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aX rg. A book on ASTRONOMY (RELEVANT TO ASTROLOGY) t u \P^ 5r" Ino-t by V. P .Iain ',t Publnsh,eil by Bharatiga Prachga Eoatn Sanatan Viggan Sansthan
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Astronomy Relevant to Astrology by v.P. Jain

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Page 1: Astronomy Relevant to Astrology by v.P. Jain

aX rg.

A book

on

ASTRONOMY(RELEVANT TO ASTROLOGY)

t u \P^ 5r" Ino-t

by

V. P .Iain

',t

Publnsh,eil byBharatiga Prachga Eoatn Sanatan Viggan Sansthan

Page 2: Astronomy Relevant to Astrology by v.P. Jain

tt q-d dzrr

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.rqr B tdfrq d rorrs fuflq Rrft frqnoq fr, (ftrt at

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Surya Mantra

In this Mantra, god Sun has been remembered bythree different names.

(Swamy Vidyaranya Ji whom we all know by the name

Swamy Moorkhananda Ji, used to recommend this

Mantra as very beneficial to all students of astrology.)

Page 3: Astronomy Relevant to Astrology by v.P. Jain

CONTENTS

Introduction.... . . . . . . .

Cneprnn I

Historical Background.... . . . . . . . . . . . . . . . . . . . . . . . . . . . g

Names of Astronomers ... . . . . . . . . . lz

Indian Astronomy.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Siddhantas.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . l?Important Astronomical Scholars .. . . . . . . . . . . . . . . . . . . . . . . . . . . Z1Revolutions of Various Planets in aMahayuga of Solar Years .. . . . . .22Surya Siddhanta and Bija Corrections ... . . . . . . . . . . . . . . . . 28

Comparison of Time of Revolutions for VariousPlanets .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

Difference between Modern and Indian Classical4stronomy.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ZG

Cxeprnn 2

Sphere, Celestial Sphere ... . . . .31

Great Circle, Small Circle, Plane ... . . . . . . . .82

Pole of a Circle in a Sphere.... . . . . . . . . . . . . . . . . . .33

Terrestrial Equator, Meridians, Longitude ............ 34Terrestr ial Lati tude ... . . . . . . . . . . . . .3b

Celestial Poles, Celestial Equator... . . . . . . . .85

Eclipt ic .. . . . . . . . . . . . . . . . . . . . 86

Page 4: Astronomy Relevant to Astrology by v.P. Jain

Zodiac

Celestial Longitude, Declination ... . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

The Right Ascension ... . . . . . . . . . . . . .37

Decil ination Circle, Hour Angle .. . . . . . . . . . . .38

Alt i tude, Azimuth ... . . . . : . . . . . . . . . . . . .39

Zenith, Nadir, Celestial Meridian

Verticals, Prime Vert ical . . . ' i r . . . . . . , . . . . . . . . . . .40

Changes in the Sun's Declination.... . . . . . . . . . . . . . . . . . . . . . . . . . 4l

Obliquity of Equator and Equinoxes .......e...........,... 42

Cneprnn 3

Stars, Planets, Satellites and Solar System ...........44

Eclipt ic .. . . . . . . . .6... . . . . . . . . . . . . . . . . . . . . . . . . 47

Formation of Seasons ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50

Earth on Vernal Equinox and Autumnal Equinox 52

The Moon ,.. . . . . . . . . . . . . . .53

Cycle of Moon.... . . . . . . ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Cneptnn 4

lrru:;:*:::::: :: : :::::::: l lllllji-ll : : llMars, Jupiter , . . . . .58

Saturn, IJranus, Neptune

Pluto .. . . . . . . . . . . . . . . . . . . . . . . .60

Comets

Halley's Comet, Encke's Comet ...............61

Minor Planets or Asteroids, Meteors....................... 61

Meteorites, Kepler's Laws

Names of the days of aWeek...... ............... 62

40

Page 5: Astronomy Relevant to Astrology by v.P. Jain

l ' Why Planets Become Retrograde.... . . . . . . . . . . . . . . . . . . . . . . . . . 64

Cneprnn 5

Precession of Equinoxes ... . . . . . . . . . . . . . . . . . . . . . . . 67

Nutation, Movable and Fixed Zodiacs.... . . . . . . . . . . . . . . . . . 69

Division of Zodiac into Signs and Constellations . 71

Cxeprnn 6

Phases of Moon . . . . . . ,74

Nodes . . . . . . .76

Rahu and Ketu .. . . . . . .77

Sidereal Period, Sidereal Time ... . . . . . . . . . . . ?8

Synodic Period ... . . . . .79

Cnlprnn 7

Lunar Eclipse ... . . . . . . .82

Solar Ec l ipse. . . . . . . . . . . .84

Occultation, Combustion ... . . . . .87

CHeprnn 8

Mean Solar Day ... . . . . . . . . . . . . . . . . . . . . .88

The Local Mean Time ... . . . . . . . . . .89

Units of Time ... . . . . . . . . 91

Units of Measurement of Distance in Space,Light Year, Astronomicql Unit. . . . . . . . . . . . . . . .92

' Parsec ... . . . . . . . . . . . . . . :

Civi l Day, Sidereal Day, Lunar Day or a Tithi. . . . . . .94' Solar Month ... . . . . . . . . . . . . . . . . . . . . . . . . . . . .94

Lunar/Anomalistic Nodical Month......'.................... 95

Lunar/Anomalistic Nodical Year............................... 96

Page 6: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg

Chapter 5

{

Chapter 6

:Chapter 7

Chapter 8

i

Chapter 9

Chapter 10

Chapter 11

Inc lud ing Extra - Saturn ineP lane t s - I nne r and Ou te rPlanets - Retrograde Motion ofPlanets - How the Seven Daysof a Week were Named- Comet

Movable and Fixed Zodiacs -

P recess ion and Nu ta t i on -

Ayanamsha

Phases of Moon - I ts SynodicPeriod - Rahu and Ketu

Lunar and Solar Eclipses andCombustion of the Planets

Local Time, Zonal Time, I.S.T.,Various Units of Time, SolarYear, Lunar Year.

Panchanga - Tithi, Day, Karan,Yoga and Nakshatra

Upagrahas (Astronomical pointson the ecliptic) - Sun and Stars.

Rising and Setting of Planetsand their combustion

Page 7: Astronomy Relevant to Astrology by v.P. Jain

The Sidereal Year, Tropical Year .............................. gb

The Calendar Year .96

98Tithi .........

Karana.... .111

Cneprnn 10

Upagrahas

Comets. . . . . . . . .

tt7

120

122

t24Galaxy, Extra Galactic Nebulae ..........,.125

Cneprpn 1l

Rising and Setting of Planets andtheir Combustion.... . . . . . . . . . . . . . , .127

Diurnal Motion

Longitudinal Motion............... ................. 128Combustion of outer planets ................. 129Combustion of inner planets ................. 131

Test Yourself .......... .................. 135

Index...... ..198

Table of Planetary Movement........... .....t42

Page 8: Astronomy Relevant to Astrology by v.P. Jain

Introduction

The present'book of astronomy has been written forstudents who want to learn Hindu Astrology andpossess knowledge of mathematics up to the 10+2standard and know the elements of plane geometry,algebra etc. Though the book contains the figures ofthree dimensions, yet the students can understandthe astronomical concepts. Using their imaginationsand graspping the points explained.

In writing this book, help has been taken fromthe class notes on Indian Astronomy by Shri R. N.Vashist (I.A.&A.S, Retd.), Elements of Astronomg byGeorge W. Parker, Spherical Astronomg by W. M.Smart and A to Z Astronorng by Patric Moore.

I hope students will find these lessons useful forunderstanding astronomy and i ts ut i l isat ion inastrology.

The book is divided into eleven chapters for a smoothand easy grasp of the su$ect as under:

Chapter I

Chapter 2

Chapter 3 and 4

Astronomy and its HistoricalBackground

Definitions

Ear th and So lar Sys tem

Page 9: Astronomy Relevant to Astrology by v.P. Jain

CHAPTER 1

General

Astronomy is the sc ience which deals wi th theheavenly bodies. Since the man saw the Sun, theMoon, Stars etc., he wanted to find out the reasonbehind them and how day and night, and seasons etc.occur. Thus started the astronomical concept in his-mind.In prehistoric times, our ancestors gazed at theSun, the Moon and other heavenly bodies in the skyand grouped the stars.into constellations and rashis.

HISTORICAL BACKGROUND

Western

His tor ica l l y speak ing , we can d iv ide westernastronomical development, in three eras: ancient,medieval and modern.

Among the ancient astronomers mention shouldbe made of the Greek geometer Pythagorus (562-500BC), who was one of the first to maintain that theEarth was not f lat. He made some study of themovement of planets known in his time. Next cameHeraclides (388-315 BC), a Greek philosopher, whobelieved that the Earth rotated on its axis in a periodof 24 hours. Aristarchus of Samos (310-250 BC) felt

Page 10: Astronomy Relevant to Astrology by v.P. Jain

l0

. J!ni'

ir -r:.

Astronomy Rchootl to Atttology

that the Earth moves in an orbit round the Sun. Hetried to measure the relative distances of the Moonand the Sun, though the results were inaccurate. Nextcame the real breakthrough when Hipparchus ( 190-120 BC) appears to have prepared a star catalogue.The original star catalogue of Hipparchus has notbeen preserved but it would be quite justified to saythat Ptolemy based his star catalogue on that ofHipparchus, who also had discovered the precessionof equinoxes and had even ventured to quantify it bysaying that its rate cannot be less than 36" of an arcper year. The last and really important astronomerof the classical times was Claudius Ptolemy (AD f20-180) of Alexandria. His bookAlmagest has corne downto us through an Arab translation. This book gives agist of the ancient scientific knowledge. Ptolemy lefta star catalogue and data on the motion of planetsand stars. There was an eclipse in Greek astronomyafter him. Their tradition was continued for morethan 1000 years by the Arabs in a subdued form.

Among the astronomers of medieval time the firstlandmark is by Nicholas Copernicus (AD f 4?3-1543)who stipulated that the Sun is the centre of the solarsystem and planets move around the Sun. He was aPolish astronomer and his book was released on hisdeath in AD 1543. The next important astronomerwas Galileo (AD 1564-L642) who was an experimentaltelescope observer. His championship of Copernicustheory resulted in his persecution by the state andthe church. A mention also must be made of theDanish astronomer Tycho Brahe (AD 1564-1601), anexpert observer astronomer of the pre-telescope era.He compiled a star catalogue and made observationson planets. Kepler (AD 1571-1630) used Brahe's data

Page 11: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg

to show that planets move round the Sun in elliptical

orbits whose one focus is the Sun.

He also enunciated the three Kepler's laws ofplanetary motion. Sir Issac Newton (AD 1642-L727)

enunciated his famous laws of motion and built the

f i rs t re f lector- type te lescope, ca l led af ter h im'Newtonian ' . Dur ing th is very per iod, l ived the

Danzig astronomer named Johann Havetius (AD

1611-1667), who had his observatory at Danzig ( in

Poland). He compiled a map of moon and is known

for h is notable s tar cata logue. Dur ing th is very(seventeenth) century, another notable observer

astronomer Christian Huygens (1629-1695), a Dutch

scientist made his contribution by recognizing, for

the first time, the nature of Saturn's rings. Mention

has also to be made of the famous royal (Brit ish)

astronomer Edmond Hailey (AD 1656-1742) who was

not only instrumental in publication of Newton's book

The Pnncipiain 1687, but he also predicted the return

of a famous Comet (Hailey's Comet) many t imes

observed in the past and observed by Hailey in 1672

and after 76 years in 1758 (Its latest return was in

1986.) - also return in 1835, 1911(earl iest seen in2467

BC).

The modern era should be counted from partlyeighteenth century (af ter Newton), n ineteenthcentury and the current twentieth century. This ismarked by building up of many observations, biggertelescopes with more signification and resolution anda large number of astronomers' Brit ish, German,French, American etc.

In the nineteenth century, spectroscopy andphotography were developed which made radical

l l

Page 12: Astronomy Relevant to Astrology by v.P. Jain

changes in experimental and observational f ields.F rom abou t 1870 l a rge re f r ac to r s we re bu i l t

3 ( te lescopes wi th lenses) . Wi th the development ofphotography, human eye was mostly replaced byrecorded photographs. During the twentieth century,larger reflectors (mirrors) superseded the refractor.Radio astronomy made its first appearance in 1930.With the advent of space age in lg57, astronomicalobservations are made from artificial satellites or bylanding of space craft (e.g. on Moon, Venus, Mars etc.).Use was also made of infra-red, X-rays, gamma rayswhich were absorbed in atmosphere. Astro-physicsand as t rospec t roscopy based on ana lys i s o ffrequencies of light received from star lead to manyimportant results regarding content material of aparticular star and its recession, velocity etc.

The name of a few astronomers of this period arementioned below:

(1 ) S i r W i t l i am Hersche l ( l ?38 -1S21) A g rea tGerman observer born in 1781, he discoveredthe planet Uranus (also called Herschel). He alsodiscovered thousands of new double s tars ,clusters and nebulae. He gave an idea of theshape of the Galaxy. His largest re f lectorte lescope had a 49- inch mir ror . His s is terCaroline and his son Sir John (l7gZ-L871) werealso astronomers of repute.

(2 ) F ranc i s Ba i l ey (1774-1894) An Eng l i shas t ronomer who i s remembered fo r h i sobservations of Bailey's beads (brilliant pointsseen along the edge of Moon's disc) at the timeof solar eclipse.

(3) Francois Arago (f786-1853) was director of

Page 13: Astronomy Relevant to Astrology by v.P. Jain

tlstronomg Reletsont to Astrologg

Paris observatory. He devoted himself to many

studies of the Sun.

(4) E W. August Argelander (AD 1799-1875) was a

German astronomer. He produced important

star catalogues.

(5) Sir George Bidell Airy (AD 1861-1892) The

British astronomer royal (7th) was responsible

to raise Greenwich observatory (in England) to

a posi t ion of eminence' and contr ibuted to' astronomy and time-keePing.

(6) Johann Galle (AD 1812-1910) was the German

astronomer, who a long wi th H.L.D. Arrest ,

d iscovered the p lanet . Neptune in 1846. Le

Verrier (AD 18f 1-L877),French astronomer and

mathemat i c ian ' s ca l cu la t i ons l ed to th i s

discovery.

(?) John Couch Adams (AD f819-1892) English

mathemat i ca l as t ronomer made co r rec tprediction of the planet NePtune.

(8) Sir Norman Lockyer (AD 1823-t920) was

English astrophysicist and spectroscopist. He

and Jansen (AD L824'1907), French astronomer,

independently of each other, discovered the

method of observing solar prominences (other

than at the time of total solar eclipse).

(9 ) Asaph Ha l l (AD 1829-1907) Amer i can

astronomer. His discovery of Phobos and Deimos(in 1877) the two satel l i tes of Mars.

(10) Sir David Gil l (AD 1843-1914) was a Scotish

astronomer. He was a pioneer in photographic

mapping of the sky.

13

Page 14: Astronomy Relevant to Astrology by v.P. Jain

t4 Atttortolty Rebooil to lrf,tvfolg

(ll) Bobert Aitken (AD 1864-f 949) was an Amcricanas t ronomer . D i rec to r o f L ick Observa tory(California, 120-inch reflector telescope) and 36-inch refractor ( largest in that category,completed in 1888). Observer of double stars.

(12) S . Wal te r Adams (AD 1876-1936) was anAmerican astronomer. He was director of WilsonObservatory. He did important work in Stellarspectroscopy.

(13) George El ler Hale (AD 1868-1938) was anAmerican astronomer who set up great 200-inch(reflector) telescope at Palomear Observatory(completed in 1948), the largest telescope in theworld for many years. He is also famous forinventing spectroheliograph.

(14) Hanrietta Swan Leavitt (AD f888-1921) AnAmerican woman astronomer discovered 2,400variable stars, four novae, several minor planets(asteroids). She discovered in 1912 the periodTluminosity law of Cepheids.

In the twent ieth centurg great research inastronomy took place also due to advent of space age,ever s ince Sputnik was launched by Russia inOctober 1957. There were Moon landings, and probesinto Venus and Mars, Jupiter and Saturn. It wouldbe di f f icul t to ment ion so many astronomers,astrophysic ists, astrospectroscopists, and spacescientists. However, mention may be made of ClydeTombangh (1907), great American astronomer, whodiscovered the planet Pluto (9th planet) in 1930, withsystematic search from the Lavell observatory inArizona.

Page 15: Astronomy Relevant to Astrology by v.P. Jain

Indian Astronomy

Now we must turn our attention to the origin andhistory of Indian astronomy. It is very ancient, i tpertains to a period much earlier than those of theGreek philosophers and astronomers. It started well,had depth of knowledge, accurate mathematicalcalcqlations, a system of observations (but there wereno telescopes etc.). But, after political subjugation ofInd i ,a , the resul t was burn ing of l ibrar ies andsuppression of intel lectual research. Hence, Indialagged behind in experimental observation especiallyduring the last three centuries

In Adi Rannagano by Valmiki (contemporary ofRama's era), Dasrath talks of start ing of his rahumaraka dasha. He is also and the consequent need ofcoronation of a successor. Then muni Vashishtha( 'ku la purohi t ' ) f ixed pushyami nakashatra asmuhurta for coronation to take place. Since Rama'sb i r t h was men t ioned as hav ing taken p lace i nPunarvasu Nakshatra in Karkat (cancer) lagna,Pushyami was considered auspicious being secondfrom birth Rashi (nakshatra). Again, Ram-RavanaYuddha was initiated on amavasya (considered goodfor starting a war) which ended on the lOth day ofshukla paksha with Ravana oadha. Even till today,navaratra and vijaya dashami are celebrated startingfrom a particular amavasya.

Again, in Mah"abharata, war was stipulated tostart from amavasya. Krishna was described to haveperformed pitritarpan, a day earlier than starting ofwar (due to diference in Ayanamsha calculation).

We have the age-old tradition of astronomy andbased on that of astrology. The two went hand in

Page 16: Astronomy Relevant to Astrology by v.P. Jain

16

\\Astronomg f,choont'f,P A"t .l"gY

glove. It was diflicult to visualise an astrologer who

was not an astronomer and vice versa' The two

sciences were linked tike body and soul' lnBhogowot

Purana, the complete position of planets at the time

of Lord Krishna's birth is given' In Mohobhototo'

Bhishma Pitamaha, the great patriarch of kauravas

andpandavas 'whohad fa l l en in theba t t l e f i e l d ,pierced with arrows shot by Arjuna, would not die

litt ttt" sun becomes auspicious by being towards the

north, uttaragano (i.e. after winter solstice) - around

ZhndDecember. iAl l theseincidentsareampletoproofofexistence

of the deep study of the two d iv ine sc iences of

astronomy and astrology, under igotish shostro' the

science dealing with jyoties, the lights, (lit planets and

heavenly bodies).

In the ancient t imes, al l shastras used to be

studied intensively in ashramas of great gurus, rishis

devoted to learning, who practised yogas and did

Research. The guru used to teach in depth and the

learning process was usually extended over decades'

The truths were committed to heart and memory

through sut ros and aphor isms which were l ike

condensed know ledge . The re was no p r i n t i ng

process. Granths were written in hand on natural

material (leaves etc.) Hence we do not have any books

of ancient times. Nevertheless, knowledge has passed

to us through scholars over the ages'

Now what are the various source-shastras on

as t ronomy and who a re the scho la rs? Surya

siddhanta is one of the oldest siddhantas on the

subject which has come down to us from ages' Even

Varahmih i ra wrote a commentary on lurye

Page 17: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg

siddhanta. Regarding the age of Varahmihira, somefixed it as (AD 550) Varah also mentions in his Pancha

Siddhant ika Arya Bhat ta- (AD 499) . But some

associate Varahmihira to the court of Vikramaditya

of Ujjain. However, everyone knows that vikrami

samvat starts from BC 57 (while saka era starts from

AD 78).

, * Iost o f the Ind ian ast ronomical works are

clairhed as divine revelations to various sages. Some

of these Siddhantas are mentioned:

1., Surya siddhanta 10. Marichi siddhanta

2. Paitamaha siddhanta 11. Manu siddhanta

3. Vyasa siddhanta 12. Angira siddhanta

4. Vashishtha siddhanta 13. Lomasa siddhanta

5. Atri siddhanta 14. Paulisa siddhanta

6. Parashara siddhanta 15. Chayavana siddhanta

7. Kashyapa siddhanta 16. Yavana siddhanta

8. Narada siddhanta 17. Bhirgu siddhanta

9. Garga siddhanta 18. Saunaka siddhanta

In the modern Sansk r i t encyc loped ia , t he

"shabdaKa lpa -Druma" , a l i s t o f n ine t rea t i ses

entitled "siddhanta" is given, which are: Brahma,

Surya, Soma, Brihaspati, Garga, Narada, Parashara,

Pulastya, Vashishtha siddhantas (S. No. 1,4,6,8, and

9 are repetitions here). A lot of research is needed to

establish their origin, era, actual authorship etc.

However, in the present imprecise state of historical

background, and pending further research, we can

broadly classify these under the fol lowing four

categories.

The f irst category clearly claims to be the

t7

I

Page 18: Astronomy Relevant to Astrology by v.P. Jain

\18 Astronoma Releuon\to Astrology

revelat ions and of very very ant ique or ig in andunknown authorship. In this category, we may nameBrahma, Su rya , Soma, B r ihaspa t i and Naradasiddhantas.

(a) Surya siddhanta is at the top of this class ofrevelations. Though it is of unknown ancientorigin, its various translations and editions areavailable. It is stated to be revealed by Sun Godto Asura Maya in 2163102 BC (verses 2-g of Suryasiddhanta Chapter-l). Surya siddhanta has threestages: the original works as it existed beforeVarahmihira; Varaha's adaptation of it with theep icyc l i c t heo ry be ing added to i t ; l a te radaptations and alterations. Its commentatorRanganatha (AD 1608) made it safe from furtherinterpolations and this can be termed as modernSurya siddhanta whose various translations andcommentaries are available.

(b ) B rahma s iddhan ta , sa id to be pa r t o f"Vishnudharamatra Purana", which work itself

i appears to us to have lost , is sa id to be arevelation of Barhma to Narada.

(c) Soma (Moon) siddhanta follows the main systemof Surya s iddhanta. A manuscr ip t o f i t wasavailable in Berlin Library (Weber Catalogue No.840) .

(d) Br ihaspat i s iddhanta is the revelat ion byBrihaspati, the guru of Gods. It is not available.but is referred to quite often as an authority inastronomical issues in many Hindu works onastronomy.

(e) Narada Siddhanta, is also not available. Thereare, however, occasional references to Narada as

Page 19: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg

,,i. an authority in astronomical works. Howeve4Narada Samhita (a course on astrology) was

, available in Berlin Library (Weber Catalotue No.862) .

In the second category, we can l is t worksattributed to ancient and renowned sages i.e. Garga,Parashara, Vyasa, pulastya and Vashishtha (the lastbeing member of the group of great seven rishis -Sapta Rish is-af ter whom a conste l la t ion is a lsonamed).

(a) 'Garga s iddhanta is a lso not avai lab le. Onlyre fe rences to i t a re made in some o the rastronomical works.

(b) Vyasa siddhanta is also not available.

(c) Parashara siddhanta. Second chapter of Aryasiddhanta contained an extract of this work.However, a work called Vrih,atta prashara (awork of system of astrology) is avaiiable in the\ Mackenzie collection (Wilson Catalogue (i) 120).

I(d) Pulastya siddhanta.It is also not available; it is

at times confused with paulisa sidChanta (whichschool of Greek origin was a rival of Arya Bhatta).

(e) Vashishtha siddhanta. Its system correspondswith the Surya siddhanta. More than one treatiseof this name is referred to by Colebrooks andBentley. A later compilation by one VishnuChandra was founded partly upon this siddhantaand partly upon material from Arya-bhatta.Vrihatta Vashishtha siddhanta was in Mackenziecollection (Wilson Catalogue (i) 121).

In the third category, belonging to authorsestabl ished in the later history, we may group

l9

Page 20: Astronomy Relevant to Astrology by v.P. Jain

t 1

Artrotwmy Rohpoa;t io Attrol4l

siddhantas of authors like Aryabhatta, Varahmihira,Brahm Gupta, Romaka Siddhanta.

(a) Arya siddhanta. Two pr incipal works ofAryabhatta-I (AD 499) are -AryaAshotako-shoto

(800 verses) and Dosho Gitiko (10 cantos). BerlinLibrary had a copy (Weber Catalogue no. 834), aworkwhich was a commentary on Dasha, Gitika.

- Bentley had two treatises called Argo Sidd'hontoandLoghu-Arga-Sid,ilhonto. tr,

(b) Varaha siddhanta. A great and knownastronomical work of Varahmihira (AD 550) was

' Ponch-Sidilhantilco (i.e. a cornpendium of 5astronomical works) founded upon Brahma,Surya, Paul isa, Vashishtha and Ramakas iddhantas . I t i s no longer in ex is tence lVrahahamihira's astrological works are howeveravailable.

(c) Brah'-a siddhanta, of Brahm Gupta (AD 628).Its complete name is Brahmo-Sphuto-S iddhonto.'Colebrooke and Bentley had its copies. On it was

' founded Bhaskra's (AD 1150) SiddhontoShiromoni. Khondokodhyoko is anotherimportant work of Brahm GuPta.

(d) Romaka siddhanta. Colebrooke links it to anauthor Srisena.It is founded partly on Vashishtasiddhanta. It has been cited by Varahmihira inhis Poneho Sidilhantika.

In the fourth category, we may put later texts of

known time and authorship. These are not so originalworks, but are mostly compilations, adaptations, and

commentaries based on earlier siddhantas.

(a) Siddhanta Shiromani, of Bhaskrra Acharya of

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Astronomg Releoont to Astrologg

twelfth century (AD 1150). It is founded uponBrahma siddhanta of Brahm Gupta (AD 628). Itis cited very frequently. It is a very prominentwork.

(b) Bhoja siddhanta. It was published during there ign o f Ra ja Bho ja o f Dhar in 10 th-1 l thcenturies.

(c) 'iSiaAhanta sundara. It was composed by Gnan,Raja in the sixteenth centurY AD.

(Q)' Graha-Laghav. A much venerated treatise, it is' a composition of Ganesha (AD 1520)-

(e) Siddhanta Tattva Viveka. It was composed by

Kamalakara (AD 1620).

(f) Siddhanta sarbhauma, authoredbyMunishavara(son of Ranganatha, commentator of Suryasiddhanta).

(g) Of the above, modern publications are those of

the Surya siddhanta of Ranganatha, theSiddhonta Shirotnani, and Groha Loghao, andthese should be available in the market with

some effort. There are numerous other minorworks of an era later than sixteenth century'

In the above historical discussion' some of the

important astronomical scholars and writers could

not be covered. A mention of those left over scholars

must also be made brieflY. These are:

NAME WOBK

2L

Lata Deva (AD 505) :(Pupil of Arayabhatta-I)

Lalla (AD 748) :

Expounder of Romakaand Paulisha siddhanta

Sisya Adhivriddhida

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22 Astronomg Releoont to Astrolory

NAME wonKManjula (AD 932)

Sripati (AD 1028)

The Laghumanasa andthe Brahma Manasa

The Siddhanta Sekhara

The basic astronomical time-frame used in Suryasiddhanta is amahaUuga, which consists of 4 yugos -sotyo or kritgo, treta, drsapor and koliyugo. Amahaguga is fixed at 4,320,000 solar years and isdivided in the four yugas in the proportion of 4:3:2:1,thekoligugo being the shortest i.e. 482,000 years. Tbismahaguga has significant in so far as all planets andall nodes and epicycles of conjuctions complete theirfull revolution in this period (with no fractions left)and, hence, all will start afresh from their originalpositions.

From compar ison o f var ious as t ronomica lcons tan ts , such as the number o f p lanetaryrevolutions (including those of Moon's nodes) in amahoyugo, dimensions of Epicycles of Apsis,dimensions of Epicycles of conjuct ion (SighraEpicycles), Geocentric orbitals etc., we observe thatthere was a Surya siddhanta even before Arya-bhatta-I (AD 499) who adopted the elements as theycame down to him. However, these constants werechanged in Khondakodhoyolco (Brahm gupta), byVarahmihira, and in the modern Surya siddhanta atthe beginning of the sixteenth century after makingBiia corrections.

Number of revolutions of variots planets andother crucial points, inaMohoyugoof 4,320,000 solaryears, is.given in the table on the next page.

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S. PlanetNo.

According Accordingto Khandak to Surya-adhyaka siddhanta

ol Varaha

According toModern Suryasiddhanta(Ranganatha's)

Number afterBijaGorrection

1. Moon

2. Sun

3. Mars

4. Jupiter

5. Saturn

6. Moon's. Apogee

7. Venus

8. Mercury

9. Moon's

Node

57,753,336

4,320,000

2,296,824

364,220

146,564

448,219

7,002,388

17,937,000

232,226

57,753,336

4,320,000

2,296,824

364,220

146,564

448,219

7,022,338

17,937,000

232,226

57,753,336 57,7s3,336

4,320,000 4,320,000

2,296,832(+8) 2,296,892

364,220 364,212 (- 8)

146,568(+ a) 1a6,580(+ 12)

448,203(- 16) 448,199(- 4)

7,022,376(- 12] 7,022,364(-121

17,937,060(+ 60) 17,9s7,044(-16)

232,2fi(+ 121 232,242(+ 4l

No. of civil days according to Khandakadhayaka= 1577,912,800 days

(from Aryabhatta-I's Ardharatriko)

No. of civil days according to Varaha's Surya siddhanta= 1577,912,800 days

(from pancha Siddhantika)

No. of civil days according to modern scientist= 1577,912,828 days

There were measurements and constants also fordimensions of epicycles of Apsis, of the .sighra'Epicycles, Geocentric orbitals inclinations of planets.The B i ja cor rec t ions were made a t about thebeginning of the fifteenth century (source Bentley).

Number of total revolutions of the asterisms(nakshatras) in a mahayuga is: l,S8Z,Zl7,g2g (Verse34 of Chapter I of Suryo Sidd.lr.antd. This gives us the

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24 Astronomy Releoont to Asfiology

number of sidereal days \n arnahaguga.

Thus f rom a compar i son o f as t ronomica l

constants we can say that Surya Siddhanta was in

existence much before Varahamihira's time and he

was one of the first to improve upon and update it.

The mean time of one sidereal revolution of the

various planets in mean solar days according to

modern Surya Siddhanta and with Bija correction is

given below:

Planet Tlme of Sidereal Revolution

In Mean Solar days as Corrected by theBUa in ltlcan SolarDaye

SunMercury

VenusMars

Jupiter

SaturnMoon Sidereal Rev.

Synodic Rev.

Apsis

Node (Rahu)

365.25875648

87.96970228

224.698567s5

686.99749394

4,332.32065235

10,765.77307461

27.32167416

29.53058795

3,232.09367415

6,794.39983121

87.96978075

224.69895152

4,332.41581277

10,764.89171 783

3,232.12015592

6,794.2828084s

The number of oscillations of Equinoxes is fixedat 600 (due to precession of the Earth's axis) in

4 ,320,000 years , wh ich means one comple teoscil lation is estimated to take 7,200 years. The

Ayanamsa was zero at the beginning of koliguga and'

was again zero at AD 499 (the time of Aryabhatta-I)421 Saka (or 3600 years reckoned from the beginning

of koligugo 3102 BC). (Chapter III, verses 9 - 12). The

Page 25: Astronomy Relevant to Astrology by v.P. Jain

No. of years of Treta andDwopar Yugas

No. of years of Kaligugaelapsed (up to AD 499)

Total

No. of oscillations ofEquinoxes (x/7200)

annual rate of precession (mean rate) works out to

54" of an arc per solar Year.

Total number of years that are estimated to have

elapsed since the beginning of creation up to AD 499

can be calculated as follows:

No. of years since creation to the

end of the last Y*itaguga 1953,720'000

2,160,000

3,600

1955,883,600 (x)

27L,65bV2

In the mean position of an oscillation, Ayanamsa

is zero. The circle of constellation was about to

oscillate eastwards at AD 499 Surya siddhanta was

thus revealed 2,163,600 years before Aryabhatta- I.

Most of the ancient Hindu scientific astronomyappears to be re-established in the era of Aryabhatta-I, as all calculations start from AD 499 according to

Aryabhatta- I and the modern Surya siddhanta.Aryabhatta is also taken to be the father of Indian

Epicyclic astronomY.

Now let us compare the times of revolutions for

various planets as given in Indian classical works like

Surya Siddhanta (as corrected from time to time, which

corrections are not very substantive) with the periods

as now known to western modern astronomers.

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26 ttstronomy Releoant to Astrolosr

Planet Dlstance Sldereal(million Period of amlles) Revolutlon

modern

Accordlng toIndlan Sources

SynodlcPerlodic(days)

Mercury

Venus

Earth/Sun

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

Moon

Perigee

Apogee

36 86 days

67.2 224.7 days

92.957 365.3 days

141.5 687 days

483.3 11.9 years

886.1 29.5 years

1783 84.0 years

2793 164.8 years

3667 247.7 years

distance time offrom Earth revolution(miles)

221,460 27.32 days

252,700

115.9 days

583.9 days

779.9 days

398.9 years

378.1 days

369.7 days

367.5 days

366.7 days

Synodicalmonth

29.53 days

87.97 days

224.7 days

365.26 days

687 days

4332 days

1 0766 days- (not given)- (")- ( ' " )

Siderealtime ofrev. according tolndian Sourcee

27.32 days

If we compare with the periods of revolutionsworked out by Aryabhatta-I, Varahmihira, BrahmGupta and in the modern Surya Siddhanta (thedifference between all corrections spread over a 1000years being quite minor compared to the original),the difference with modern astronomical values ofthe same are found to be astonishingly small. It is awonder how the aneient astronomers could work outthese time periods so accuratelywithout even havingthe advantage of modern powerful astronomicalinstruments and facilities.

Main points of difference between modern westernastronomy and Indian classical astronomy

1. The Western astronomical calculat ions areheliocentric. Taking the Sun as stationary in the

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Astronomg Releoont to Astrologg

solar system, all the planets are moving round itin somewhat Elliptic Orbits in time periods oftheir own. Of course, now the Sun is also takenas moving (along with the solar system) in ourGalaxy (the milky way) and this Galaxy is alsomoving in space and the space itself is expandingoutwards. The Indian classical system, on theother hand, is Geocentric with the observer (onthe Ear th ) as the cen t re and a l l ne t (o rcompounded or resultant) motions of the planets(including the Sun, nodal and other points) beingmeasured relative to the Earth.

The planets (as well as astronomical crubialpo ints l ike Nodes, Equinox, the Apsis , andMandochha, the Conjuction or the Shigrochhae tc . ) have a l l been a l l o ted a number o frevolutions in a mahaguga of 4,920,000 solaryears. The mean period of a revolution is fixedon ly by d i v id ing th i s ( common t ime o f atnalr,agugo) by the number of revolutions foreach. The time is reckoned from the beginningof the L]niverse. No such absolute motion fromtime of the commencement of the Universe isfollowed in the western astronomy. Of course, theIJniverse is now stated to have originated in asplit second, with a big bang (out of nothingness),about 20 billion years ago. How the two ideascorrelate to each other is a matter for modernresearch.

The sidereal location of stars is fixed from zerodegree of a fixed Aries (Ashivini) with a starryreference point at the end of Revati Nakshatraand the star Revati.lnchitrapaksha system, thiszero point of Aries is 180' exactly opposite the

3.

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28 Astronomy Releoont to Atttology

star Spica (chitra). The western astronomers'however, follow a moving point of zero reference,

i.e. the Equinox posit ion of the Sun each year is

the first degree of Aries. The zero Aries of the

west is at present actually about 6Yt" in Pisces of

the Indian system. The angular distance between

first point of the fixed Aries and of the movable

Ar ies , i s ca l l ed Ayanamsa . I t i s (Lah i r i

Ephemer les or Chi t ro Poksho) 23"45 '51" on

1 .1 .1993 .

The Wes te rn as t ronomy fo l l ows Eqa to r i a lLongitudes of al l the heavenly bodies, while

Indian c lass ica l ast ronomy fo l lows s idereal

longi tudes. The former are ca l led Sogtono

longitudes and the latter, Niragana longitude =

Sayana Longitude - Ayanamsa. The Ayanamsa

changes every year by about 50.3" of an arc due

to the p recess ion o f Equ inoxes o r due to

wobbling circular motion of the Earth's axis(which is 23Yz' inclined to the perpendicular to

the plane of the ecliptic but is also performing a

conical rotation).

The system of measurement of time is different.

Day is related to the Earth's spin on its axis and

in Indian system it is measured from sunrise to

next sunrise. Month is related to Moon's motion

round the Earth and related to Phases of the

Moon. It is measured from arnauas to next

arnauas (Moon's exact conjuct ion i .e . same

sidereal longitude as that of the Sun). Year is

measured w i th Sun ' s s ide rea l ( re la t i ve o r

apparent motion in the Ecliptic) from zero Aries

to next zero Aries or from Equinox to Equinox.

Thus, we have civil days,lunar months and solar

4.

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Astronomg Releoont to Astrology

Year or about 365y4 days, with months dividedinto 30/31128129 days and each day divided into24 hours (midnight to midnight). F\rrther, localt ime was fo l lowed in Ind ian sys tem wh i lestandard zonal times are followed for countriesor zones in a country in the modern (Western)

system. This local noon is mid-day locally andlocal midnight ls Ardharotri (half point of ratrt-rnan).

Indian system followed observations by thenaked eye and calculations were by structureslike Sun-Dial, making use of geometric shapesand algebraic and trigonometric calculations.The concepts of Deoatas of. Mandochho andSighrochh,o (the point of the slowest motion i.e.Apsis, and the point of the fastest motion etc.)that is, accelerating and retarding the relativemotions by pulls on the planets (of differentastronomical points) in different directions(forward and retro) were followed. Later on' anepicyclic theory was adopted.

The Western astronomy followed Kepler's lawsof planetary motion, modern mathematics anddetailed calculations. Telescopic observationswere taken. Photographic records of position ofheaven ly bod ies and sk ies were made.Spectroscopes were used to analyse light spectra,and from the study of shift of the frequencies ofl igh ts emi t ted by s ta rs , the i r mot ion wasdetermined; from the study of their individualspectra, their composition was ascertained. Ftomparallax studies, the distance of various heavenlybodies (of planets, stars, galaxies and supernova)were estimated. With telescope of very high

29

5.

Page 30: Astronomy Relevant to Astrology by v.P. Jain

6.

resolution power, the double (twins) stars werediscovered.

In Indian, astronomy and astrology developedas a twin science. If former is the body of thisscience, the latter is its soul. Both were part andparcel of this divine knowledge and were linkedto philosophy - cyclic origin of the Universe, itsmaintenance and destruction by the AlmightyBrahma and its regeneration. Jyotish was aVedanga.

In the West, astronomy developed more as asecular, physical, science.

Both, however, tried to fix the position of planets,Sun and Stars, and determine the i r mot ion(velocities and directions). But, whereas, Indiansystem concentrated on angular posit ion andmotion only, the western system also worked outlinear distances and linear velocities.

In Indian system, position and motions of certainastronomical points were studied in addition tothose of physical bodies e.g. Nodal points of theMoon and various planets, Motion of the Apsisof the orbit, motion of Conjunction points, andother astrologically important positions (Mandi,upagrahas , yogas , Ka ranas , ascens iona ldifferences, right ascensions, meridian cusp etc.)were also astronomically calculated.

*,

{ :i)

7.

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CHAPTE R2

Important Definitions

1 SPHEBE

If a circle is rotated around one of its diameters,

the f igure so formed is a sphere. Examples of

spherical surfaces are: ball, football, orange etc.

The centre of a circle is equidistant from all thepoints on its circumference and the centre of the

circle is the centre of the sphere and equidistant from

all the points on its surface.

Radius: Half the diameter of a circle or sphere is

called radius. In other words, the distance betweenthe centre of a circle or a sphere and any point on its

circumference or surface is radius of the circle or the

sphere.

2 CELESTIAL SPHERE

The Earth is also spherical and if the surface of

the Earth is projected infinitely in the heavens, the

figure so formed will be celestial sphere.

In other words, celestial sphere is a sphere of

infinite radius compared with any distance on the

Earth, so that the Earth occupies the position in the

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Astronomg Releuont to Astrologg

centre of this imaginary sphere.

. It can be explained as under:

If two persons are standing at two diametrical lyoppos i te po in t s on the Ear th , each w i l l see an

. apparently concave hemispherical surface of theheavens. I f both the hemispher ica l sur faces arejoined, a celestial figure of a sphere is obtained.

3 GREAT CIRCLE

Any plane passingthrough the centre of asphere cuts the surfacein a c i r c l e wh i ch i scalled a great circle, or

A great circle on thesurface of a sphere is acircle whose diameterspass through the centreo f t he sphere i . e . t he Figure 7

centre of the sphere is the centre of the great circleAOB is a diameter of the sphere. The circle AEB is agreat circle in figure 1. A great circle always dividesthe sphere in two hemispheres.

4 SMALL CIRCLE

Any plane not passing through the centre of thesphere cuts the surface of the sphere in a small circle.Its diameter or radius is shorter than the diameteror radius of the sphere or great circle. Circle CFD isa small circle in figure 1.

5 PLANE

If a plane surface is extended infinitely, it is called

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Astronomr Relersant to Astrology

a plane (in mathematical terms) i .e. i f the top of thesmooth table is extended infinitely, the surface soformed by the top of the table will be a plane.

6 POLE OF A CIRCLE IN A SPHERE

The concept canbe well explained withthe help of the figure 2.

In figure 2, APBQis a sphere whosecentre is O. The plane AAEB cuts it and makesa g rea t c i r c le AEBwhose centre is O.

The p lane CFDwhich is parallel to theplane AEB is cutt ingthe sphere in a smallcircle with i ts centre at O'. Now OO' is producedupwards and downwards to meet the sphere at p andQ. The points P and Q are the poles of circles on theparallel planes to these circles.

The properties of the pole are:

(1) The straight line joining the poles cuts the circlesat right angles of which these are poles.

(2) The lines on the surface of the sphere joiningthe two poles also form an angle of 90" with thesecircles.

(3) A pole'has only one great circle on which the' line joining the poles form a right angle.

(4) Every great circle will have two opposite poles. on the sphere, where all lines (circular) drawn

Ftgtre 2

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Astronomg Releoont to Astrologg

at right angles to the circumference of the said

<rf circle will meet.

7 TERRESTRIAL EQUATOR

In the figure 2 on the prepage' let the Earth be

the sphere, P and Q be its poles, the great circle AEB

will be the terrestrial Equator. The terrestrial Equator

i s a g rea t c i r c le d rawn round the Ear th bu t

perpendicular to its axis. The Earth's axis is passing

through its North Pole P and South Pole Q. In the

figure 2 P and Q are called the terrestrial poles.

Te r res t r i a l Mer id ians : Any g rea t c i r c le

terminated by P and Q is a terrestrial meridian. In

the figure 2 the curved lines joining the poles of the

Earth P and Q are terrestrial meridians.

F i rs t Mer id ians: Pr inc ipa l Mer id ian: The

meridian passing through Greenwich observatory(near London in England) has been regarded as theprincipal meridian by universal agreement.

8 TEBRESTRIAL LONGITUDE

Let PRQ (f igure 2) be the principal meridian,

cutting the Equator at R, and let PLQ be any other

mer id ian cu t t i ng the Equa to r a t L . The ang le

subtended by these two meridians is called longitude

i.e. angle ZPcOL is the longitude of meridian PLQ

there O is the centre of the earth. If this meridian is

in east of the prinipal meridian, the longitude will be

east and if it is in west, the longitude will be west.

Spherical angle RPL between the two meridians (one

is the principal meridian) at the pole also measures

the terrestrial longitude of the meridian PLQ.

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Astronomy &eleoont to Astrologg

9 TERRESTRIAL LATITUDE

In figure2,let M be a place at meridian PMLQ,themeridian cutting the Equator at L. The great circlearc ML is the latitude of the place. Angle ZMOL willalso represent the same thing (as the great circle arcwill also be measured in angles). If the place is inNorth of Equator, it is called north and if it is in south,it is called south. All the plaies lying at one meridianwill have the same longitude.

All the places lying at the srr,all circle passingthrough, say, M, and parallel to the Equator will havethe same latitudes. So, latitudes are also defined.asparallel circles to the Equator at different angulardistances i.e. all the places lying on the circle CMFDwill have the same terrestrial latitude.

Note.' Celestial Poles, Celestial Equator, CelestialLongi tude, etc. wi l l be wr i t ten Pole, Equator,Longitude in the following pages.

IO CELESTIAL POLES

If the axis of the Earth is extended infinitely itwill cut the celestial sphere at two points known ascelestial poles. The extension of the axis northwardswill meet at the North Pole and extension of the axissouthwards will meet at the South Pole.

ll CELESTIAL EQUATOn

Celest ia l equator is the great c i rc le on thecelestial sphere whose plane is at right angles to thedirection of Celestial pole.

It can also be termed as the projection of Earth'sEquator on to the celestial sphere. The great circlethus projected on the celestial sphere will be known

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Astrotwmg Releoont to Astrologg

as the celestial Equator.

12 ECLIPTIC

Ecliptic is the apparent annual path of the Sunamongst the fixed stars on the cosmic sphere. It isinclined at 23'28' to the celestial Equator.

Actually it is the Earth that is moving round theSun. So exactly it is the projection of the earth'sannual path round the sun on the cosmic sphere.

t3 zoDIACZodiac is an

imaginary belto f about 9onor th and 9osou th o f t he E

ecl ip t ic where c

the Moon andall the planetshave the i rmovement.

In theFl,gure 3

figure 3 of the celestial sphere, EQ is the celestialEquator, AB is the ecliptic inclined at angle of 23o28'to the Equator, CD and FG are circles parallel to ABat a distance of 9o in north and south. The beltbetween CD and FG is known as Zodiac and eclipticis in the middle of this belt i.e. the space covered byCAF moving around the sphere passing through Dand G is known as Zodiac.

The following are the definitions which areexplained in2.l7.

Celestial Latitude of a heavenly body is its

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Astronomg Relevant to Astrologg

distance from the'ecliptic measured north/south ofthe ecliptic on an arc perpendicular to it.

14 CELESTIAL LONGITUDE

Celestial Longitude of a heavenly body is theangular distance between the first point of Aries andan arc perpendicular to the ecliptic drawn throughthe body. It is also defined as angular distance of theheavenly body measured along the ecliptic from thereference zero point.

15 THE DECLINATION

The declination of a heavenly body is its angulard is tance f rom the Equator measured on an arcperpendicular to the celestial Equator drawn throughthe body.

16 THE RIGHT ASCENSION

The r ight ascension is the angular d is tancebe tween the f i r s t po in t o f A r ies and an a rcperpendicular to the celestial equator drawn throughthe body, this first point of Aries being on Syanasystem i.e. the Vernal Equinox.

17 In figure 4, S is the star,

EOE'is the Equator,

AOB is ecliptic,

OO' points. of inter-section of EE' and AB,

O is the first point of Syana Aries (Vernal Equinox),

P & Q are North and South poles,

P', Q'are Eclipt ic poles,

P'SN is perpendicular from P'on ecliptic through S,

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Astronomg Releoont to Astrobry

PSM is perpendicularfrom S to Equator,

Arc SM is Declination

Arc OM is RightAscension (RA),

Arc SN is Latitude,

Arc ON. is Longitude(Syana).

Note: The defini-t ions of terrestr ia llatitude and longitudeare totally differentfrom those of celestial

C.l.dhl Sphcr.

Fiaurc 4

latitude and longitude.

18 DECLINATION CIRCLE

Parallel of Declination is a small circle throughthe star parallel to the celestial Equator. Each starrotates round the celestial pole on its parallel ofdeclination.

Secondaries to a great circle are the great circleswhich are perpendicular to i t . Thus, meridianthrough a star will be a secondary through it on thecelestial Equator.

19 HOUR ANGLE

The angle which the meridian makes through astar with the observer's meridian is known as hourangle. When the star is at the observer's meridian itshour angle is zero. It is said to transit or culminate.Then star's meridian moves gradually towards westand completes a circle (with the Earth's rotationbeing West to East) in 24 hours. When the star is to

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AstronomA Releoont to AstrologA 39

the West of the observer's meridian, its hour angle isbetween 0 hour and 12 hour: when it is in the East itshour angle is between 12 hour and 24 hour.

20 ALTITUDE

The altitude of a heavenly body is its distancefrom the horizon measured on the vertical drawnthrough the body, form the zenith of the observer tothe horizontal circle. It has been explained in figure5 below.

2T AZIMUTH

Azimuth of a heavenly body is i ts angulardistance on the horizon between the North point ofthe horizon to the foot of the vertical drawn throughthe body from the zenith of observer as explainedbelow.

NCS is the horiz-on ta l g rea t c i r c lecalled horizon, O isthe observer and Z,the Zenith. N

P i s t he Nor thPo le ,andXas ta r .

The p lane NCS,the ho r i zon , i s a tright angles to OZ.

C.l..tl.l Sph.r.

Figure 5

Great circle ZXC is perpendicular to the horizonmeeting at C.

CX is altitude of the star. AXB (small circle) iscalled the parallel of altitude. Vertical circle throughP and Z cuts the horizon at S and N. The point S is

Horizon W C

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Astronomg Releoant to Astrologg

the south point and N, the north point of the horizon.The west (W) and East (E), also cardinal points onhorizon, have an angle of 90" from N and S points.

The arc NC expressed in the angle is called theAzimuth (W) as it is towards west.

Thus, the position of a heavenly body can also bedescribed completely with reference to the horizon.

22 ZENITH

Zenith is the.point of intersection of the celestialsphere with the plumb line produced upwards i.e. apoint on the celestial sphere which is vertically abovethe observer's head.

23 NN)IN

Nadir is the point of intersection of the celestialsphere with the plumb line produced downwards i.e.a point on the celestial sphere which is just belowthe observer's foot.

24 CELESTIAL MERIDIAN

Celest ia l meridian is a great c i rc le passingthrough the celestial poles and zenith of a place. It isalso called observer's meridian or prime meridian.

25 VERTICALS

Great circles drawn perpendicular to horizonform the zenith are called verticals. These are alsocalled secondaries to the horizon.

26 PRIME VERTICAL

The vertical drawn due east and west and at rightangles to the celestial meridian is the prime vertical

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Astronomy Releoont to Astrologg

of a place

Changes in the Sun's Declination

At the spring (Vernal) equinox the declination ofthe Sun is zero, it being at A (Figure 6) on 2lst March,this point is also the first point of movable (Syana)

Aries. The declination increases every day as the Sunis moving on the ecliptic until it reaches the point C(Figure 6) , the point o f greatest dec l inat ion i .e .23'28'(N). This point is called the summer solstice.It happens on or about 2lst June. After that thedeclination of the Sun starts decreasing as the Sunstarts moving southwards. It decreases and becomeszero on (or about) 23rd September when the Sunreaches at B (another point of intersection of eclipticand Equator). Now the Sun goes to south of theEquator and its declination becomes south.It reachesat point D on (or about) 21st December which is calledthe \trinter Solstice

Fl,gure 6

The declination of the Sun becomes 23"28'(S)after that the Sun starts moving Northwards and its

4 l

?1a

21st Junr

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42 Astronomg Releoont to Asfiolory

south declination decreases gradually till it reacheszero on 21st March.

Sun's declination at Vernal Equinox on 2lst Marchis 0o.

Longitude and RA = 0o

Sun's declination at Summer Solstice on 21st Juneis 23"28'(N).

Longitude and RA = 90o

Sun's decl inat ion at Autumnal Equinox on 2lstSeptember is 0o.

Longitude and RA = 180"

Sun's declination at winter solstice on 21st Decemberis 23"28'(S).

Longitude and RA = 2?0"

It is also pointed out that the latitude of the Sunis always zero as.it moves along the ecliptic.

When the Sun starts moving northward from.position D (Figure 6), it is said that the Sun hasbecomd Uttragan and it remains uttrayan from D toC i .e. 2 lst December to 21st June and becomesDakshinagon while moving from C to D i.e. duringthe period 21st June to 21st December.

Obliquity of Equator and Equinoxes

The angle between the planes of Ecliptic andEquator is 23'28'. It is said to be the obliquity of theecliptic to the Equator.

Every year on two days the Sun crosses theEquator and its diurnal path almost coincides withthe Equator rising in the east and setting in the west.One-half of its diurnal path is above the horizon andthe other half below. So the day and night are equal

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Astronomg Releoont to Astrologg

on these two days. These two points are ca l led

equinoxes. When the Sun is going from south to north

of the Equator, the point of intersection with the

ecliptic is called the first point of (Sayan) Aries and

when it is going from north to south, it is entering

Libra. The position of first point of Aries occurs on

or about 21st March and that point is called spring

Equinox or Vernal Equinox. When the Sun is on the

other point i.e. about 23rd September, that point is

called the Autumnal equinox.

The altitude of the star is greatest when it is onthe meridian i.e. when the star is on the observer'smeridian, it is at upper Culmination or in transit.After that the altitude starts declining.

The altitude of the celestial pole at any place isequal to the latitude of the place i.e. at Equator itwill be zero which means the poles will lie on thehorizon.

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CHAPTER 3

General

Before proceeding to the Solar System, we mayexplain the terms stars, planets and satellites.

Stars: Stars are self-luminous bodies which emitlight and heat in the space. The Sun is a star. Starsare grouped into constellations.'

Planets: Besides the fixed stars, the Sun and the '"'

Moon, there are other heavenly bodies visible to thenaked eye and moving around the Sun. As theirmotion is whimsical among the fixed stars, they arecal led planets or wander ing stars. A f ixed starappears twinkling while the planets shine with steadylight. The planets which can be seen by the nakedeye are Mercury, Venus, Mars, Jupiter and Saturn,while the other planets lJranus, Neptune and plutoare seen only with the help of telescopes.

Satellite: Satellites are those heavenly bodieswhich move around the planets and in turn movearound the Sun along with the planets and arenormally called moons of the planets, like the Moonwhich is a satellite of the Earth.

Solar System: The Solar System made up of the

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Astronomg Releuont to Astrologg

Sun, planets, satel l i tes, comets, minor planets, andinterplanetary dust, gas etc. It is a very small part ofthe Universe and seems important to us only becausewe happen to l ive inside it .

As the Sun is also a star and is at one focus of theorb i ts of a l l the p lanets revolv ing around i t , thesystem is called the Solar System. In this system, onlythe Sun is emitting light. Rest of the family membersof the Solar System are revolving around it and arenon-luminous. The other important members of thisfamily viz. the planets, satellites to various planets,comets, minor planets, meteors, meteorites etc. alsoform part of the Solar System.

Our Solar System is centred round the Sun andthe planets are moving in elliptical orbits around it.There are nine planets in al l i .e. Mercury, Venus,Earth, Mars, Jupite4 Saturn, IJranus, Neptune andPluto, out of which we are living on the planet Earth.Our ancients could see Mercury, Venus, Mars, Jupiter'and Saturn (in addition to the Sun and Moon whichare also called planets (grahas) in astrology) by thenaked eye. Actually, both of these are not planets.While the Sun is a star, the Moon is a satel l i te. Butthe word Grahas is loosely understood as planets.

With the invention of telescope, several otherlarge planets and many small ones could also be seen.The names of the planets known at present in theirorder of distance from the Sun are:

inner planets orinferior planets

MercuryVenusEarth

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46 Astronomg Releoont to Astrologg

MarsThe asteroidsJupiterSaturnLJranus (Herschel)NeptunePluto

Their orbits are shown in order of their distancefrom Sun i.e. the nearest orbit to the Sun is nearerand the farthest orbit is away from the Sun. (figure 7).

The planets whose orbits are between the Sunand orbit of the Earth are called inner or interior orinferior planets i.e. Mercury and Venus are innerplanets. While the planets whose orbits lie outsidethe orbit of the Earth are called outer or exterior orsuperior planets. Mars, the asteroids, Jupite4 Saturn,tfranus, Neptune and Pluto are the exterior, outerplanets or superior planets.

Sun: The Sun is the most important of all theheavenly bodied to the inhabitants of the Earth. Itsrays supply light and heat etc. not only to the Earthand those who live on it us but to the other planetsand other family members of the Solar System. TheSun controls the motions of all its family members.Its influence on our day-to-day life is supreme andwe cannot imagine our existence without it.

I ts diameter is 865,000 mi les, i ts volume is1,300,000 times that of the Earth, and its mass is330,000 times the mass of the Earth. It is producingenergy by a nuclear reaction, converting hydrogeninto helium and losing its mass at the rate of 4 milliontons per second. It lies well away from the centre ofthe Galaxy, nearthe edge of a spiral arm. The distance

touter planets Ior superior planets

L

I

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Astronomy lteleoont to Astrologg

FVue 7

between the Sun and the galactic centre is about30,000 light years. It is sharing the general rotationof the Galaxy with velocity about 135 miles per secondand take s 225 mill ion years to complete onerevolution.

Ecliptic Ecliptic is a great circle on the celestialsphere whose plane passes through the Earth whichis at its centre. It is the apparent yearly path of theSun round the Earth in that plane. Here we haveassumed that the Sun is moving round the Earth- IfSun was to move in a circle round the Earth, thediameter of its disc would not have changed atdifferent times during ayear it goes through a regularcycle of changes throughout the year. Being 32'36',Itis greatest in early January and it is least in earlyJuly, when it has a value 3L'32'which shows that inearly January it is nearest to Earth and in early Julyit is farthest from it. The difference between the twovalues of the disc is not much and, therefore the path

47

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is nearly, circular.

Earth: The Earth is the planet on which we live'

Though we claim that we know a lot about our planet

but the fact is that our knowledge about the planet is

very limited.

It is the third planet in order of the distance from

the Sun. The mean distance from the Sun and the

Earth is92,957,209 miles. As the orbit of the Earth is

not a perfect circle, it is an ellipse, and the Sun is at

one of its foci. The minimum distance (when the

Earth is at perihelion) is 91,400,000 miles and the

maximum distance (at aphelion) is 94,600,000 miles'

Its mass is about 6 x 102t tons and its mean density is

5.52 times that of water. Its atmosphere is made up

of nitrogen (??.6 per cent) and oxygen(20.1per cent).

Earth is not a perfect sphere but is called an oblate

bpheroid. Its diameter is ?,926 miles when measuredalong with the Equator and ?,900 miles as measured

through the poles.

The lengths of one degree latitude at differentparts of the Earth are as under:

at the Equator = 68.704 miles per one degree

at latitude 20" 68.786 do

,at latitude 40" = 68.993 do

at latitude 60' = 69.230 do

at latitude 80o = 69.386 do

the arc of Equatorfor one degree = 69.17 miles

= 60 nautical miles

The Earth is revolving round the Sun in an orbitnearly circular and it completes one revolution

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Astronany fuboont to Astrologg

around the Sun in nearly 365y1days.

The Earth is rotating round its axis from west toeast and it causes the formation of day and night andthe daily revolution of the Sun and fixed stars fromeast to west. The axis of the Earth is perpendicularto its Equator i.e. its North Pole is on one end of theaxis and its South Pole on the other. In turn, the NorthPole of the Earth is facing the Polar Star.

Change of Appearance of Sky Due to Change ofPlace of Observer on the Earth

When the obser-ver is at the Equator,his horizon wil l begreat circle passingthrough the poles(see f igure 8) and Npoles will be on thehorizon. If a personon the Equator likesto see the Pole star,he can see just on thehorizon in the Northdirection i.e. at the

Ftgure 8

point where the Earth and sky appear to be meeting.

As the observer starts moving northwards, thePolar Star will appear to rise in latitude which canbe seen in figure 9. Let the observer be at O. Hishorizon will be a great circle AB and he will be seeingthat the Polar Star has an angle equal to the latitudeof the place of observer.

The Polar Star will go on rising and will be seenabove observer's head i.e. in the zenith, when he

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Astronomg Releuont to Asttologg

reaches at the NorthPole of the Earth (see

figut" 9). In this case, hishorizon coincides withthe celestial Equator.

As the observer goesto the South o f theEquator, the Polar Starw i l l be be low thehorizon of the observerand he will not be in aposition to see it.

From the above diagrams it will be noticed that

an observer can see only half the sky at a time while

on the Earth and half the sky below the horizon is

invisible to him.

FONMATION OF SEASONS

Seasons are formed due to the constant obliquityof the Earth's axis with the plane of its orbit (90' -

23o28'= 66o32').

The Earth is revolv ing round the Sun andcompletes one revolution in a year = 365.2422 dayswhich is also called the tropical year.

In the figure 9A the Earth is revolving round theSun. EQ is the Equator, AB and MN are tropics ofCancer and Capricorn respectively. ab and mn arethe arctic and antarctic circles. N and S are NorthPole and South Pole respectively of the Earth, andNS is the axis which is inclined at an angle of 66o32'to the ecliptic. O is the centre of the Earth. Considerthe paper on which the figure is printed as the planeof ecliptic, the axis NS is inclined to the plane of paper

Figure 9

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Astrotw.mg Rz<boont to Astrologg

trtryre 9.tl

by 66o32' in all the four positions. In positior. l, ttJeEorth is ot sumrner solstice (right side fiWre).In thiscase, the North Pole is bent towards the Sdn.

The Sun is making an angle of g0o with the tropicof Cancer i.e. it is shining vertically at it and there isno light at the South Pole as secn by the position I infigure 9A. \ilhcre thc South Pol'e rc.mains incontinuous darkness i.e. continuous day onthe NorthPole and 6 months night on the South Polc. Thichappens on 21st June every yeen In thic cese, the Sunremains ebovc horizon for morc than twclvc hourrin Northcrn hemlsphcrc and lcss than 12 hourr lnthe Southcrn hcmlrphcrc "and it ls rummcr lnNorthcrn hcmirpherc but wintcr ln Southcrnhcmlrphcrct'.

Ecrtlr ot thr ulntc rohtlcr 0qft.rld..tlgrr.) tnporltfon E.

Thc Sun lr mrklng tn tnglc of g0o wlth thc truplcof Crprlcorn and thc North Folc lr rwry fbom thc SunmrLlng rn obturc rnglc. In thr cur thr porltlon lr

5 1

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52 Astronomg R eboont to Astrobgg

reverse of position 1 i.e. in the Northern hemispherenights are longer (of more than 12 hours duration),winter season. It is middle of 6 months long night atthe North Pole and middle of 6 months long day onthe South Pole. In the Southern hemisphere, the daysare longer than nights and season is summer. Thishappens on about 22nd December every year.

Eenrn on Vnnxer, Eeurxox eno AUTUMNAL Eeurnox

In positions 4 and 2, the Earth is on the vernaland autumrial equinoxes. On these times the Sunshines vertically on the Equator of the Earth and boththe hemispheres and both the poles are equidistant(angular) from the Sun. It happens on about 21stMarch and 23rd September every year. The days andnights are of equal duration all over the world.

In position 1, the Earth is at a greater distanceform the Sun (near aphelion point) and Northern Poleis inclined towards the Sun while the Southern Poleis away from the Sun. In position 3, the situation isreversed. The seasons are not due to the distance ofthe Earth from the Sun but there are two reasons forit: (1) The Sun remains for a longer time above thehorizon every day in summer than in winter. (2) Insummer, the Sun attains a greater meridian altitudethan in winter i.e. the rays fall more slanting in winterthan in summer. It can be illustrated as under:

From S (Sun), rays AB are falling on the Earthand covering lesser area AB in cone SAB. With thesimilar cone SCD the rays are covering more areaCD on the Earth which can be explained in the waythat shorter surface AB is receiving the same amountof heat as CD (which is greater surface) is receiving.

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Astronomy Releoont to Astrology

Figure 70

The amount of heat received by 'ihe unit area in ABwill be more than that of CD. So, AB will be hotterthan CD.

THE MOON

Moon is the Earth's only satellite. Moon is themost important of all the heavenly bodies to us afterthe Sun.It is also having its diurnal motion from eastto west like other heavenly bodies due to rotation ofthe Earth on its axis. Like the Sun and other planets,it is also moving among the fixed stars in oppositedirection (west to east) making a complete rwolutionin about 27 days 7 hours and 43 minutes i.e.27.3217days i.e. the sidereal month is defined to be theinterval given by the Moon's complete circuit of thestars as seen from the Earth, being its mean value,27.32L7 mean solar days.

The synodic month of the Moon is the period fromone ornooosgo to another omooosoglo and is29.5305887 mean solar days. It is more than siderealmonth, because during the Moon's one revolution,Sun too moves by about one sign, and some moretime is required for the Moon to catch up with theSun to have next corfunction (omooasogo).

53

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Astro*omg F.ebo ont b Aslr.obgg

If the Earth's 0orce of gravitational attraction isto be considered, the orbit of the Moon would havebeen an ellipse but due to the Sun's attraction andthat of other planets, the orbit undergoes intoconsiderable hanges. Its mean distance from theEarth is 238,000 'les

wl^l -h varies from 22L,460 milesat perigee to 252, 100 miles at apogee.

Owing to these perturbations, the direction of itsperigee is altering. The time taken by the Moon inmoving around the Earth from perigee to perigee isknown as animalistic month which is equal to 2?.5546mean solar days.

A nodical month is the time taken between twosuccessive passages of the Moon through ascendingnode which is equal to 27.2122 mean solar days.

The Moon's orbit can be inclined to the eclipticmaximum by an angle of 5o15' on either side of theecliptic i.e. North and South latitudes of the Moonwill nevcr exceed 5o15'.

Moon's apparent diameter varies between 29'22"and 33'31" and the mean diameter is 31tt'nearly. Thcalbedo is low which is about ? per cant only (i.e. only? per cent of the light received by it iJ reflccted). Thcsurface grivity is only one-sixth that of the Eerth.

The Moon ls having a captured rotation i.e. ltkccps the samc face turned towerds thc Eerth. \[tccan sGs 59 pcr cent of thc total surfacc of thc Moon atono timc or anothan

Man flrst reeched the Moon ln July 1965 whcnNeil Armstrong stcpped out from spacccraft Eejlc.

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Astronomg Releoont to Astrologg

CYCLE OF MOON

Meton discovered in 433 BC that in every 19 yearsthere are 235 lunations i.e. 365.25 x 19 = 6939.75 daysin 19 years and 29.530588?x235 = 6939.688 days in235 lunar months. It shows that all the phases of Moonwill occur again on the same days of the month as 19years ago, the only difference being that they willoccur about one hour earlier. It is called metonic qcle.It gives a readymade method of predicting dates ofpuntima, arnaoosya etc. without much calculations.Study of ancient Hindu astronomy shows thatMetonic cycle was known to our rishis and they added7 oilhik or extra lunar months in 19 solar years toproduce an exact correspondence in solar years andlunar years (year of 12 lunar months).

55

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CHAPTE R 4{ i

General

We have already studied in chapter 3 that the planets

are moving around the Sun in elliptical path and thatthe Sun is at one of their foci.

Though there is no direction in the space, alld i rec t ions are re la t i ve ones . Suppose you arestanding in front of a pedestal fan which is movingin the clockwise direction. If you stand behind it, you

will see it moving in anticlockwise direction, whichis our direction too round the Sun.

For the inner planets, a planet will be called inlnfertor coniunction when it come between the Earthand the Sun'and in supertor conjunction when theSun is between the Earth and the planet. Conjunctionis actually due to the two being in the same line ofour sight.

For superior or outer planets, a planet will be saidto be in opposition when the Earth is in between theSun and the planet. An outer planet can never comein between the Sun and the Earth and cannot havean inferior conjunction. It has superior conjunctionwhen it is on the far side of the Sun.

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Astronomg Releoont to AstrologY

MERCURY . :

Mercury is the first planet in order of distancefrom the Sun i.e. it is the nearest planet to the Sun.It was earlier believed that Mercury had capturedrotation (88 Earth days), but now it is known that therea l ro ta t ion per iod o f Mercury i s 58 .65 days ,approximately two-thirds of a Mercurian year. Theinterval between one sunrise to another will be 176days or two Mercurian years. The orbit of Mercury ismore eccentric than of other planets of the Sunexcept Pluto. The maximum distance of Mercuryfrom the Sun is 43,000,000 miles and the minimumdisteance is 28,000,000 miles which is due tothe orbitbeing more eccentric. Maximum inclination of itsorbit is about 7o on either side of the ecliptic. Itsdiameter is about 3000 miles.

VENUS

Venus is second nearest planet to the Sun i.e.after Mercury it is the next planet nearest to the Sun.

The maximum inclination of its orbit to theecliptic is about 3o24' on either side of the ecliptic. Itis brighter than any other planet or star and casts itsshadow many times. Its mean distance from the Sunis about 67 million miles and its diameter is about7,500 miles.

Venus and Mercury are inner planets which canbe seen near the Sun (either east or west). These aretherefore called the morning or evening stars as theyare visible either just after the sunset or before thesunrise.

Its sidereal period of revolution is 224.7 days, butsynodic period (with the Sun) is 584 days.

57

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Astrorwmg Releo ont to Astrobgg

MARS

Mars is the fourth planet in order of distance fromthe Sun and the nearest outer planet to the Earth.Its diameter from the Sun changes from 127,000,000miles to 153,000,000 miles.Its diameter is 4,200 miles.When the Mars is closest to us, it is within 35 millionmiles form the Earth and it occurs when the Mars isat the least distance from the Sun and the Earth is atthe greatest distance from the Sun. In this case theplanet outshines the other stars except Venus. Butwhen i t is the fa intest , i t s inks to the secondmagnitude and can be confused with a star. Near thequadrature, it appears strongly gibbous. Its siderealperiod of revolution is 687 dyas and synodic periodis ?80 days.

There are two satellites of Mars, named Deimosand Phobos, which were discovered on 5 September,1877 when the Mars was in opposition.

JUPITEB

Jupiter is the largest planet. It is more massiveplanet than all the other planets combined togethenIts mass is only 1/104? times of the Sun. As it flattenson the poles, its Equatorial diameter is over 88'000miles and polar diameter is less than 8{,000 miles.Its mean distance from the Sun is 1183.3 million miles.Its sidcrcal perlod is 11.9 yeers.

Juplter shows ycllowish dlsc, crosscd by famouseloud bclts.

Therc sro llxteen satcllltcs of whlch the mostimportant erc four, namcly, Ior Europa, Ganymcdcand Cellirto.

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Astronomg Releoont to Astrolagg

When seen through a telescope, a number ofbright belts or bands are seen encircling the planetparallel to its equator which may be of clouds orvapours in its atmosphere.

SATURN

Saturn is the sixth planet in order of distancefrom the Sun. Its mean distance from the Sun is 886million miles and diameter is about 74,000 miles. Itsdensity is less than water. It is much larger and moremassive than any other planet (except Jupiter). Itsorbit is nearly circular and inclined about ZYz" to t}reecliptic. It is surrounded by circular rings which donot touch the surface of the planet. Formerly, onlynine satellites were known but now 20 of its satelliteshave been d iscovered. I t s s iderea l per iod o frevolution is about 29.5 years.Its synodic period (withthe Sun) is only 378 days.

UNANUS

fJranus was discovered by William Herschel inMarch 1781. The planet is known as lferschel alsoafter the name of its discoverer. Five satellites areknown till now.It is very far.Its distance is about 1783million miles and its diameter is only about 32,000miles. Hence, it is invisible to the naked eye.It is alsovery dim.

NEPTUNE

As a result of calculations by Leverrier andAdams, Neptune was discovered in 1846 by J Galleand H D Arrest, at the Berlin observatory. Its distanceis 2?93 million miles and sidereal period 164.8 years.Its brightness is even much less than that of Uranus,

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Astrono.ny Releoont to Asttologg

and it is very faint. :

PLUTO

The pluto is the ninth planet. It was discoveredby Clyde Tombaugh in 1930.Its orbit is most eccentricof all the planets. For most of the 248 years period, iti s much fu r ther ou t than Neptune; bu t nea&perihelion, it is closer to Sun than Neptune. Its meandistance from the Sun is 3667 million miles, and itsdiameter merely 1800 miles, and extremely lowmagnitude.

COMETS

Comets differ widely from the planets, both intheir physical state and in the nature of orbi tsdescribed around the Sun. Comets are generally abril l iant nucleus surrounded by nebulous matterstretching out into an elongated tail. All the cometsdo not develop tails and many are nothing more thantiny patches of luminous haze in the sky. They appearshining due to the reflection of sunlight by them.

The masses and density of comets are small andcan easily be perturbed by planets. They appearsuddenly in the sky and can be seen for some days,weeks, or months and when they reach near the Sunand then recede from it and disappear.

The comets whose motion can be calculated andthe dates of their return predicted are called periodiccomets. The .notion of some comgts is direct whilethat of others retrograde. It is to be noted that thennotion of all the planets around the Sun is in onedirection i.e. direct if viewed from the Sun.

Among the'periodic comets', Halley's c6met and

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Astronong Releoont to Astrologg

Encke's comet are more remarkable.

Halley's Comet

Ha l ley 's comet was f i rs t seen in 1531 andafterwards in 1607, 1682, 1758-59, 1835, 1910 and laston 9 February 1986. It has a period of 76 years. Itsnext return is expected in 2061.

Enckets Comet

Its periodic/time is 3.3 years. At perihelion, itcomes closer to the Sun than does Mercury and ataphelion, i.e. at its greatest distance, it is more than4 times the Earth's distance from the Sun.

Non-periodic comets are much more numerousthan periodic. These comets are seen only once andafter that they are lost in the space and never comeback.

Minor planets or asteroids. The diameter of theasteroids is small, and the largest of them has adiameter of 623 miles. Their orbits are very eccentric.The number of asteroids is very great which isestimated to be 40,000. Due to their low masses, theescape velocities will be low. All of them have theirindividual orbits in an asteriod belt between theorbits of Mars an Jupiter. But, some of these, becausetheir orbits, are very eccentric, come inside the orbitof the Earth or even that of inner planets.

METEORS

Meteors are small particls, usually smaller thana grain of sand, moving freely around the Sun. AMeteor cannot be seen in space as it is very small butis heated by friction when it enters the Earth'satmosphere.It is destroyed but during the process it

6t

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62 Astronom! Releoott,to Astrolqr

produces luminous effect. Due to their luminouseffect meteors are also called the shooting stars.

Meteorites: These are relatively larger bodies,big rocks etc., which do not get completely burnt upin atmosphere before reaching the Earth's surface,and which produce craters etc. or get buried deep.

Keplerts Laws

The laws according to which the planets movearound the Sun were discovered by John Kepler(1571-1630) which are given below.

I Each planet moves in an elliptic orbit with theSun in one of the oci.

U Equal areas are covered in egual times by theradius of the planet i.e., by the line joining theplanet and the Sun.

UI The squares of periodic times of the planets areto one another as the cubes of their meandistance from the Sun.

Though the three laws of Kepler have beenstated, the use of the same is otside the scope of theselessons.

The Scheme trbllowed for Keeping the Names ofthe Days of a Week

In Indian Jyotish, the duration of day and nighthas been divided into 24 parts which is called hora.One hora is equal to an hour. The names of the daysare kept on the basis of the lord of the first hora ofthe day. The lords of the horas are according to theplanets. Now see the following scheme. Verse 31(shloka 31) of chapter XII of Surgosidhonto of

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Astronomg Releoant to Astrologg 63

Mahabir Prasad Srivastava, Edition II.

q<z4l_q8{ga qd gfr"g+€-{,qft etdr: t tAg t t

According to thearound the earth ofo rder o f Saturn ,Jupi ter , Mars, Sun,Venus, Mercury andMoon. Keep theplanets in a circle inthis order.

Th is o rde r i sactually the order ofthe p lanets in the i rdecreasing s iderealperiod or increasingangu la r mo t ion ,Sa tu rn be ing theslowest and the Moon

shloka, the orbits of revolutionthe various planets are in the

Figwe 77

being the fastest.

Now we start from Sunday (the name kept afterthe lord of first hora), the second hora on Sundaywill be of Venus (counting anticlockwise), the thirdhora of Mercury, the fourth of Moon, the fifth ofSaturn, the sixth of Jupiter, the seventh of Mars, theeighth of the Sun and so on the fifteenth of the Sunthe twenty second of the Sun, twenty third of Venus,twenty fourth of Mercury, twenty fifth hora i.e. firsthora of the next day will be of the Moon, so the nextday was named after Moon i.e. Monday.

Now we count from Moon.

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Astronomg Reboont to Astrolagg

Hora 1

Lord Mon

23Sat Jup

56

Sun Ven

4

Mars

Hora 8 15 22

Lord Mer Mon Mon

23 24 25Sat Jup Mars

twenty fifth hora is the first hora of the next day,so the day was named after Mars (aapl the name ofday (aa77a7V1i.e. T\resday. Similarly, of other week-days were named as given in the table below.

Lord of Name of thefirst hora day

Lord of Name offirst hora the day

Sun

Moon

Mars

Mercury

Jupiter

Venus

Saturn

Sunday

Monday

Tuesday

Wednesday

Thursday

Ftiday

Saturday

Ravi

Soma

Bhauma/Mangal

Budha

Guru

Shukra

Shani

Raviwar

Somawar

Bhaumawar/Mangalwar

Budhawar

Guruwar

Shukrawar

Shaniwar

WHY THE PLANETS BECOME BETROGNAI)E

First of all we take up the case of an inner planet.Let it be Mercury. The Sun is in the centre aroundwhich all the planets, including the Earth, aremoving. Mercury is nearer to the Sun and i tcompletes one revolution in 88 days. The Earth isaway from the Sun and completes one revolution in365yt days. So, the angular velocity of Mercury isfaster than that of the Earth. The arrows in the figureare showing the direction in which Mercury and theEarth are moving. The arrow on zodiac indicates thedirection in which the longitudes among the fixed

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Astronomg Releoont to Astrology

Figure 72

stars are increasing.

As the longitudes are geo-centric, suppose theobserver on the Earth is stationary and Mercury ismoving in the direction of arrow with a relative speedof the Earth (i.e. Mercury's speed - Earth's speed).Let the observer be at O. As we are considering theobserver and the Earth to be stationary and Mercurymoving with a relative speed, let the Mercury be at Aand it will be seen at A,; in the zodiac, it moves furtherto B and seen a t Br ; in zod iac , C, D, a re thecorresponding positions of C and D. Here, longitudesare increasing. When it comes to E, the longitude isincreasing at E, which is nearly the position of atangent from the observer to the orbit of Mercury. AtE, the planet will appear stationary as you will seethat it is going to change its motion from direct toretrograde. It can be well understood by an examplethat a boy runs straight and touches a point and runsback. He will have to stop for a moment for reversingthe speed. Similarly, here the planet will appear

65

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Astronomg Releoont to Astrologg

stationalry at E. Consider its further positions 4 G,H and I . I t w i l l be seen that the correspondingbackground at the zodiac will be seen backward atFr, Gr, H, and Ir t i l l i t reaches J and its correspondingpos i t i on J , i s seen a t t he zod iac . I t i s seen i nretrograde motion as its geo-centric longitudes aredecreasing. When it is at J and the line OJ,, which isnearly tangent to the orbit of the planet, it will beseen as stationary in the zodiac as the longitudes willne i t he r i nc rease no r dec rease fo r some t ime .Afterwards it goes to K etc. when the correspondingposition in the zodiac will be K, etc, It will be furtherseen that the longitudes have started increasing i.e.the planet has become direct.

Similarly for the outer planets we can justify theretrograde motion by making the observer move andplanet being stationary as the outer planets moveslower than the Earth.

iIt is to be noticed that the inner planets become

retrograde when they are in between the Earth andthe Sun and the outer planets become retrogradewhen the Earth is in between them and the Sun i.e.they are nearer to the Earth.

Note: See Toble of Planetary Mooement on pageno. L42.

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CHAPTER 5

Precession of Equinoxes

By continuous observation our rishis found out thatthe longitudes of stars are increasing. Later on, thesame phenomenon was no t iced by the Greekas t ronomer H ipparchus (190-120 BC) . Theyconsidered two possible explanations for this: (1) Thestars are moving but the movements of all the starswere mostly identical which was impossible. So theydiscarded it. (2) The first point of Aries twhich is the, intersect ion of ecl ipt ic and celest ia l equator) isshifting backward. They also observed that there wasno appreciable change in the latitudes of the stars..So, they came to the conclusion that the ecliptic wasa fixed plane. Accordingly, it was necessary to assumethat celestial equator and the first point of Aries weremoving in such a way that the longitudes of the starswere increasing. It clarifies that the vernal equinoxis moving backwards. The precession of equinoxesis mainly due to the attraction of the Sun and theMoon on the protuberant portions of the Earth at theEquator. The result is that the Earth has a slowwobbling motion, so that the point in the heavens (thecelestial pole) describes a small circle of about 47oangular diameter round the pole of the ecliptic. This

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Astronomg Rehoont to Astrologg

results also in change in the identity of the polar starfrom one era to another.

I t can be we l lcompared w i th thewobbling of the axis ofrotation of a spinning-top, which has beendisturbed to createwobbl ing f rom i tss. teady spin state,when its axis gets outof the vertical.

The weight of thetop wh ich , ac t ing

. A

FlAtre 73

vertically downwards at G, tends to pull the axis ofrotation AB away from CA (the vertical), but, due tothe fast speed of spinning, it will not fall down andthe axis AB will describe a cone round AC such thatthe angle CAB remains constant. Similarly theexpanded Earth's pole (celestial pole) is revolvinground the pole of the ecliptic in a small circle. As aresult of this, the Equator plane is also changing andcutting ecliptic plane at shift ing point. The slowbackward motion of the first point of Aries is calledthe precession of equinox.

When the attracting body reaches its greatestnorth or south declination, the disturbance is greatestand it is zero when they are on the celestial Equator.The luni-solar precession is in the ratio of 7:3 i.e. theeffect of Moon's attraction is more than twice that ofthe Sun i.e., two-thirds of the whole. The total of thetwo affects amounts to about 50'.35 yearly while thatof planetary precession the affect is 0".11 annually.

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Astronomg Releoont to Astrologg

:'The mean net annual precession, which is also calledgeneral precession, is about 50'.24 each year, on an

average.

As the distances of the attracting bodies i .e. the

Sun, Moon, planets, asteroids, comets etc. change,

the value of precession also changes. The circle on

the celestial sphere is of only 47o diameter viz DB =

47" and takes 25,800 years to complete.

Its effect is important. Due to shifting of poles,

the celestial Equator also moves ,'rnd, in tunn, theposition of vernal equinox, that is the first point ofAries, also changes.

NUTATION'

The effect of Sun's and Moon's attraction is not

constant. Moon is sometimes above and sometimesbelow the ecl ipt ic and therefore i ts pull on theequatorial bulge of the Earth is not always in the samedirection as that of the Sun which results in the

nodding of the celestial pole to and from the pole ofthe ecl ipt ic. This nodding is cal led nutation. Theresult is that the precession is sometimes more andat other times less than its mean value by about 9seconds of arc to either side in a period of 18 years

220 days or, say, 182/, years in which Moon's nodesmake complete revolution in the heavens.

ITIOVABLE AND FIXED ZODIACS'

Zodiac is an imaginary belt of about 9o North orSouth of the ecliptic within which the Moon and allthe planets (except Pluto) remain in the course oftheir movement.

The fixed zodiac is one in which the first point of

69

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Astronomy Releoont to Astrologg

Aries is always fixed in the nakshatras i.e. always atan angle of 180" to Chi t ra star. The longi tudesmeasured with reference to this fixed first point ofAries which has a permanent position on the eclipticfixed among the stars are called Niragana longitudes.They are divided into twelve rashis such as Mesh,Vrish etc. This fixed zodiac is also divided into 27nakshatras. Thus the Nirayana rashis always containthe same star groups/constellations.

The other zodiac is called movable zod,iacltropical zodiac. In this the first point of Aries is thevernal equinox i .e. the point where the ecl ipt icintersects the celestial Equator and it precedes byabout 50".3 each year as already explained earlier inthis chapter. Due to attraction of the Sun and theMoon on the protuberant portions of the Earth onthe Equator, the first point of Aries moves slowly inthe direction opposite to that of the yearly motion ofthe Sun. The longitudes measured in this system arecalled tropical or Sayana longitudes. The twelve signsin this system are of 30o each starting from springequinox and these signs do not always cover the samespan of 30' over the ecliptic as in Nirayana system.Under this system, the star composition of zodiacsigns goes on changing with the passage of time.

The angular distance between the first point offixed Aries and the movable Aries i.e. vernal equinoxis called Ayanamsa. In other words, it is the angulardistance by which the vernal equinox has movedbackwards from the time the two zodiac systemscoincided.

The year in which the two first points of Ariescoincided is taken as 285 A.D. according to which the

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7 1

\

Astronomg Releoont to Astrology

Ayanamsa on 21st January 1993 was 23"45'55" (as per

Rash t r i ya Panchanga) . I t i s based on therecommendation of the Calendar Reform Committeeappointed by the Government of India which adoptedth i s sys tem o f Ayanamsa in 1953 . Under th i sAyanamsa system both first point Aries were deemedto have coincided on Sunday the 22nd Mareh of AD285 and hence Ayanamsa on that day was zero.

Therefore,Sayana longitude = Nirayana longitude * Ayanamsa.

In Indian astrology, we use Nirayana longitudes.

DIVISION

Zodiac has been divided into twelve rashis eachof 30 ' and the i r Ind ian names have been g iven

according to the shape of the stars in it.

(3) Gemini = Mithuna (9) Sagittarius = Dhanus

(4) Cancer = Karkata (10) Capricorn = Makara

(5) Leo = Simha (11) Aquarius = Kumbha

(6) Virgo = Kanya (12) Pisces = Meena

From ancient times, the Nirayana zodiac has alsobeen divided by our rashis into 27 constellations(nakshatras). These nakshatras are group ofstars andeach nakshatra is of tto/r, = 13o20' portion of thezodiac. Their names are:

(1) Aries = Mesha

(2) Taurus = Vrisha

(1) Ashwini(3) Krittika(5) Mrigashirsha

(7) Libra = Tula

(8) Scorpio = Vrischika

(2) Bharani

(4) Rohini

(6) Ardra

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Astronomg Releoont to Astrologg

(7') Punarvasu (8) Pushya

(9) Ashlesha (10) Magha

(f 1) Purvaphalguni (I2) Uttaraphalguni

(13) Hasta (14) Chitra

(15) Swati (16) Vishakha

(17) Anuradha (18) Jyeshtha

(19) Mula (20) Purvashadha

(21) Uttarashadha (22) Shravana

(23) Dhanistha (24) Satabhisha

(25) Purvabhadrapada (26) Uttarabhadrapada

(27) Revati

The Nirayana rashis and nakshatras have anunchanging relationship with each other. Thesenakshatras and rashis are in the order as given above.Corresponding longitudes of nakshatras startingfrom the first point of Nirayana Aries are as shownbelow.

Each nakshatra has a prominent identifying starafterwhose name the nakshatra is called. These starsare called Yogataros

After completing one cycle of 0o to 360" again thesame rashis and constellation come i.e. after 360o =

0o Mesha and Ashwini start.

1. Mesha 0o to 30"

2. Vrisha 30o to 60o

3. Mithuna 60o to 90'

Ashwini 0o to 13o20'Bharani 13o20' to 26o40'

Krittika 26o40' to 40'Rohini 40" to 53"20'

Mrigashirsha 53o20' lo 66o40'Ardra 66o40' to 80oPunarvasu 80" to 93'20'

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Astronomy F'eleoont to Astrology 73

4. Karkata 90oto 120"

5. Sinha 120'to 150'

6. Kanya 150'to 180o

7. Tula 180 ' to 210 '

8. Vrishchika 210' lo 240"

9. Dhanus 24O"1o270"

10. Makara 270o to 3fi)'

11. Kumbha 300'to330'

12. Meena 330'to 360'

PushyaAshlesha

MaghaPurvaphalguni

UttaraphalguniHasta

ChitraSwatiVishakha

AnuradhaJyeshtha

MulaPurvashadha

UttarashadhaShravanaDhanishtha

SatabhishaPurvabhadrapada

UttarabhadrapadaRevati

93'20' to 106o40'106'40' to 120"

120" to 133'20'133'20' to 146'40'

146'40' to 160"160' to 173'20'

173'20' to 186o40'186'40' to 200'200" to 213o20'

213"20'ts. 226"40'226"40 to 240o

24O" to 253"20'253o20'to 266'40'

266'40' to 2801280' to 293o20'299"20' to 3'06"40'

306o40'to 320"320' to 333'20'

333"20 to 346'40'346'40' to 360'

A Glimpse of

KERALA ASTROLOGY -o. P. vermaThe present work A Glimpse of Kerala Astrology iscondensation of three recognised Kerala classics KeralaJyotisha, Kerala sutra and Gopala Ratnakara which are uniquein their own way & speak out the essential, principles of KeralaAstrology. We suppose our readers will be enlightened by thesei l luminatingpearlsof KERALA ASTROLOGY. RS. 100/-

Page 74: Astronomy Relevant to Astrology by v.P. Jain

CHAPTER 6

Phases of Moon

The Moon has no light of its own but it reflects thelight received from the Sun. It revolves round theEarth and i ts path is incl ined at an angle of 5oapproximately to the ecliptic. So, the eclipse cannottake place on every arnap&sga and purnimo. (It willbe explained in the next chapter.) The Earth is in thecentre wi th O as i ts centre and there are eightpositions of the Moon shown around the Earth (seefigure 14 on the next page). The sunrays are comingfrom the left. L is the centre of the Moon and O thatof the Earth. Join OL and draw a perpendicular to it.Name it AB which bisects the sphere of the Moon intwo hemispheres. The hemisphere towards the Earthwill be visible from the Earth. The sunrays are comingfrom the left as the Sun is very big and at a very greatdistance as compared to the Moon's diameter and itsdistance from the Earth. We can easily assume therays to be parallel. Draw CD perpendicular to the raysof the Sun on the Moon. The side opposite to thedirection from which the sunrays are reaching theMoon will be dark as no sunrays are falling on thatportion of the Moon. It has been shown as shaded.The other position on which the sunrays are falling

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Astronomg Releoant to Astrologg 75

---+Sun rays

+

-_+

-------+

- t -

- 6

->Sm rays

-)

Figure 74

is le f t b lank and th is hemispher ica l por t ion isreflecting light in the space and seen by the observeron the Earth as bright portion of the Moon.

When the Moon is in the position l with respectto the Earth and the Sun i.e. the Earth is in betweenthe Sun and the Moon, AB and CD coincide, theilluminated portion of the Moon being towards theEarth and the full disc of the Moon i.e. illuminatedhemispherical position is seen. This is the positionon purn ima. In pos i t ions 2 and 8, about three-quarters of the disc of the Moon is seen as the portionvisible are BLC and DLA which is more than half ofthe hemisphere of the Moon receiving light from theSun. In positions 3 and 7, the CD is perpendicular toAB. So, only half of the illuminated hemisphere of

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76 Astronomg Releoont to Astrolory

the Moon can be seen and as such half of the disc i.e.BLC and ALD is visible. The remaining half of thehemisphere towards the Earth is not receiving anylight of the Sun; so, it does not reflect any light, and,as such, is invisible to us. It happens on'oshtorni' daysof the shukla paksha as well as the krishna paksha-

The only difference is that the half disc that is brighton shulclo ashtami is dark onkrtshno oshtami and viceversa. When the Moon is in positions 4 and 6, lessthan half of the disc is visible as less than half theilluminated hemisphere is BLC, ALD being towardsthe Earth.

In position 5, AB and CD coincide again and darkportion of the Moon is towards the Earth. So, theMoon cannot be seen and it happens on arnavosAa-The shape of the Moon seen on a particular positionis a lso shown near each pos i t ion . Here , thehemisphere of the Moon towards the Earth is shownas a circle with bright half as blank and the darkportion as black.

NODES

Nodes are the points at which the orbit of the' Moon, or any planet cuts the plane of ecliptic. Duringthe course of its movement (i.e. of the Moon or therespective planet) when the said heavenly bodycrosses the ecliptic plane, the crossing points arecalled nodes of the Moon or of the respective planet.

When the Moon or the respective planet crossesthe ecliptic while going from north to south, thecrossing point is called descending node. In theformer case, the latitude of the Moon or the saidplanet is zero while changing from the positive to the

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DescendingOrbit ofMoon

Ecliptic

' Figwe 75

negative. The line joining these two nodal points issaid to be the line of nodes or the axis of the nodes.

RAHU AND KETU

Rahu and Ketu are the nodes of the Moon. Whenthe Moon crosses the ecl ipt ic while going from southto north of the ecl ipt ic, i t is the ascending node ofthe Moon which is called Rahu. The latitude of theMoon at Rahu is zero and is on the increase from thenega t i ve ( sou th ) t o the pos i t i ve (no r th ) . Wh i l ecrossing the ecliptic going from the north to the southi.e. the descending node of the Moon is cal led Ketu.In figure 15, while there appear four points of inter-section, in space (3 dimensions) there wil l be onlytwo, i.e. between thick (front) lines and the thin linesonly. So, Rahu and Ketu are actually not any physicalplanets but are the points on the plane of eclipticwhere the Moon crosses it.

This is the reason for calling these two as chhagagrahas, i.e. shadowy planets. At these points, theMoon and the Sun get ecl ipsed on poornima otarno,DosAa respectively, if on these tithis they are onor near these chhaga grah"as. These are also called

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78 Astronomg Releoont to Astrologg

dragon's head and dragon's tail. These points are notstationary but take about 18 years 220 days i.e. 18.60years in making a revolution around the Earth. Thismotion is non-uniform like that of all planets. Givenhere is the average period of motion. Their motion isin reverse direction than that of other planets. Inother words, they move in the zodiac in reversedirection. So, they are said to be having a retrogrademotion at an average or mean rate of about 19.36"each year or about 8" an hour. They have true or meanlongitudes according to whether we have used meanmotion or calculated actual position.

SIDEREAL PEBIOD'

Sidereal period or periodic time of a planet is thetime taken by it to make a complete revolution withreference to the fixed stars. In the case of the Moonit is 27 days 7 hours and 43 minutes. This is theminimum sidereal period among nava grohos. Themaximum sidereal period is that of Saturn which is29.46 so lar years. Af ter consider ing the ext raSaturnine planets, the maximum sidereal period isthat of Pluto i .e.248.4years.

SIDEREAL TIME

Time, includingsidereal time, can be measuredin many ways. Sidereal day is the time elapsed sincethe precedding transit of Sayana first point of Ariesto the next transit of the meridian of a place.In otherwords, one sidereal day is the time taken by the Earthin completing one rotation with respect to a fixed starwhich is equal to 23 hours 56 minutes and a fewseconds.

This sidereal day is expressed in sidereal hours

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Astronomy Relersont to Astrologg

and minutes. one sidereal day is equal to 24 siderearhours. One such hour comprises of 60 minutes etc.

It can be observed that a fixed star which is risingalong the Sun will rise about 4 minutes earlier thanthe sunrise next day i.e. the sun has moved r. in thezodiac.

If an observer continues to observe the sky forone month, he will notice that the sun has risen lrashi after the fixed star. After one year he wilr noticethat the same star is rising again with the Sun.

As the Earth is moving round the Sun and theSun is f ixed, the earth completes one revolutionaround the Sun in one year. The Earth rotates aroundits axis once in a day. The same part of the Earthappears approximately 365 + I = 366 times in frontof the same fixed star in a year (appro_ximately 36bsolar days) or the lst point of Aries has transited themeridian 366 times in a year of 365 days and 36? timesin a year of 366 days i.e. a leap year. Therefore, asidereal day is shorter than the solar day by 2ah.rs/365 .25 = 24 x 60 /365 .25 = B m inu tes 56 secapproximately

SYNODIC PERIOD

Synodic period is the interval of t ime whichelapses between two oppositions or two conjunctionsof a superior planet. In case of inner-planets it is thetime between two conjuntions of the same typewhether they are both inferior or superior.

It can be explained as under:

The Sun is stationary. The planets (including theEarth) are revolving around it. The earth compietes

79

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80 Astronomy Releoont to Astrology

one revolu-t ion in ap-proximatelY365 dayswhile Merc-ury com-pletes it in 88days.

In thefigure 16, letE be theEar th , M,

For inner plan€ts

Figure 76

Mercury and S, Sun. EMS is the inferior conjunctionof Mercury. Now the Earth and Mercury start moving.The Mercury completes one revolution in 88 days andwhen it comes at M, the Earth is not at E but it has

moved ahead and the next conjunction takes place

when Mercury comes at M, and Earth at E,. So in

moving from M and completing one revolution andafter that coming to M, is its synodic period or thetime taken by the Earth in moving from E to E, isSynodic period of Mercury.

Similarly, for supe-rior conjunction SMzEz t',

and SMrEr , the t imetaken by Mercury inmoving from M2 andcompleting one revolu-tion and coming to M, isits Synodic period or thetime taken by the Earthin moving from E, to E,is the synodie period ofMercury. Figlne 77

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Astronomy Reletsont to Astrologg

The outer planets move slower than the Earth.Earth completes one revolution in I year and Jupiterdoes it approximately in 12 Years.

Here S is the Sun, E, and E, are the positions of

the Earth and d and Jr positions of Jupiter at the time

of opposition, while Ez, E3 are positions of the Earth

and J r , J , pos i t ions o f Jup i te r a t the t ime o fconjunction.

SEJ is the opposi t ion and SErJr is the nextopposition. The time taken by Jupiter in moving fromJ to J, or by the Earth moving from E and completingone revolution and then coming to E, is the synodicperiod of Jupiter.

8 l

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CHAPTE R7

Eclipses

The sun is the only illuminated heavenly body whichis actually a star in the solar system and Mercury,Venus, Earth, Mars, Jupiter, Saturn, tfranus, Neptuneand Pluto are its planets, reflecting the light receivedfrom it. All the planets are revolving around the sunas already explained in chapter 3. The Earth ismoving around the Sun under the gravitational pullof the Sun. The Moon is moving around the Earthand along with the Earth, it goes around the Sun also,under the gravitational pull of the Earth. The Moon,in turn has its own pulling force like that of the Earth.

LUNAR ECLIPSE

A lunar eclipse takes place when the Moon passesthrough the shadow of the Earth in the heavens. Thiswill only occur when all the three i.e. the Sun, theEarth and the Moon are nearly in a straight line. TheSun and the Earth are always on the ecliptic but thepath of the Moon is inclined to the ecliptic at an angleof about 5o. So the Moon may or may not be on orvery near the ecliptic when the Earth is in betweenthe Sun and the Moon i.e. on poornima. When theMoon is on the ecliptic or near to it and the Earth is

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Asllonomg Releoont to Astrologg 83

, - - O - -

t ^ ) o - ' oOrbit of Moorf

Figure 18

in between them, such a position will occur when theMoon is either on Rahu or Ketu or nearby becauseRahu and Ketu are the nodes of the Moon i.e. thdpoints where the Moon crosses the ecl ipt ic.

When the whole of Moon's disc is obscured, theeclipse is said to be a total ecl ipse and when only apart of i t is obscured it is said to be a part ial ecl ipse(see f igure 18).

In the figure, S is the centre of the Sun and C ofthe Earth. The cone ABD is not receiving any lightfrom the Sun because the rays from all areas up toeither extreme of the disc of the Sun i.e. p or X areintercepted by the Earth and the cone ABD dark-shaded is in complete darkness. Cones QAD and YBD(light-shaded) are receiving light from some part ofthe Sun lrrr i not from the whole disc of the Sun. Thedark-shaded port ion i .e. cone ABD is cal led umbraor complete shadow while the l ight-shaded zones i.e.QAD and YBD are called penumbra.

When the Moon goes from penumbra to umbra,its brightness decreases till it vanishes when it is fullyin the umbra. This is the case of total lunar ecl ipse.

A lunar eclipse cannot occur until a portion of

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84 tlstronomg Releo ont to Astr ologg

Moon's surface enters in umbra. It is because inpenumbra the Sun's light falling on the Moon is only

diminished and not stopped directly while in umbra

no direct rays from the Sun can enter.

So, when the Moon is at position M, or M, as in

the figure it receives light from the one end of the

Sun and hence its brightness is diminished' This

diminution is smaller when the Moon is at the edge

of the penumbral cone. Totality of the Moon's eclipse

never exceeds 1% hours. Moon loses heat and cools

down more during an eclipse- During the totalityperiod, the Moon is travelling through the width of

the Earth. (The Sun moves about ZVz' per hour')

SOLAB ECLIPSE

The solar eclipse will occur when the Moon is in

between the Earth and the Sun i.e.

(1) It will be an arnauoago.

(2) The Moon must be on or near Rahu or Ketu so

that i ts lat i tude is near zero and the three

heavenly bodies, the Moon, the Earth and the

Sun, are in a line.

The reasons for a solar eclipse are the same as

for lunar eclipse i.e. the Sunrays should be stopped

by the dark (non-luminous) Moon from falling on the

Earth. It can happen only when the Moon comes in

the line of the Sun and the Earth and in between them

so that the rays can be stopped. The Earth and the

Sun are on the ecliptic; so, the Moon should be either

on the ecliptic or very near to it i.e. the Moon should

be on either of its nodes (Rahu or Ketu) or near the

same.

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Astronomy Releoant to Astrologg

In the case of lunar ecl ipse, the Moon loses l ight

when it enters umbra and the ecl ipse is visible al ike

to the whole part of the Earth which is facing the

Moon. The Moon, being much smaller than the Earth,

can obstruct the Sun's rays for a smaller area on the

Earth and as such the eclipse is visible to a limited

area of the Earth at a time.

Solar ecl ipse is of three kinds: (L) total ecl ipse,

(2) partial eclipse and (3) annular eclipse.

In the total eclipse the whole cif the Sun's disc is

not seen by the observer while in the case of a partial

eclipse only a part of the Sun's disc is covered by the

Moon and as such cannot be seen.

The Moon's angular diameter varies from 33'31"

to 29'22". The angular diameter is 29'22" when the

Moon is at the greatest distance from the Earth i'e'

at i ts apogee. The diameter is 33'31" when the Moon

is nearest to the Earth i .e. at perigee. In the case of

the Sun, the angular diameter of the Sun when at

apogee is 31'32" and when at perigee it is 32'36"'

By the above fact it can be noticed that if at the

time of eclipse the Moon is nearest to the Earth and

the Sun far thest , the Moon's apparent angular

diameter will be greater than that of the Sun and it

can hide the whole of Sun's disc from the observer

on the Earth in the line of the Sun and the Moon' It

will be a total eclipse for that observer.

In the case of partial eclipse, only a part of the

Sun's disc will be hidden by the Moon. The reason

being that the centres of the Sun and the Moon not

being in an exact line with the observer i.e. when the

Sun and the Moon are not exactly at Rahu or Ketu,

85

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86 Astronomy Releoont to Astrologg

Figure 19

or the observer is at a point outside the umbral coneof the Moon.

The annular solar eclipse takes place when theSun is the nearest to the Earth and the Moon is thefarthest and other conditions remain the same as thatof total eclipse. It will be an annular eclipse becausein this case the Moon's apparent angular diameter isshorter than that of the Sun. The Moon's disc willnot be able to fully cover the Sun,s disc but willobscure only the central portion of the Sun. At theedges, the Sun is seen in this position in the form ofa bright ring, as shown in figure 19.

The umbra created by the Moon is cone ABCwhen the observer is at E within umbra i.e. the Moonis the nearest and the Sun is the far thest. Theobserver thus can see the total solar eclipse. But whenthe observer is at F i.e. outside the umbra, which willhappen when the Moon is the farthest from the Earthand the Sun is the nearest, he will not be chservingthe total eclipse and instead he will be able to see theSun's disc like a ring. Only the shaded portion of theSun wil l be hidden by the Moon and the rest i.e.c i rcu la r r ing w i l l be v is ib le over the en t i rehemisphere of the Earth. F\rrther, the track of totalitycan never be more than 16g miles in width and thetotality can never last more than eight minutes.

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Astronomg Releoont to Astrologg

OCCULTATION

Moon's sidereal period of revolution is about 27r/,days and it moves eastwards with reference to thestars and at an average of more than half a degreeper hour. In its movement, it continually interposesi ts disc between us and the stars. The suddendisappearance of a star by the Moon's disc is caslledthe occultation of the star by the Moon.

Actually, the covering up of one celestial body byanother is general ly cal led occul tat ion. Str ict lyspeaking, the solar eclipse is also an occultation ofthe Sun by the Moon.

COMBUSTION

The planets are called combust when they arenear the Sun in longitudes and their rays which arethe reflection of the Sun's rays are intermingled withthat of the Sun whose rays are much stronger.Therefor, the effect of the planets becomes much less.The planet under combustion is not visible, being toonear the Sun, and is called Asta.

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CHAPTER 8

Time

Mean Solar DaY

We have seen that the Sun appears to describe

an elliptical orbit around the Earth and its rate of

changeofd i rec t ion in theorb i t i sno tcons tan t , i .e .the Sun appears to move somewhat non-uniformly

in the zodiac. It moves faster when the Earth is at its

perihelion, i.e. the nearest point from the Sun'-Corr.r"rr"ly

the angular speed is slowest when the

Earth is at aphelion point (the farthest from the Sun)'

The other factor is that the Sun appears to move in

the ecliptic and not in the celestial equqtor, so its right

ascension does not increase uniformly, it being

measured along the celestial equator'

The apparent solar day is the interval elapsed

between two successive transits of the sun across the

observer's meridian.

As the Sun's motion is not uniform throughout

theyear, theapparentsolardayswi l lbeofdi f ferentduration. It will be much troublesome in day-to-day

working of the society. So, a fictitious body called the

"mean Sun" was devised which is assumed to move

on the celestial equator at a uniform rate' The

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Astronomg Releoont to AsttologY

successive transits of this fictitious body or the mean

Sun across the observer's meridian is defined as a

mean solar day which is equal to the average daily

motion of the real Sun in the ecl ipt ic. The duration

of such a mean solar day is divided into 24 hours. It

imp l i es tha t t he r i gh t ascens ion o f mean Sun

increases at a uniform rate. When the mean Sun is at

the meridian of a place, it is local mean noon there

and the hour-angle of the mean Sun is zero. When

the hour-angle of the mean Sun is 12 hours, it is said

to be midnight there and this is the moment when

the new civil day begins there.

The Local Mean Time

The time elapsed from the midnight of the place

is known as local mean time. Thus LMT at midnight

is zero hours. This is different from the hour-angle

of the mean Sun.

The Earth is rotating from the west to east and it

completes one rotation with respect to the Sun in one

civil day. However, it completes one complete rotation

with reference to any distant star in one sidereal day.

Its spin in a sidereal day is 360", while the same is

about 361' for a civil day. A mean solar day is of 24

hours 3 minutes and 56.56 seconds in sidereal tiine.

Mean sidereal day is equal to 24 hours, in sidereal

hours, and is 23 hours 56 minutes 4.09 seconds in

mean solar time. For simplicitg both solar day and

sidereal day are taken as 24 hours in terms of their

own hours. Thus, the Earth rotates 360" in 24 hours

or, say, 1" in 4 minute. The places which are in the

east will see the rising of the Sun early and those in

the west will see it later. If the difference is 10' in

terrestrial longitude, the difference in sunrise will be

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90 Astronomg Releoqnt to Astrologg

of l0 x 4 = 40 minutes provided the terrestr ia llatitude is the same. This way, we can see that thelocal mean time of places at different terrestriallongitudes will be different in a country or a zoneand the day-to-day work of the society will face a lotof trouble and practically be disrupted in the presentera. The terrestr ia l lat i tudes and longi tudes ofMumbai are 18'58'(N) and 72"50'(E), and of Calcutta22"35' (N) an 88'23' (E).

The difference between latitudes is only 3o3?'while in the longitudes it is 15o33', i.e. the differencebetween their local time will be of 15"33' x 4 = 62minutes 12 seconds, i.e. I hour 2 minutes 12 seconds.The person at Mumbai will at his noon say that thetime is 12 hours while at Calcutta he will say no, it isI hour 2 minutes 12 seconds p.m. and the scheduleof railway timing, plane timing, radio, television, etc.will not be possible. So, a way was devised that withina country or a zone (in large countries), one standardmeridian is fixed and the time of that meridian istaken as standard time for that country or the zone.It is called the standard time of a country or zonalstandard time of that zone.

In India the standard meridian is having alongitude 82o30'(E) and this meridian passes througha place near Varanasi. The local mean time of thisplace is the Indian standard time and is followedthroughout India.

Similarly, other countries or zones have also fixedtheir standard meridians. When going through thelast few pages of the table of ascendents, it will beseen that the standard meridians of a country or azone are fixed in such a way that normally the time

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Astronom Releoant to Astrologg

difference between that of Greenwich is a murtipleof half an hour. The difference between the IST(Indian Standard Time) and that of the Greenwhichmean time is 572 hours.

Units of Time

The following are the units of t ime as per SzryoSiddhanta

6 pran

60 pal

60 ghati

21,600 pran

100 truti

30 tatpar

18 nimesh

30 kashtha

30 kala

2 ghatika

30 muhurta

The following are the units of t ime as prevalentduring the modern time.

60seconds = lm inu te

60minutes = lhour

24hours = lday

= I pal. (also called vinadi)

= I ghati (also called nadi)

= 1 day (Civil Day or solar day)= I daY = 86,400 seconds

I tatpar

I nimesh

l kashtha

l kala

L ghatika

I muhurta

l day

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In degrees anil raslis

60" (seconds) = 1'(minute)

6o'(minute) = 1'(degree)

30" (degree) = 1 rashi (sign)

12 rashis = zodiac

Units of Measurement of Distances in Space

Three systems for measuring distance in space

are in vogue.

(1) light Year

(2\ astronomical unit

(3) Parsec

Light Year

Light travels at the rate of 1,86,000 miles (or

3,00,000 km) per second. The distance traversed by

the light in one year is known as light year'

light year = 3,00,000 x 60 x 60 x 24 x 365'25 km'

So, one light Year = 9'46 x 1012 km'

i.e.9,460bil l ionkilometresor5,8S0bil l ionmiles'

Astronomical Unit

The semi-major axis of the Earth's orbit is known

as astronomical unit. In other words, the half of

maximumdistance*minimumdistanceoftheEarthfrom the Sun is known as astronomical unit (AU)'

One AU = 930 lakh miles

In other words, the distance between the Earth's

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Astronorng Releoont to Astrologg

two positions at extreme points is two AUs. It canalso be expressed as the mean distance of the Earthfrom the Sun.

Parsec

The distance corresponding to a parallax of 1" is

called a parsec.

1 parsec = 2,06,265 astronomical units

= 3.26 light years

= 3.086 x 1013 km.

S is a fixed Star.Distance E,E, = 249where E, and E, are thetwo positions of the Earthon its mapr axis.

S (Fired Star)

Eailh's Orbil

Figure 20

The distance is corresponding to a parallax of 1"and is inversely proportional to it. If the parallax is0.001", the distance is 1000 parsecs and not 1i1000parsec (see figure 19).

93

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94 AstronomA Releoant rc Astrologg

Civil Day

Nowadays, the time from one midnight to anothermidnight is a civil day. According to our ancientsystem, the time interval between one sunrise toanother sunrise is called one'savan day'i.e. civil day= 24 solar time hours.

Mean solar day = 24 hours 3 minutes 56.5 secondsin sidereal time hours, etc.

Sidereal Day

The time interval from one rising of anakshatrato its rising next t ime is called a sidereal day ornakslwtra din.lt is of about 23 hours 56 minutes and4 seconds in solar day hours.

Lunar Day or a Tithi

Lunar day or a tithi is the average time taken bythe Moon from one tithi to the next tithi. Each tithirepresents 12o phase difference between the Moon'spos i t ion f rom the Sun 's pos i t ion , i .e . Moon 'sadvancement over the Sun by another 12". Thisaverage time is 23 hours 37 minutes 28 seconds.

MONTHS

Solar Month

When the centre of the Sun enters from one rashito another, it is the sonlcronti of the other rashi. Thetime taken by the Sun from one so.nlcrontito anotheris called a solar month. The time interval of everysolar month differs because the angular velocity ofthe Sun is not uniform. When the angular velocity ismore, the Sun crosses one rashi or sign early and that

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Astronomg Releoant to Asttologg

solar month is smaller. Conversely, when the angularvelocity of the Sun is less, the solar month is bigger.The average time of a solar month is 80.438 days.

Lunar Month

When the longitudes of the Sun and the Moonbecome exactly equal the amaaasgro ends. The periodbetween the ending of one arnauclsya to the end ofnextamauosgo is called a lunar month.It is also calledthe synodical month, i.e. 2g.S30G mean solar days.

Anomalistic Month

The interval required by the Moon to move fromperigee to perigee is called the anomalistic month.Its duration is 27.5546 mean solar days.

Nodical Month

The interval between two successive passages ofthe Moon through the ascending node is called anodical month. It is of 27.2122 mean solar days. It issmaller than the sidereal month (2T.gZ days) becauseduring a month's interval Rahu moves backwards onthe zodiac towards the Moon.

YEARS

Astronomically, there are several kinds of .years'.

The sidereal year is the true revolution periodof the Earth around the Sun.It is of 865 days 6 hours9 minutes 10 seconds, i.e. of 365.256 days.

The Tropical year is the period between twosuccessive passages of the Sun across the first pointAries (Sayana). As the first point of Aries is notstationary, the tropical year is shorter by 20 minutes

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Astronomg Releoo,nt to Astrologg

"from the sidereal year. Its duration is J6S.Z4Z days,i.e. 365 days 5 hours 48 minutes 45 seconds.

The calendar year is the mean length of the year.Its duration is 365.24 days, i.e. 365 days 5 hours 49minutes 12 seconds.

The anomalistic year is the duration betweentwo successive passages of the per ihe l ion of theEarth. As the Earth's perihelion also moves about llseconds in its orbit every year and completes onerevolution in about 108 thousand years, this year isslightly longe4 i.e. of BG5.Z6 days, er 965 days 6 hours

.13 minutes and 53 seconds.

f ,unar year: Twelve lunar months make a lunaryear, i.e. of 12 x 29.5806 days = 854.36?2 days approx.

Luni -Solar Year : S ince ear ly Vedic per iod,fndians followed solar year with lunar months and asynchronized lun i -so lar year . One system wasprescribed in Rigo edanga, another in Atharaa_aed'anga. varahamihira made some modifications forodhik and kshga tithis and adhik rnaas. The Luni_Solar year as at present used in our panchangas.Tithis of most of the religious and social festivals arebased on a mixture of solar year and lunar monthsby the pandits. The months are the lunar months butevery 19 years there is an increase of ? months inthis calendar (see page b5). The principal of making13 months in a year is that if two times arn&uos1aendsin a solar month, the month which followed the firstonxaaasAa will be repeated again after the secondonaavesAa, i.e. there will be two lunar months of thesame name. This name of two lunar months (for aparticular solar month) will be after the name of thesaid solar month. This is in accordance with the

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Astronomy Releoont to Astrologg

Moon's nakshatra on which the Moon was on thepoornfuna day during the said solar month. This way,after every two to three years, we have a year of 13lunar months and the difference between the solarand lunar ydars is adjusted.

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CHAPTER 9

Panchanga

Panchongo is a Sanskrit word which consists of two

words poncho * anga. Paneha means five and anga

means parts or limbs. So, ponchanga means five

limbs.

These five limbs are:

(1) day

(2) tithi

(3) nakshatra(constellation)

(4) karna

(5) yoga

1. DAY

Day here is the weekday to decide the lordshipof the concerned day. In the Indian astronomy the

day is considered to be form sunrise to just beforethe next sunrise.

In the Western system, the name of the day is

calculated easi ly f rom the dates of Gregor iancalendar. The exact interval between the twosuccessive vernal equinoxes, i.e. a tropical year, is 365

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Astronorny Releuant to Astrology

days 5 hours 48'and 45.3" or, say,365.2422 days. Whenit is mult ipl ied by 100, i t gives 24.22 extra days (inexcess of 365 days per year) in a century. So, PopeGregory XIII adopted a calendar in 1582 accordingto which normally years will be of 365 days each butthe years which are divisible by 4 without remainder,such as 1988, L992, etc. will have 366 days, but thecenturies, i.e. the year which are multiple of 100 butnot multiple of 400 will only 365 days and the yearswhich are multiple of 100 and also multiple of 400will have 366 days.

Because there were 24.22 days extra in a centgryso 24 days have been added 4, 8 ,L2... up to 96 andnot 100; and 0.22 x 4 = 0.88, i .e. approximately I dayhas ben added in the 400 years.

In one year when 365+7 leaves a remainder of 1so if the January 1, 1949 was Saturday, the January1, 1950 wil l be one week day extra i .e. Sunday.In onecentury i.e. in 100 years the number of remainingdays will be 100 * 24 leap days i.e. 124 extra daysthan complete weeks, which means (124+? leaving aremainder of 5) 5 extra days only after omitt ingcomplete weeks.

In 100 years (one century), the number of daysmore than the complete weeks = 5.

In 400 years (four centuries), the number of daysmore than the complete weeks = 20 + 1 as the 400thyear is also a leap year = 21 which is divisible by 7.Thus, a period of four centuries folds up in completeweeks. This implies that the day on January 1, 1201wil l be the same as on January 1,801, or 1601, or 2001.

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Astronomg Releoant to Astrologg

Example

The following is an illustration how to calculatethe day of a week in Gregorian calendar which ispresently in vogue.

To find out the day on March 4, 1988.

Number of days more than completeweeks in 1600 years = Q

.' Number of days more than completeweeks in 300years = 5 x 3 + Trremainder = 1

Number of days more than complete weeks(as 87 years pass) = 87 * 7, remainder = 3

Leap days in 87 years = 2l * 7, remainder = 0

Number of days more than completeweeks in January 88 = 31 * 7, remainder = 3

Number of days more than completeweeks in February 88 = 29 + 7 t remainder = 1

Number of days more than completeweeks in March 88 = 4 i 7, remainder = 4

Total =L2

Now, L2 + T leaves the remainder 5.

Now count it Monday if the remainder is l,I\resday if it is 2, Wednesday if 3, Thursday if 4, Fridayif 5, Saturday if 6, and Sunday if 0 or ?.

. The day on March 4, 1988 is thus Friday as theremainder is 5.

2. TITHI

A lunar month is from the end of one orrr';aoeayo

100

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Astronomg Reletsont to Astrologg

to the end of succeedin g amaoasAo, i.e. the differencebetween the longitudes of the Moon and the Sun startincresing. As there are 360'in the zodiac, so in a lunarmonth the Moon moves 360o more than that of theSun. There are 30 t i this in one lunar month.

So, one tithi = 399" = rz'30

The following table shows the tithis and thedifference of the longitudes of the Moon and the Sun.

Shukla Paksha (Bright Halfl

r0r

Name Tithi No. Longitude ofMoon - Sun

Pratipada

Dviteeya

Triteeya

Chaturthi

Panchami

Shashthi

Saptami

Ashtami

Navami

Dashami

Ekadashi

Dwadashi

Trayodashi

Chaturdashi'Poornima

(F\rll Moon)

1

2

3

4

5

6

7

8

I

10

11

L2

13

L4

15

0o to 12"

L2' to 24o

24' to 36o

36o to 48o

48" to .60o

60o to 72"

72" to 84'

84' to 96'

96o to 108"

108" to t20"

L20" to t32"

132" to L44'

144' to 156"

156' to 168'

168' to 180"

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t02 Astronomy Reletsont to Astrology

Yyrishna Paksha (Dark Halfl

Name Tithi No. Longitude ofMoon - Sun

Pratipada

Dviteeya

Triteeya

Chaturthi

Panchami

Shashthi

Saptami

Ashtami

Navami

Dashami

Ekadashi

Dwadashi

Trayodasi

Chaturdashi

Amavasya(New Moon)

180" to L92"

192' to 204"

204" to 216"

216' to 228"

228" to 240o

240" to 252o

252' to 264o

264" to 276o

276" to 288'

288" to 300'

300" to 312"

312" to 324"

324' to 336'

336' to 348'

348" to 360o

16t71819202L222324252627282930

The lst tithi starts when the Moon starts movingahead of the Sun, i.e. more than 0o difference. Whenthe differnce becomes just more than 12o, lhe tithibecomes Dviteeya. Similarly, it is for other tithis.

The above is the scheme for the tithis but these30 tihtis falls in approximately 29.5 days and not in30 days. The Moon moves sometimes fast, i.e. about15o in 24 hours and sometimes slow, about 12. in 24hours. Tithis are depending upon the net differenceof motion of the Sun and the Moon. Their individual

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Astronomg Releoont to Astrologg

motions depend upon their distances from apogee orperigee.

This fast and slow movement of the Moon causessometimes the losing of a tithi and sometimes gaininga t i thi. The principle behind it in the Indian lunarcalendar is that the tithi which is at the time of sunriseis the tithi of the day. Whether that tithi may remainfor a few minutes in that day or it may prolong uptothe next sunrise. A tithi which starts after sunriseand ends before the next Sun rise is said to be missedin that fortnight. If a tithi which starts just beforesunrise and ends after the next sunrise will be havingtwo days in its name in that fortnight. The systemwas introduced for day-to-day working of the society.

The formula for the calculation of tithi:

Longitude of the Moon - Longitude of the Sun

IT

Example

. Calculate tithi at 11.30 a.m. on October L2,2000

Sun's Moon'sLongitude Longitude

103

On Oct. 13,2000 at 5.30 a.m.

On Oct. 13,2000 at 5.30 a.m.

Difference for 24 hours

Difference for 6 hours

Longitude at 11h.30'a.m. (A + B)

As one sign = 30o, so

7127" 25' 2. 190 56'

7126" 24' ',ll 2" 50 1',A

10 I' 14" 55'

15' 'B' 30 44' .8 '

7 '260 39' 2 ' go 45'

236'39' 6go 45'

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104 Astronong Re|r'oont to Astrolagg

68" 45' - 236" 39'By the above formula,

As 68" 45'is less than 236o 39', add 360" in 68" 45'

4280 45', - 2360 39' 19r 6'= -

L2

. -.00 6'= to 12

which shows that 16 tithis have passed and the 17this running at that time and its 0o 6'have passed outof 12".

The tithis at a particular moment are calculatedin the above manner.

Now you will see how the tithis last for two daysor are missed. The principle behind it is that for socialpurposes the tithi of a day is the tithi which is at thet ime o f the sunr ise on tha t day . I t shou ld beremembered that it is for social purposes and it doesnot mean that tithi will in reality remain for the wholeof day.

Examples

How a tithi is missed or tithi kshago.

T\po such examples are given below:

(1) Take the case of October 18, 2000 and of October19, 2000.

Sunrise at Delhi on October 18 is at 6h28'a.m.

Tithi on October 18, 2000 is calculated as under:

T2

L2

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Astronomg Releoont to Astrology

Tithi =

i Longitude of the Moon - Longitude of the SunLT

2" 10 4 ' - 6 . 10 5 ' ,Ti th i=--T

, = 61o 4' - 181o 5'

L2

As 61 is shorter than 181, add 360 in 61.

610 4' + 360' - 1810 5'Tithi = -

L2

239o 59' ,^11o 59'- -.L2L2

It shows that 19 tithis have passed and 20th isrunning. So, the tithi of October 18,2000 will be calledkrt shna paksha panehmi.

Tithi on October 19, 2000 is calculated below.sunrise at Delhi on that day is at 6h 28' a.m.

Tithi_ 2' 15o 9' - 6" r 5'

L2

. =Ys, 75o 9' + 360o - 182o 5'

105

L2

253. 4'. -,lo 4'= i

= zLi which shows 22nd

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106 Astronomg Reboont to Abtrologg

tithi is running on 19th October.

Hence, the tithi on October lg, 2000 is KrishnoPaksha Saptami.

It is seen that 2lst tithi has been missed.

(2 ) Take another case o f miss ing t i th i , i .e . o fFebruary 2,200L and February 3,2001.

Sunrise at Delhi on 2nd February is at 7.13 a.m.

Sunrise at Delhi on 3rd February is at 7.12 a.m.

Colculation of tlthi on Znd Febntory:

Tithi =

Longitude of the Moon - Longitude of the SunIT

0" 250 2l' - 9' 19" 24'L2

250 zl'. - 289 24',L2

250 21', + 360 - 2890 24'.L2

95o 57 ' , ' l lo 57 '= . _

L2 t2

Saptami has passed and Shulclo Polcsho Ashtomiis running.

Calculation of tithi on 3rd Febru,ory:

1'8" 50' - 9' 200 25'Tithi =

L2

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Astronomy Releoont to

380 50' - 290 25'L2

10go 25' ^00 25'= rz

=o Lz

Nine tithis have passed and tenth is running. Sotithi on February 3rd, 2001 is Shulclo Poksha Dashami.It may be seen that Navami has been missed.

Example qf Adhik Tithi

(3) Take the case of October 6, 2000 and October ?,2000. ;

'

Sunrise at Delhi on October 6, 2000 and October ?,2000 is at 6.21 a.m.

Tithi colculation on October 6,2000 is as under:

Tithi =8' 250 29'. - 5' 1go 13'

L2

265" 29'. - 169o 13't2

96" 15' ^00 15'= -= - -t2 L2

Eighth tithi has passed and ninth is running. So,the tithi of October 6, 2000 will be called ShukloPoksho Naaami.

Tithi on October 7,2000 is caleulated, os under:

9" 70 16' - 5" 20 L2'Tithi =L2

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r08 Astronomy R.eleoont to Astrology

277" 16', - 170" Lz',t2

1o7o 4' ^11o 4'= s -

12 L2

Eight tithies have passed and gth is running atthe time of Sunrise. Hence, the tithi of October 7,2000is Shukla Paksha Navami. By this it is seen that thetithi for October 6, 2000 and October 7,2000 is Navamifor both the days.

(4) Calculation of tithies on January 31, 2001 andFebruary 1, 2001 are given below.

Tithi of 3lst January, 2001

Tithi = 11'290 z?', - g', L7" 22'.t2

359" 27' - 2870 22',t2

7? 5' ^0P 5'= O -

t2 L2

i.e. Shulclo Polcsho Soptomi

Tithi on February 1, 2001

0' l2g 13' - I' 18" 23'L2

11 13' - 2880 23'

Tithi =

L2

Page 109: Astronomy Relevant to Astrology by v.P. Jain

1? 13' + 360" - 2ggo 23't2

37r 13' - 2ggo 23'L2

)83o 50' ^11e 50'

= U _

t2 L2

,rvhich shows that Shutcla Paksha Saptmi is runningat Surrrise of February 1, 2001.

..r_ So, Shulclo Polcsha Saptmi is for two days, namely,January 31, 2001 and February 1, 2001.

3. NAKSHATRA

The division of the zodiac in 27 nakshatras hasbeen shown at in chapter 5. However, the calculationsfor finding out the number of nakshatras is as under:

The 27 nakshatras are in 360.

So, one nakshatra

= rr1. i.e. t3o2o,3 '

Example

Now, we have to find the nakshatra of the Moonwhose longitude is, say, 24S"lG'.

The.nakshatra number will be arrived at

2450 16'

130 20'

3600= -

27

Page 110: Astronomy Relevant to Astrology by v.P. Jain

(245x60+16)--

(13 x 60 + 20)'

14700' + 16'= ?80 '+ 20 '

14716'800'

= 1g316'800'

i.e. the 2nd quarter, or pada, or charan of 19th

nakshatra (Mula nakshatra).

If the remainder is from I'to 200'it is lst quarter;

i f i t is 201' to 400' i t is 2nd quarter; i f i t is 401' to 600' i t

is 3rd quarter; if it is 601' to 800' it is 4th quarter'

Names of Nakshatras

(1) Ashwini

(3) Krittika

(5) Mrigashirsha

(7) Punarvasu

(9) Ashlesha

(11) Purvaphalguni

(13) Hasta

(15) Swati

(17) Anuradha

(19) Mula

(21) Uttarashadha

(23) Dhanistha

(25) PurvabhadraPada

(27) Revati

(2) Bharani

(4) Rohini(6) Ardra

(8) Pushya

(10) Magha

(12) Uttaraphalguni

(14) Chitra

(16) Vishakha

(18) Jyeshtha

(20) Purvashadha

(22) Shravana

(24) Satabhisha

(26) UttarabhadraPada

Page 111: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg l l l

; This way by changing the signs and degrees intominutes and dividing by 800', the quotient gives thenumber of nakshatras passed and the remaindergives the minutes of the next nakshatra which haspassed out of 800'.

In the above manner, we can calculate thenakshatra of any planet at any moment, provided theNiragana longitudes are known.

But, when we say what nakshatra is running atpresent, the reference in Panchango is always to theMoon's nakshatra which is required for doshaphal aswell as muhurta.

4. I(ARANA

In each tithi there are two karanas. The firstKarana ends at the middle of the tithi and the secondends with the ending of the tithi. The two halves arenot obtained by dividing the time of the tithi in twohalves. Each Karana is decided by the time taken bythe Moon to gain over the Sun by a margin of 6' (asagainst 12o in the case of a tithi).

'The method of colculating the tithi is:

Tithi =

Longitude of the Moon - Longitude of the SunLT

Quotient * 1 gives the Tithi.

The fortnula for colculating Karono is:

Karana =

Longitude of the Moon - Longitude of the Sun60

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Lt2 Astronomg Relerso,nt to Astrology

The quotient + l will give the number of Karanasrunning.

Names of Karanas

1. Bava

2. Balava

3. Kaulava

4. Taitila

5. Gara

6. Vanij

7. Vishti

which repeat eight times, i.e. ? x 8 = 56 such Karanasplus four others, namely,

i \ Shakuni

ii) Chatushpada

iii) Naga

ia) Kintughna

Making a total of 56 + 4 = G0 Karanas in 30 tithis.

In other words, there are e leven d i f ferentKaranas:4 non-recurring and seven recurring 8 timesduring a lunar month. Alll these ll Karanas havedistinctive characterstics attached to them. SomeKaranas like Vishti (Bhadra), Shakuni, Chatuspada,Naga, Kintughna are inauspicious and some are good.for muhurta of various rituals, ceremonies, etc.

Example

Take the case of October 18, 2000 at 6.25 a.m.(given in this chapter in the example of missing tithia t page.)

Page 113: Astronomy Relevant to Astrology by v.P. Jain

Karana =

Longitude of the Moon - Longitude of the Sun

Karana =

6o

2 " l 4 ' , - 6 " 1 0 5 '

6

6lo 4' - 1910 5'6

As the longitude of the Moon is less than thelongitude to the Sun, add 360'to the longitude of theMoon.

42'- 4', - 1910 5'

i.e. 40th Karana was running or the 2nd Karana of20th tithi (40 + 2) was running. The table shows thatthe 2nd Karana of 20th is 4th Karana, i.e. Taitila.

Tithi lst 2nd Tithi lst 2ndKarana Karana Karana Karana

23go 59'

6

3g5o 59'

6

2

4

6

1

3

I

3

5

7

2

I2

345

Kintughna

2

4

6

1

16

L7

18

19

20

3

5

7

2

4

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tl4 Astronomg Releoont to Astrologg

Tithi lstKarana

Tithi lst 2ndKarana Karana

2ndKarana

6

7

8

I

l0

11

t2,13

L4

15

3

5

7

2

4

6

1'3

5

7

4

6

1

3

b

I

2

4

6

1

2156

2271

2323

2445

2567

26L2

2734

2856

29 7 Shakuni

30 Chatushpada Naga

5. YOGA

Yogas are the result of combined movement ofthe Sun and the Moon. These can be inauspicious orauspicious for arriving at proper muhurta.

Names of Yogas

1. Vishakumbha

3. Ayushman

5. Shobhana

7. Sukarma'9. Shula

11. Vridhi

13. Vyaghata

15. Vajra

L7. Vyatipata

19. Prigha

2. Priti

4. Saubhagya

6. Atiganda

8. Dhriti

10. Ganda

12. Dhruva

L4. Harshana

16. siddhi

18. Variyan

20. Shiva

Page 115: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg l 1 5

21. Siddha 22. Sadhya

23. Shubha 24. Shukla (Shukra)

25. Brahma 26. Indra

27. Vaidhriti

The names of Aogas themselves indicate (fromtheir word meaning) where these are auspicious(good) and were these are inauspicious (bad).

So,each yoga= Y

= 13o?0 '= 800 '

The fortnula for calculating goga:

Yoga =

Long. of the Sun * Long. of the Moon (in minutes)800'

Example

Any moment for which the yoga is to be foundout, say, for example, Sun's longitude be 9* 3o 23' andMoon's longitude be 2"6o 36'(January 18, 1992 at 5.30a.m.)

q'39 23' + 2' 6o 36'. Yoga at that time tithi =

ff

_ [(9' x go)+3"]x eo+ze' + [(z' x go)+e"]x oo+ge'800'

16403' + 3996'= -- 8oo--

Page 116: Astronomy Relevant to Astrology by v.P. Jain

20399'800'

_ 25 3gg'900'

25th yoga has passed and 26th yoga, i.e. Indra wasrunning at that time.

Page 117: Astronomy Relevant to Astrology by v.P. Jain

CHAPTE* 10

Upagrahas and Stars

UPAGRAHAS (astronomical points on the ecliptic)

These are secondary p lanets (upagrahas in

Indian astronomy). Of course' there are tert iaryplanets also. The secondary and the tertiary planets

are invisible (not physical bodies). Actually, these so,

called planets are astrological ly sensit ive points,

mathematically computed positions with reference

to the Sun ' s l ong i tude . These po in t s a re o f

considerable importance with the birth chart as well

as in the progressed horoscope of the individual (or

a rlation).

These upagrahas are Dhuma, Paridhi, Indrachapa

and Sikhi. The method of calculation from the Sun's

position is given below:

1. Dhuma Sun's Nirayana longitude (S)

+ 133"20' or 133"20 '+ S(10 nakshatras ahead of the Sun)

2. Patha

3. Paridhi

4. Indrachapa

360o - Dhuma

Patha +180"

or 226'40'- S

or 46o40'- S

360" - Paridhi or 313"20' * S

Page 118: Astronomy Relevant to Astrology by v.P. Jain

1 1 8 Astronolrg Releuant to Astrologg

5. Sikhi : Indrachapa + 16o40' or 330" + S

Example

Presume that, in a horoscope the Sun's locationis at 12" in Gemini.

So, the Sun's longitude = 7Zo (S)

1. Dhuma

2. Patha

3. Paridhi

4. Indrachapa

5. Sikhi

Peha 154" rO'

72 '+133"20 '=205 '20 '(133"20' + 72. = 205"20')

360" -205 '20 '=154"40 '(226'40' - 72" = 154"40') nt'

154"40'+ 190. = 334040'(46'40'-72o = 334'40')

360'- 334"40' = 25"20'(313"20 '+72"=25"20 ' )

25"20'.+ 16'40' = 42o(330"+72 '=42" )

25'20' Indrachapr

Flgve2l

934'rO' Paridhi

Page 119: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg

The above sens i t i ve po in ts ca lcu la ted w i threference to the Sun's longitude serve as Amshas ofplanets Mars (for Dhooma), Rahu (for patha), Moon(for Paridhi), Venus (for Indrachap), and Ketu (forSikhi or upaketu). But for calculating the position ofupagrahas of the other four planets - the Sun,Mercury, Jupiter and Saturn, other methods are used.

Upagrahas (Astrological)

Astrologically speaking (not astronomically),there are nine upagrahas relating to the nine grahas.They are considered their (adverse) Amsha.

Upagrahas:

1 1 9

Amsha of:

Paridhior

PariveshI

IY

Moon

Kala

IJ

Sun

DhoomIII

Mars

Ardhyamor

Ardhaprahara

IAmsh"a of: U"Jurv

Yama-gantak

I*

Jupiter

Indrachapaor

KodandaI+

Venus

Gulikaor

MandiII

SatYrm

Pathaor

VyatipataI+

Rahu

sikhior

Upaketu

IxXuAmsha of:

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Astronomg Reletsont to Astrologg

: The ca lcu lat ion procedure fo l lowed for the

upagrahas, Ardhyam, Yamagantak and Mandi (or

Gulika) is as follows:

Birth During Day

Divide the daytime (dinamaan) into eight equal

parts. Al loted to the various weekdays, the f irst

belonging to the planet ruling the weekday - the first

seven in the weekday's cyclic order, eighth always

called nireesh, i.e. without lordship

Birth Dunng Night

Divide the night span (rotrimaan) also into eight

,equal parts. Allot the first part to the lordship of the

fifth upagraha (in the cyclic order) from the lord(planet) of the day. Eighth part will be Nireesh.'

Thus, on Sunday: It is Yamagantak (the first part

of the night), followed by Kodanda, Gulika, Kala,

Paridhi, Dhooma, Ardhyam and,lastly, the unalloted.

l i le have to ca lcu late the ascendant at the

commencement of each period of upagraha and that

will give the longitude of the related upagraha.

STARS

Stars are self-luminous gaseous bodies in the

celestial sphere. They are grouped into constellations(conspicuous grouping forming a small solid angle,

with the Earth as the apex). The most conspicuous

stars in a constellation are given a Greek letter ('cr'

being the brightest), but in ancient Indian astronomy,

the nakshatra is named after the brightest or most

conspicuous star (such as Rohini or Chitra, etc.).

Some stars have the i r own names ( l ike Spica,

Anteres, Polaris, Arcturus, Sirius, etc.).

Page 121: Astronomy Relevant to Astrology by v.P. Jain

Astronomy Releoont to Astrologg

The nearest star to our Solar System is ProximaCentauri but everi its distance is very great, i.e. 4.2light-years. Sirius (Lubdhaka), the brightest star inthe sky , i s 8 .7 l i gh t - yea rs away (S i r i us i s i nconste l la t ion Canis Major is) . Arcturus (Swat i ) inBootes is 36 light-years away. Anteres (Jyeshtha) inScorpio is a red star, which is 330 light-years away.Betelguese (Ardra) in Orion is at 310 l ight-years.Regulus (Magha) o - Leonis in Leo is 425light-yearsfrom us. A light-year is 5,880 billion miles.

No telescope, however strong in magnification,wil l show a star as a measurable disc. We have,therefore, to depend upon the astro-spectroscope.S ta rs have g rea t range i n l um inos i t y andtemperature.

The main sequence stars (such as the Sun) areclassified as dwarfs. Then there are the giant branch,and white dwarfs, neutron stars and black holes.

The usual sequences are like this:

, From Nebulus, mass of 1 solar mass, a mainsequnece star exists for 10 billion Solar Years, oftenit expands into a red giant branch and then coalescesinto a white dwarf. A star of higher mass (10 solarmass) carries on for main sequence life of a millionyears, becomes a red giant, explodes as a supernovaand then becomes a neutron star. A star of still highermass (10 to 30 solar mass) has a main sequence life ofa mi l l ion years, becomes a red g iant and thencollapses into an extremely dense mass forming ablack hole, from which even l ight cannot escape.(Main sequence stars with hot white or bluish stars,i.e. types O and B and end with feeble red stars, i.e.type M. The Sun is a yellow dwarf star of type G.)

t2l

Page 122: Astronomy Relevant to Astrology by v.P. Jain

L22 Asftonomg Releoont to Astrology

Mean Places of Stars t

S. StarNo.

IndianName

NirayanaLongitude

Magni- Distancetude LightYrs.

1. p Arietis

2.4hrieties

3. Alcyone -Z(q Tauri)

4. Aldebaran(c Tauri)

5. Capella(c Aurigae)

6. p Tauri

7. l, Orionis(f )

Ashwini

Bharani

Krittika

Rohini

Brahmahrd

Agni

Aries 10'6'

Aries 24'20'

Taurus 6'8'

Taurus 15o55'

Taurus 28o0'

Taurus 2843'

2.72

3.68

2.96

1.06 68.0

0.21

1.78

3.66

2.1v 680

0.6v 310

-1.58 8.7

-0.86 1200

4 .17

3.48

1.95 75

1.34 425

2.58

2.23

8. Polaris

9. Betelguese(a Orionis)

10. Sir ius

Ardra

Lubdhaka(cr Canis Majoris)

11. Carropus Agastya(c Carinae)

12. Pollux Punarvasu(p Geminorum)

13. 6 Cancri Fushya€.tn^'A{r*

14. e'Hydrae Ashlesha

15. Dubhe Kratu(c Ursae Majoris)

16. Regulus Magha(o t"on'tl,fr-

17. 6 Leonis a- P. Phalguni

18. Denebola U. Phalguni

Mrigashirsa Taurus 29"50'

Dhruva Gemini4'42'

Gemini4'53'

Gemini20o13'

Gemini21"06 '

Gemini 29"21'

Cancer 14"51'

Cancer 18o29'

Cancer 21o20'

Leo 5o58'

Leo 17"27'

Leo 27o45'

1 .21

Page 123: Astronomy Relevant to Astrology by v.P. Jain

AstronomV Releoant to Astrologg 123

Star IndianName

Magni-tude

NirayanaLongitude

DistanceLightYrs.

19. 6 Corvi ,Jr.L,.

20. Spica(cr Virginis)

-21. Arcturus

_ (o Bootis)

22'. aLibra

23. p Centauri

24. a Centauri

25. 6 Scorpii

26. Antares(c Scorpii)

.27. l, Scorpii

f8. 6 Sagittarii

29. o Sagittarii

30. Vega' (cr Lyrae)

31. Altair(c Aquilae)

32. p Delphini

33. l. Aquarii

34. Markab(a Pegasi)

35. y Pegasi

36. ( Piscium

Hasta

Chitra

Swati

Vishakha

Anuradha

Jyeshtha

Mula

P. Ashadha

U. Ashadha

Abhijit

Shravana

Dhanishta

Satabhisha

P. Bhadra-pada

U. Bhadra-

Revati

Virgo 19'35 3.1 1

Virgo 29'59' 1.21

LibraO'22' o.24

Libra 21"13' 2.90

Libra 29"56' 0.86

Scorpio 5'38' 0.06

Scorpio 8'42' 2.54

Scorpio 15'54' 1.2v

Sagiftarius 0"43' 1.71

Sagittariusl O" 43' 2.94

Sagit tar iusl 8o31' 2.14

Sagittarius 21"27' 0.1 4

Capricorn 7'55' 0.89

Capricorn 22"29' 3.72

Aquarius 17"43' g.g4

Aquarius 29"37' Z.S7

Pisces 15"17' 2.97

Pisces 26"01' 5.S7

260

36

330

4.2

4.3

330

26

16.6

Uq (.

fcta,t--r. I

Z"V-'on January 1, 1991 . Tropicar Longitude = Nirayana Longitude + 23"43,53.

HR d iagram is p repared by p lo t t ing sur facetempera ture f rom 3 ,000"C to 40 ,000oC, aga ins tluminosity (Sun = 1), varying up to 1,00,000 timesthat of the Sun. For the main sequence stars, the

Page 124: Astronomy Relevant to Astrology by v.P. Jain

t l 2 4 Astronamg Releoont to Astrologg

,"luminosity, increases proportionally (in a logarithmicsca le ) to sur face tempera ture . But fo r someluminosity is high though surface temperature iscomparatively low (like Betelguese, Antares) whilefor others (like Sirius, Procyon B) luminosity is loweven with high surface temperature. Stars l ikeBetelguese (supergiants) are well advanced in theirevolution. W-type stars have surface temperatures,of up to 80,000"C, and have bright lines (nitrogen,calcium, etc.) in spectra. Highly luminous Spica(Chitra) is B type star with helium lines dominant.Siriys (Lubdhaka) is a type (temperature 10,000"C)with calcium lines dominating. G type (Capella andthe Sun) both giants and dwarfs, with surfacetemperature 5,000oC - 6,000oC have numerousmetallic lines. Arcturus (Swati) is a K-giant typetemprature with weak hydrogen lines and strongmetalic lines. Betelguese (Ardra) is M-giant type withsurface temperature 3,000oC - 3r400oC, havingcomplicated spectra with many bands. S type (XCygni) have prominent bands of titanium oxide andzirconium oxides.

The source of stellar energy is nuclear reaetions,mainly four hydrogen nuclei being merged to form ahelium nucleus. In this nuclear reaction, the Sun islosing its mass (converted to energy) at the rate offour million tons per second. Still, it will last, in thepresent irom, for 5 billion years more.

COMETS

Members of the Solar System, move round theSun in an orbit much more elliptical than that of aplanet. A large comet is made up of small solidparticles surrounded by an envelope of tenuous gas;

Page 125: Astronomy Relevant to Astrology by v.P. Jain

The tail of a comet consists of excessively rarefiedgas and a fine dust released by star heat and generallypoints away from the sun due to solar wind and solarradiation pressure. There are manyshort periodcomets with periods of a few years, but these are verydim. The only bright comet of a period less than acentury is the Hailey's comet (its period is about ?6years). It was last seen in 1gg6. Comets are seen byreflected light of the Sun when they are near enoughand in a position to be seen.

THE GALAXY

The Galaxy is a huge star system of which theSun is a memeber. It is seen in the sky as the Milkyl{ay. It consists of about 100,000 million stars andgaseous nebula. Herschel, more than a century anda half ago, was the first to postulate the shape of tn"Galaxy, - i.e.like a double convex lens, with diameterof 100,000 light-years and thickness of 10,000 light-years. The Sun lies at a distance of 25,000 to 3O,0OOlight-years from the galactic nucleus (which is placedbeyond the star c louds in the constel lat ion ofSagittarius).

The Galaxy is a spiral and is in rdtation round itsnucleus. The Sun takes some 225 million years tocomplete its rotation in the Galaxy. The great spiralis Andromeda, a member of local group oflalaxy, andis larger than the Galaxy.

EXTRA GAIITCTIC NEBULAE

Extra galactic nebulae are the separate stellarsystems lying far beyond the Galaxy. Only three arevisible to the naked eye. Two Magallenic clouds andthe Adromeda spiral. The Megallanic clouds are

Page 126: Astronomy Relevant to Astrology by v.P. Jain

t26 Astronomg Reboont to Astrologg

200,000 light-years away.

The most distant galaxy observed is 3C-295 in the'Bootes', and is estimated to be 5000 million light-years away. The galaxies are expanding with red shiftin spectra.

Page 127: Astronomy Relevant to Astrology by v.P. Jain

CHAPTE" 11

Rising and Setting

T\vo types of motion of planets with respect to theEarth are generally considered.

(1) Diurnal motion.

(2) Longitudinal motion.

I DIUBNAL MOTION

The earth rotates around its axis from west to east in24 hours or, approximately, a day. Due to this rotationan observer on the Earth sees the Sun and otherheavenly bodies moving from east to west. Thisapparent west-ward rotation of heavenly bodies iscalled their diurnal motion.

due to this motion, the heavenly bodies appearto rise in the east and set in the west.

In figure 23, N E S W is the celestial horizon(where N is for north, E is for east, S is for south andW is for west) of an observer at O. P and Q are polesof the celestial equator. Star X appears moving in thedirection shown by the arrows, meeting the horizonat B while going down, and meeting at A while cm-ing up. The star is rising when it is coming up the

Page 128: Astronomy Relevant to Astrology by v.P. Jain

128 AstronomV Releoont to Astrologg

CGlestial Equator

hor izon a t Aand rema insv is ib le to theobserver duringits course fromAtoB.A tB , i tculminat at D asi ts a l t i tude isthe highest andaf te r tha t i tstarts decliningand goes downthe horizon arid

Fl,gtre 23

cannot be seen by the observer. So, it is said to besetting and remains set from B to C and then to A. Itis the rising and setting once in a day or, say, in onerotation of the Earth. This rising and setting is likethat of the Sun. In this case, there is no change oflongitudes as in the case of fixed stars.

2 LONGITUDINAL MOTION

The planets, the Sun and the Moon have little changein their longitudes due to their revolution in thezodiac.In astrology, the meaning of rising and settingof planets including the Sun and the Moon is differentfrom that as explained above. In astrology, when aplanet cannot be seen by naked eye due to i tsnearness to the Sun, it is said to have set or combust.The same becomes invisible on account of dazzlinglight of the Sun. It is well known that Sun is thesource of light in the solar system and other planetssimply reflect the light received from the Sun.In casethe planet moves a certain distance away from theSun, it becomes visible and is said to have risen.

Cel$ii8lHtrizon

Page 129: Astronomy Relevant to Astrology by v.P. Jain

tAstronomg Releoont to Asttology t29

WqfEryfErciu {€Qreff ffilgqTq;w: t

wu: sTalati qrfu e#F-dt 4fu"rt dw t t2 t t

frrr: fuqtgat qltz.:rqmt dEeraratet: t

erqffireqfhqr; q€qrg.{{ €fts qrfu4: t tA t I

(qd ft?Frd-J<qzar&r€ru)' There are two types of planets, namely, (a) outer

planets (Saturn, Jupiter and Mars) whose orbits are

larger than the Earth and whose sidereal period is

also greater, i.e. their angular velocity is shorter than

the Earth, in other words, it can be said that the Sun

moves faster than outer planets. (b) Inner planilts

(Venus, Mercury, Moon and can also be included in

this category) as they move faster than the Sun. The

paths of Venus and Mercury are shorter than that of

the Earth. The Moon revolves round the Earth and

their sidereal period is shorter than that of the Sun.

COMBUSTION OF OUTER PII\NETS'(i)

As the Sun moves faster than the outer planets,

viz., Saturn, Jupiter and Mars, it appears to be'

moving towards them. In such a case ' the i r

longitudes are more than the Sun. They are seen

in the western sky after sunset. After some days

when the Sun comes nearer to these planets, they

are invisible by naked eye and are said to have

set or combust. After some time, the Sun is in

conjunction with them i.e. they are in a position

of deep combust. The Sun starts moving ahead' of them. When it goes ahead by a certain distance,

outer planets are visible in the east before the

sunrise and are said to be rising in the east.

Page 130: Astronomy Relevant to Astrology by v.P. Jain

130 Astronomg Releoont to Astroloqu

Let us now see the direction of movement ofplanets and zodiac. Since the Earth rotates fromwest to east, all the planets including the zodiacappear to move from east to west. The position(the sign) of zodiac which is rising in the east atany movement is called ascendant. At the time ofsunrise. Let the longitude of the Sun be 15o Aries.At mid-noon, the Sun will be in the mid-heaven.

, So the Ascendant at that time may be 15'Cancerapprox ima te l y . A t t he t ime o f sunse t t helongitudes of the Sun will be roughly 15"30'Aries.

, It shows that the zodiac from east to west and. completes one round daily.

It shows that the longitudes are increasing in thedirection from west to south to east to north i.e.in the direction in which the Earth is rotating.

(ii) Moon is never retrograde as it is revolving aroundthe Earth. It moves much faster than the Sun andwhen reaches near i t is seen in the west andbecomes invisible in the east. Helical setting of

, the Moon takes place once in a month. It sets ineast on lcrishana paksh,a chaturdashi i .e. i tbecomes combust and rises in the west after

. shukla paksha pratipada.

T

1 :

i ,

a{ezrgd fuflr' sraa@fu; effiftlqr+erfr€rflr' qearq gezr: vraanageaaffit t

(qd ft?grd Tqatffitr€1-g)

When the Moon is within L2" of the Sun it is notseen by naked eye i.e. it becomes combust.

Page 131: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg

COMBUSTION OF INNER PLANETS

Mercury and Venus do not remain direct andbecome retrograde when they come near the Earth.Their motion is faster than the Sun. When they aredirect and their longitudes are less than the Sun, theyare visible in the east before the sunrise. Due to theirfaster motion after some days, they reach near theSun and cannot be seen; they become combust. Whenthey move sufficiently ahead of the Sun and theirlongi tudes are more than the Sun by a cer ta inamount, they become visible in the west after thesunset. Mercury and Venus do not remain direct andbecome retrograde when they are near the Earth astheir motion is faster than of the Sun.

When the longitudes of retrograde Mercury andVenus are more than the Sun, they are seen on thewestern hor izon af ter the sunset and becomeinvisible in the west. After some time, their longitudesbecome lesser than the Sun due to their retrogrademotion. In such a case, they can be seen in the eastbefore the sunrise.

The apparent diameters of the planets as seenfrom the Earth are:

Mars

Mercury',

Jupiter

,, Venus

Saturn

The planets become combust when they are at alongitudinal distance as given on next page.

131

9',.4

6".6

190".4

16".6

158".0

Page 132: Astronomy Relevant to Astrology by v.P. Jain

132 Astronomg Releoont to Astrologg

Moon

Mars

Mercury

Jupiter

Venus

Direct

12"

17"

14"

1 1 0

10'

Retrograde

Saturn 15o' From the above. table, it is seen that there isnothing in the retrograde column against the Moon,Mars Jupiter and Saturn. Since the Moon is neverretrograde, the question of its being in the retrogradecolumn does not rise.

The outer planets (Saturn, Jupiter and Mars) arecombust only when they are in conjunction with theSun and not in opposition. When they are near theSun i.e. near conjunction, they become combust. Incase of opposition, their longitudinal distance isnearly 180". The outer planets become retrograde,when they are nearer to opposition than conjunction.

Now, consider the tables of apparent diametersand their distance of combustion.

Though Saturn is more distant from the Sun thanthe Jupiter's distance from the Sun yet the degree ofcombustion of Jupiter is llo while that of Saturn is15". The reason is that the diameter of disc of Jupiteris bigger than that of Saturn. So, Jupiter is visible tonaked eye when it is nearer to the Sun.

The longitudinal distance of combustion of Venusis lesser than that of Mercury in spite of its distancebeing more than the later. This is so on account of

L2"

80

Page 133: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoant to Astrologg

bigger diameter of the disc of Venus

It might have also been noticed that in the caseof Venus and Mercury the longitudinal distance oftheir combustion is more while they are direct than

when retrograde. At the time of direct motion, theSun is in between the planet and the Earth. By thisi t can be i n fe r red tha t a t t he t ime o f supe r io rconjunction the planet is farthest from the Earth andat the t ime of inferior conjunction it is nearest to i t .The disc of the planet wil l appcar bigger when it isnearer and shorter when it is farther.

Latitudes of the planets have not been considefedfor the combustion of planets but only longitudinald i s tances have been accoun ted fo r . By no tconsidering latitudes sometimes there is a differenceof many days between the theoretical combustion ofp lanets and the actual combust ion which is byobservation in the sky as shown in between the figure.

Let N W S E be the ecliptic. Let O.be the centreof the earth or, say, observer.

S be the Sun.

P be t heplanet position asper the longitude.

6tEc td ic P l i s the

actual posit ion ofthe planet.

Now, a fast -moving planet isbeh ind the Sunby a ce r ta in

133

Figure 24

Page 134: Astronomy Relevant to Astrology by v.P. Jain

134 Astronom! fuleoontto Astrobgg

longitudinal distance. The ZSOP is that longitudinaldistance, at the time when the combustion starts, theplanet is actually at P,. The distance p,S i.e. Zp,OSis more than ZPOS. Hence the planet will actuallybe combust when its actual angular distance from theSun will be equal to ZPOS. The planet will have tomove nearer to the Sun i.e. it will take some moredays before it becomes combust. For this, the methodof correction has been given in the Surya siddhanta.

Page 135: Astronomy Relevant to Astrology by v.P. Jain

,.b

Test Yourselfd .

Q f. Define Mahayugas. What are its divisions andtheir lengths of time?

Q 2. Write short notes on:(a) Surya siddhanta(b) Varaha siddhanta(c) Arya siddhanta

Q 3. What is the diflerencg between the approachof Indian tstronomjl and that of Westernastronomyt

,Q 4. Write Short notes oru

(a) Galileo(b) Sir Issac Newton(c) Nicholas Copernicus

,(d) Sir William Herschal(e) John Couch Adams

Q 5. When is the altitude of a planet greatest during

f d"y and why?

\Q 6. Name any four great circles on the celestial

shpere. Give their importance.

Q 7. What is the relationship between planets andnames of weekdays?

Page 136: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrologg

Q 8. Do the planets move retrograde? Give reasonin support of your answer.

Q 9. Which is the most luminous planet (excludingluminaries Sun and Moon)?

Q f0. What is the highest latitude north or south atwhich it is possible to see the Sun in the Zenithat noon.

Q 11. Why the Sun is never seen in Zenith at Delhiwhen it can be seen at Madras? Give reasonsto justify your answer.

Q 12. Which planets cannot be seen by naked eyeand why?

Q 13. How does the solar eclipse take place? Whatis the maximum limit of its totality? What are

' the various kinds of solar eclipses?

Q 14. Under what conditions does lunar eclipse takeplace? What is the maximum l imi t o f i tstotality? r' q,!

Q 15. What is the role of Rahu and Ketu in theeclipses? Can an clipse take place when theMoon is not near Rahu or Ketu?

Q 16. Write short notes on:(a) Local time(b) Indian Standard Time(c) Zonal Standard Time

Q 17. What are the different units for measuringdistances of stars?

Q f8. What is a Luni-Solar year? How is it related

Page 137: Astronomy Relevant to Astrology by v.P. Jain

Astronomg Releoont to Astrology

to Lunar year and Solar year?

Cl f9. What is Panchanga? How the tithi and Karanaare calculated? Find out tithi and Karana ar2.30 p.m. on December 12, 2000.

Q 20. How the nakshatras and yogas are found out?What nakshatra and yoga will be on December28,2000 at 5.30 p.m.?

Cl21. Sometimes a tithi is missed and on anotheroccasion one tithi is named for two days.Explain the reason and explain with the helpof an example.

q?z. Find out the day on February lg, 2000 by thecalendar method. Explain it with the help ofan example.

The presenr work is an effort to derineare the rrr-i;tuTh,, in a texr bookfashion. The Transit of plae"un,pr.,ai,.,!;;'';;;il""Ti:"":TL?ix;lff Iliff i;:.,::,r";h o w t h e t r a n s i t i n f a c t e f f c c t l i l e e v e n t s . ' - - \ ' . " " " "^

?? x,r"*]s""^rl ?,lJg y I D E_R s rA N D r N c r RA N s r r F o R

Text book ofTRANSIT OF PLANETS

BECTNNERS AS wELL AS ADVANaE; iiurji*ii,oTf ASrRoLocy _

- : l ^ . _

Page 138: Astronomy Relevant to Astrology by v.P. Jain

INDEXA

Altitude 39Anomalistic Month 95Anomalisticyear 96Astronomical Unit 92Azinuth 39

B

Bija corrections 23

cCalendar year 96Celestial Equator 35Celestial Longitude 3?Celestial Meridian 40Celestial Poles 35Celestial Sphere 31Changes in the Sun's Decli.

nation 4lCivil Day 94Combustion 87Combustion of Outer planets

129Combustion of Inner plenets

131Comets 60, 124Comparison of Time of

Revolutions for VariousPlanets 26

Cycle of Moon 55

D

Day 98Declination 37

'l

Declination Circle 38Difference between Modern

and Indian ClassicalAstronomy 26

Diurnal Motion 12?Division of zodiac into signs

and constellations 71

E

Earth 48Earth on Vernal Equinox and

Autunal Equinox 52Ecliptic 36, 47Encke's Comet 61Extra Galactic Nebulae 125

F

Five limbs of Panchanga g8Formation of Seasons 50

G

Galaxy 125Great Circle 82

H

Halley's Comet 61Historical Background IHour Angle 38

I

Important AstronomicalScholars 21.

Indian Astronomy 15Inferior Coqiunction 80, 56

Page 139: Astronomy Relevant to Astrology by v.P. Jain

J

Jupiter 58

K

Karana 111Kepler's Laws 62

L i

Light Year 92Local Mean Time 89Longitudinal Motion 128Lunar Day or a Tithi g4Lunar Eclipse 82Lunar Month 95Lunaryear 96Luni-Solar Year 96

M

Mars 58Mean Places of Stars 122Mean Solar Day 88Mercury 57Meteorites 62Meteors 6lMinor planets or asteroids

62Moon 53Movable and Fixed Zodiacs

69

N

Nadir 40Nakshatra 109Name of Astronomers 12Names of the Days of a Week

62Neptune 59Nodes 76

Nodical Month 95Nutrtion 69

oObliquity of Equator and

Equinoxes 42Occultation 87

P

Panchanga 98Parsec 93Phases of Moon 74Plane 32Planets 4rlPluto 60hle of a Circle in a Sphere

33Precession of Equinoxes d?Prime Vertical 40

R

Rehu and Ketu ?7Revolutions of various

Planets in a MahayugaofSolarYears 23

Right Ascension 3?Rising and Setting 12?

s(

Satellite 4lSaturn 59 \Siddhantas 1?Sidereal Day g4

Sidereal Period ?8Sidereal Time 78Siderealyear 95Small Circle 32 ' I

Solar Eclipse 84Solar Month 94

Page 140: Astronomy Relevant to Astrology by v.P. Jain

Solar System 44Sphere 31Stars 44, 120Superior Conjunction 80' 56Surya Siddhanta 18Synodic Period ?9

T

Terrestrial Equator 34Tbrrestrial Latitude 35Tierrestrial Longitude 34Tbrrestrial Meridians 34Ttthi 100Tropicalyear 95

UUnitsof Measurement of

Distances in Space 92Units of Time 91Upagrahas l1?,119Uranus 59

vVenus 57Verticals 40

YYoga ll4

zZenith 40Zodiac 36

$

Page 141: Astronomy Relevant to Astrology by v.P. Jain

Errata {n,

: . . .

Page 62 Twelfth line read 'foci' instead of ,oci'.

Page 80 Figure 16 delete lDrErEr' ,

Page 80 Tenth l ine from bottom read .E,SM,'for.SMrErl,

'Page E0 Eleventh l ine f rom bot tom read ,ESM", for' sM ,E r '

Page 80 Thi rd l ine f rom bot tom read ,E ' for .Er 'and .E, '

for 'Er '

Page E l Seven th l i ne read ' J ' and ' J , ' f o r , J r ' and . J . '

respectively.

Page 129 Twelfth line delete ',' after .Mercury' and bring'and' befote 'Moon'.

Page 129 Eeventh line from bottom delete words .such,

and 'a ' . j

Page 129 Tenth l ing frg{ $gorn put' l 'after Sun insteado f ' . ' . '

Page 130 Twelfth line insert 'moves' after .zodiac,.

. j '

Page 142: Astronomy Relevant to Astrology by v.P. Jain

Table of Planetary Movement

Namesolplan€te

Meandistancefrom theSun

(ln mlles)

Meanorbitalvelocityin mllesperlecond

Albed,o SiderealperioclIn Earthdays

Synodicperlodin Eafihdays

Periodof rotal-lon inEarthdays

EquatGrialdiame.ter inmlles r

Eccent-rlclty ottheorbit

Orbltallncllna-tlon toEcllptlc

Mags(Earth =1 )

Ilensity(Water= 1 )

SurfaceGravity(Earth =1 )

Volume(Earth =1 )

Escapevelocitymilespers€cond

Maxl-mumMagn.!!-udo

lnclina-tlon ofEquatorto orblt

Arcawhichtheyretro-grade

NumberotSatellite

Mercury 36,000,000 29.7 0.06 88 1 1 5 . 9 58.65 3,otr, , 0.206 7"O', 0.055 5.5 0.38 0.055 2.6 (-) 1.e 12" 0

Venus 67,200,000 21.7 0.76 224.7 583.9 243.16 7,523 0.007 9"24' 0.815 5.25 0.90 0.86 6.4 (-l4.4 178' 16" 0

H : M : S

Earth 92,957,000 18.5 0.36 365.3 23:56:04 7,926 0.017 1.0 5.52 I 1 6.94 23"27' 1

Mars 141,500,000 15.0 0 .16 687 779.9 24:37:23 4,218 0.093 1's1 ' 0.107 3.94 0.38 0.15 3.2 (-) 2.8 23"59' 18' 2

Jupitel 483,300.000 8.1 0.43 1 1.9 yrs 398.9 09:50:30 88,378 0.048 1'18' 3 1 8 1.33 2.64 1310 37.1 (-) 2.6 3"5', 9' 1 6

Saturn 886,100,000 6.0 0.61 29.5 yrs 378.1 10:39:0O 74,145 0.056 2"29' 95 o.71 1 . 1 6 74 22 (-) 0.3 2e44' 6' n

Uranus 1,783,000,000 1.2 0.35 84.0 yrs 369.7 17:0O:0O 32, t90 o.o47 0'46' 14.6 1 . 7 1 . 1 7 67 r3.9 3.6 98" 4" 5

Neptune 2,793,000,000 3.4 0.3It 164.8 yrs 367.5 l7:57:0O 30,760 0.009 r"46' 17.2 1 . 8 1 . 2 57 1 5 . 1 7.7 28"$', 3" 2

Pluto t,667,000,000 2.9 o.47 247.7 yrs 366.76days

thrsl7min

1,800 o.28 17'10'below

0.11 4 1

Sun 13525.4

days8,65,000 330,000 1.41 28 r,3(n,00c 384

Moon 239,000hom the Eadh

1.02km/sec

7% 27.321 29.s327.3

days2,160 0.055 5'15' il41 3.34 0.16 1.5 (-l12.7

Ab€(b ls ho r6fl*ttn9 por,er ol a dan€t in th€ lalio otth€ amount oa llgt r€i€clsd lron tho body to t|€ srnount ol lighl whk* lalh Won it ftom an ouElde sourc€.

Magnitude|satemlorbdghtn€55.Thegr6t6rthemagn|tUd6,het€5s€ri6th.bdghtt6.wl€t€the'|gut€bin'|rnusitrrl€ansthetp|a