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
Aug 30, 2014
aX rg.
A book
on
ASTRONOMY(RELEVANT TO ASTROLOGY)
t u \P^ 5r" Ino-t
by
V. P .Iain
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Publnsh,eil byBharatiga Prachga Eoatn Sanatan Viggan Sansthan
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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.)
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
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
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
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
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
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
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
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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
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
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
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
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.
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
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
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
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\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
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
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
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
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.
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
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
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.
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
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.
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.
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.
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.
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
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
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
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.
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
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
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,
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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.
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
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.
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
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.
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
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.
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,
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
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
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
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.
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
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
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.
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
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.
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
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
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
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'
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/-
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
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
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
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
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
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
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
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
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
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
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.
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
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.
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.
87
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
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
89
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
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
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
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
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
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
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
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.
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
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.
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
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"
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
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'
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
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
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
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
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
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
(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
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
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.)
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
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
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--
20399'800'
_ 25 3gg'900'
25th yoga has passed and 26th yoga, i.e. Indra wasrunning at that time.
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
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
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:
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.).
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
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
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
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;
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
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.
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
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
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.
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.
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
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
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
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.
,.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?
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
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 ^ . _
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
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
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
$
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{ $gorn put' l 'after Sun insteado f ' . ' . '
Page 130 Twelfth line insert 'moves' after .zodiac,.
. j '
Table of Planetary Movement
Namesolplan€te
Meandistancefrom theSun
(ln mlles)
Meanorbitalvelocityin mllesperlecond
Albed,o SiderealperioclIn Earthdays
Synodicperlodin Eafihdays
Periodof rotal-lon inEarthdays
EquatGrialdiame.ter inmlles r
Eccent-rlclty ottheorbit
Orbltallncllna-tlon toEcllptlc
Mags(Earth =1 )
Ilensity(Water= 1 )
SurfaceGravity(Earth =1 )
Volume(Earth =1 )
Escapevelocitymilespers€cond
Maxl-mumMagn.!!-udo
lnclina-tlon ofEquatorto orblt
Arcawhichtheyretro-grade
NumberotSatellite
Mercury 36,000,000 29.7 0.06 88 1 1 5 . 9 58.65 3,otr, , 0.206 7"O', 0.055 5.5 0.38 0.055 2.6 (-) 1.e 12" 0
Venus 67,200,000 21.7 0.76 224.7 583.9 243.16 7,523 0.007 9"24' 0.815 5.25 0.90 0.86 6.4 (-l4.4 178' 16" 0
H : M : S
Earth 92,957,000 18.5 0.36 365.3 23:56:04 7,926 0.017 1.0 5.52 I 1 6.94 23"27' 1
Mars 141,500,000 15.0 0 .16 687 779.9 24:37:23 4,218 0.093 1's1 ' 0.107 3.94 0.38 0.15 3.2 (-) 2.8 23"59' 18' 2
Jupitel 483,300.000 8.1 0.43 1 1.9 yrs 398.9 09:50:30 88,378 0.048 1'18' 3 1 8 1.33 2.64 1310 37.1 (-) 2.6 3"5', 9' 1 6
Saturn 886,100,000 6.0 0.61 29.5 yrs 378.1 10:39:0O 74,145 0.056 2"29' 95 o.71 1 . 1 6 74 22 (-) 0.3 2e44' 6' n
Uranus 1,783,000,000 1.2 0.35 84.0 yrs 369.7 17:0O:0O 32, t90 o.o47 0'46' 14.6 1 . 7 1 . 1 7 67 r3.9 3.6 98" 4" 5
Neptune 2,793,000,000 3.4 0.3It 164.8 yrs 367.5 l7:57:0O 30,760 0.009 r"46' 17.2 1 . 8 1 . 2 57 1 5 . 1 7.7 28"$', 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