Indian astronomy: an introduction
S. Balachandra Rao
Rao, S. Balachandra;
Indian astronomy: an introduction
Universities Press (Orient Longmans) 2000, 207 pages
ISBN 8173712050, 9788173712050
topics: | astronomy | india | history
Summary
Sketches the basic astronomical ideas as developed in Indian in ancient times. Calculation of astronomic events require precise conceptualization of time. Particularly, it calls for computing compute the total elapsed time or ahargana from a reference event (start of epoch) - i.e. one must refer to the calendar.
Time is defined from certain celestial events, defined in chapters 2 and 3. Suryasiddhanta onwards, Indian calendars were generally lunisolar - i.e. the pattern of lunar phases control the month boundary, but the transition of the sun determines what name the month will have. This enables the lunar month to be roughly in the same part of the solar year.
The ecliptic is divided into twelve equal rAshis (signs of the zodiac, chapter 3), and there is a lunar month for each episode when the sun enters a particular rAshi. The month vaishAkha is so named because the full moon on this month occurs near the asterism vishAkha (Libra). This is ensured by calling the month when the sun is in meSha (Aries) as vaishAkha (in new-moon based systems of South India, this would be the month of chaitra). Note that the mesha rAshi, covering the nakshatras asvini, _bharaNI, and krittika, is roughly opposite vaishAkha on the ecliptic. Sometimes, the sun may remain in the same rAshi for more than a lunar month; in such situations, one has an extra month (adhikamAsa, chapters 5 & 6) Occasionally, the sun may transition into two rAshis during the same month, here one has a lost month (kshaya mAsa). This makes it difficult to compute the total elapsed time. In the pure solar calendar which is also used in most regions, the months are defined only by the solar transitions. This method of solar year reckoning is similar to the Besselian year used in astronomy today. Thus the year usually begins with the same Mesha transition (around April 14-15), but because the sun at sunrise may remain in a rAshi for 29 to 32 days, the length of months are not fixed; but the overall year length is within a day or two of 365. All this means that the Indian calendars are always fixed to the sun, there is no need for leap years or other corrections. However, this also means that the number of days elapsed are a bit variable. Thus, it is a problem to determine the astronomical time, the period elapsed from a given epoch. This is the computation of ahargana, the total elapsed time, given in Chapter 7. Once we have the total elapsed time, one may compute a "mean" position, which assumes uniform velocity across the sky (chapter 7). Since planets don't move uniformly across the sky, a manda (slower speed, retrograde motion) or shighra (faster speed) correction has to be applied (chapter 8). This of course, correlates to a geocentric view of the heavens, and the process, of obtaining a mean position, and then the corrections, is pretty much the same as the Ptolemaic system (about 2nd c. AD). Whether the Indian system is likely to be derived from it (though the surya siddhAnta is most likely older), is not commented on by Balachandra Rao. Thus, finally, we have a prediction for the "true positions" of each celestial object at any given time. This can also be used together with measurements on a gnomon (sanku) to compute latitude. Also, one may compute the time of sunrise and sunset (chapter 10). Ultimately, one may also predict solar and lunar eclipses, (ch 11/12).
Excerpts
Six vedangas and authors
shikShA - phonetics - gargeya [phonetics was systematized for sounds - so that vedic texts could be pronounced properly. the word shiksha gained the current meaning - training / education - because this was how it was pronounced] vyakAraNa - grammar (lit. analysis) - ashTAdhyaya panini nirukta - etymology - yaska chhandas - prosody - pingala jyotisha - astrology - lAgadhi kalpa (ashvalayAna-shrautA) - ritual / procedure - kautsa vedAMgajyotiSha: appears in two rescensions: Rigveda jyotiSha and yajurveda jyotisha. One verse says: "I shall write on the lore of time, as enuciated by the sage Lagadha." Based on this, the authorship of the vedAMgajyotiSha is attributed to Lagadha. At the time of its composition, the winter solstice was at the beginning of the ShrAviShThA (Delphini) constellation and summer solstice in the middle of the AshleShA. VarAhamihira stated that in his own time the summer solstice was at the end of three quarters of punarvasu and the winter solstice at the end of the first qtr of uttarAShARhA, there had been a precession by 1 and 3/4 of a nakshatra (7 pAdas, each pAda = 3 deg 1/3), or about 23deg 20' x rate of precession = 72 years per degree --> 1680 years or about 1150 BC. Generally agreed period is between 14th c BC and 12th. r^gveda maNDalas --> knowledge of moon phases, newmoon, etc. nakShatra: very old system, used for days (27 and 1/4); moon covers one nakshatra each day (lunar month = 27.3217 days) agrahAyaNa - old name for mr^gashira - means beginning of the year - corresponds to about 4000 BC. vedAMgajyotiSha mentions that the longest and shortest days on the two solstices as 36 and 24 nARikas (1/60th of day, as measured by a certain quantity of water flowing through a small hole [clepsydra]). Year was known to be 360 days plus 5 (4 is too less, and 6 too much). Alternately, 254 days (lunar years) + 11 days = 11 days of sacriice. shortest day : 24/60 x 24 hrs = 9h 36m : dinArdha = 4h 48m longest day : 36/60 x 24 hours = 14h 24m: dinArdha = 7h 12m Thus diff from 6hrs = +/- 1h 12m = ASCENSIONAL DIFFERENCE sin (asc diff) = tan(phi) tan (delta) where phi = latitude, delta = declension of sun - about 23 deg 53 min - vj takes it as 24 deg --> leads to a latitude about 35 deg --> Vj was written from a lat about 35deg [may be gAndhAra 5] -- "siddhAnta" : the word has a connotation of "established theory" - several arose around 100 BC to 100 AD - introduced the twelve signs of the zodiac - more precise value for the year - computations of planet motions, solar and lunar ecpipses - idea of parallax principally 18 siddhAntas : surya, paitAmaha, vyAsa, vAsiShTha, atri, parAshara, kAshyapa, nArada, gArgya, mArIchi, manu, AngIra, lomasha (or romaka), paulisha (paul of alexandria?), chyavana, yavana, bhr^gu, shaunaka. but only five extant during varAhamihira (505 AD): surya or saura, paitAmaha (or brahma), vAshiShTha, romaka and paulisha. --> compiled by varAhamihira as panchasiddhAntaka
Historical Texts in Indian Astronomy
1 AryabhaTa I 499 AD AryabhaTiyam, AryasiddhAnta
2 varAhamihira b.505 pañchasiddhAntika, br.hatsaMhitA
3 bhAskara I c. 600 bhAShya on AryabhaTiyam, mahAbhAskarIyam
laghubhAskarIyam
4 brahmagupta b. 591 bhamashpuTasiddhAnta, khaNDakhAdhyaka
5 vateshvara 880 vateshvarasiddhAnta
6 mañjula 932 laghumAnasam
7 AryabhaTa II 50 mahAsiddhAnta
8 bhAskara II b. 1114 sidhhAntashiromaNi, karaNakutUhala
9 parameshvara c.1400 dr.ggaNitam, sUryasiddhAntavivaraNam,
bhaTadIpikA
10 nilakanTha somayaji 1465 tantrasaMgraha, AryabhaTabhAShya
11 gaNesha daivajn~a 1520 grahalAghava
12 jyeShTadeva 1540 yuktibhAShA
13 chandrashekhara b. 1835 siddhAntadarpaNa
14 shankara varman 19th c. sadratnamAlA
15 venkatesa ketkar 1898 jyotirgaNitam, grahagaNitam
(p.11-12)
Coordinate Frames
There are three systems for assigning coordinates to a star, using the
ecliptic, the celestial equator, and the horizon as reference. The ecliptic
is stable, the equator wobbles slowly, the horizon changes all the time but
is good for immediate reference.
Ecliptic system:
celestial latitude of star S = angle from ecliptic up to S
longitude : In Indian system, longitude is measured from meshAdi (start of
mesha) - this is a fixed point, and hence this sidereal or
nirayana longitude ls is measured w.r.t. the stars . Because of
the precession of the equinoxes, this point varies a little and
immediate measurements of longitude w.r.t. the equinox, called the
tropical longitude, lt, varies from the nirAyana by an amount
called ayanAMsha (degrees of precession of equinox).
Right ascension and declination system (celestial equator)
angle along celestial equator from first point of Aries is the right
ascension (R.A., alpha), and the elevation of the object from the
equator is the declination
Azimuth and altitude (celestial horizon)
Angle along horizon from north is azimuth; angle from horizon is
elevation.
Contents
Diacritical Marks for Roman Transliteration of Devanagari;
Preface;
Acknowledgements;
1. Historical Introduction 1
2. Celestial Sphere 16
3. Co-ordinate Systems 25
4. Rasi And Naksatra Systems 32
5. Time in Indian Astronomy 39
6. Calendars and Indian Pancanga 56
7. Mean Positions of the Sun, Moon and Planets 71
8. True Positions of the Sun and the Moon 87
9. True Positions of the Star-Planets 102
10. Triprasna-Direction, Place and Time 126
11. Lunar Eclipse 141
12. Solar Eclipse 156
Computer Programs 166
Bibliography 187
Glossary of Technical terms in Indian astronomy 191
Index 203
from the blurb:
The first comprehensive book of its kind on Indian Astronomy. Surveys the
development of astronomy in India from the Vedic times to the present day.
Discusses the concepts, techniques and computational procedures developed by
Indian astronomers like Aryabhata, Brahmagupta and Bhaskara II, over more
than a millennium and a half.
This book should be studied along with Balachandra Rao's
Indian Mathematics and Astronomy,
which contains more details and historical information.
amitabha mukerjee (mukerjee [at-symbol] gmail) 2012 Apr 20