88, 454 88

456

Ephemeris transit

198

Horizontal parallax

198

Fraction illuminated

88

Longitude and latitude, geocentric apparent

197

Sun's Selenographic Co-long., Lat.

88

Longitude and latitude, heliocentric

196

Position angle of axis, bright limb

88

R adius vector

196

Right ascension and declination for 0h and 12h TT

64

Reduction to astrometric places

198

S emi-diameter at 0h and 12h TT

48

Right ascension and declination, apparent

198

True Geoc. Distance (A. U.)

48

Apparent places of

272

Azimuth of

275

Latitude of place from altitude of

275

Polaris

Moonrise and Moonset for lat. 0 to 50, central M eridian and for some places in India

296, 297

C orrection for Latitude

313

M ethod of calculation

315

Precession

Reduction of the L.M.T. of rising or setting

In l ongitude

for the meridian 82½ E. to the L.M.T. of

In R.A. and Declination

other meridians

312

Nakshatras

Rotation Matrix Precessi onal elements

Ending moment in I.S.T.

384

Pref ace

Names of

384

Refraction, Atmospheric, Tabl e X

Neptune

18 443 257 443 III 364

Saturn

Distance from the Earth

188

Distance from the Earth

E longations

343

El ongations and Magnitudes

343

Ephemeris transit

188

E phemeris transit

160

Horizontal parallax

188

Horizontal parallax

160

L ongitude and latitude, geocentric apparent

184

Longitude and latitude, geocentric apparent

156

L ongitude and latitude, heliocentric

182

Longitude and latitude, heliocentric

154

Radius vector

182

Radius vect or

154

R i ght ascension and declination, apparent

188

R ight ascension and declination, apparent

160

Semi-diamet e r

188

Semi-diameter

160

Noon, Apparent At meridian of 82½ E

Second-order day numbers 384

Nutation In longitude

18, 445

I n obliquity

18, 445

Rotation matrix

160

252

Semi-diurnal and Semi-nocturnal arcs

373

Solstices, dates of

344

Stars Apparent places of Polaris

272

257

Apparent place, r eduction of Longitude and latitude

204

Mean

451

Magnitude

204

True

18

Mean places of

215

Obliquity of the Ecliptic

457, 460

478

INDEX Page Stars --- contd.

Page T ithis, ending moment in I.S.T.

Spectral Type

215

Sun Aberration Co-ordinates, rectangular Eccentricity

18

374

Standard Times

375

Twilight

34 451

E phemeris transit

19

Latitude , ecliptic of date

18

Longitude, apparent

18

384

Trigonometric functions, natural

Correction for southern latitudes

290

Duration of

288

Time of beginning and ending at n orthern latitudes

280

Uranus

mean

17

Distance from the Earth

174

g eometric

18

E longations

343 174

Mean long. and anomaly

17

Ephemeris transit

Parallax, horizontal

17

L ongitude and latitude, geocentric apparent

170

Physical observations

42

L ongitude and latitude, heliocentric

168

Radius vector

168

Radius Vector

451

Right ascension and declination at 0h TT

19

Right ascension and declination, apparent

174

Semi-diameter

19

Semi-diameter

174

Distance from the Earth

118

S ynodic rotation number

452

Venus

Sunrise and Sunset Correction for latitude

313

Elongations and Magnitudes

342

Correction for southern latitude

290

Ephemeris transit

118

For certain places in India

292

Horizontal parallax

118

For northern latitude

280

L ongitude and latitude, geocentric apparent

114

Method of calculation

315

L ongitude and latitude, heliocentric

112

Radius vector

112

Time Conversion to Arc, Table IV

354

Right ascension and declination, apparent

118

Ephemeris

434

Semi- diameter

118

Equation of

450

Greenwich mean

434

Year

Reduction of L.M.T. to I.S.T. for

Anomalistic

2

Eclipse

2

certain longitudes

314

S idereal

2

Reduction of L.M.T. of certain places into I.S.T.

369

T ropical

2

S idereal, mean

13

Tables of conversion of solar to sidereal and v ice versa, Tables - I and II

351, 352

T .A.I. (International Atomic Time)

433

Terrestrial time (TT)

434

Time-Scales

433

Reduction tables

436-439

U niversal Time

434

Yogas Ending moment in I.S.T.

384

Names of

384

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