Precession and Trepidation in Indian Astronomy before A.D. 1200

Abstract

(ProQuest: ... denotes formulae omitted.)The process by which various non-Ptolemaic elements of the Greek astronomical tradition were transmitted to India and were there transformed into the astronomy of the siddhantas is a subject of complexity and of obscurity. Its elucidation, however, is of great historical importance, both for the understanding it will afford us of the motivation for particular Indian solutions of problems in mathematical astronomy, and for the insight we will obtain from it into those areas of Hellenistic astronomy that, being almost totally eclipsed in Greek by the brilliance of Ptolemy's Almagest, can be discerned, though dimly, in the poetry of jyofihsastra. present paper contains an investigation into one aspect of this process, that in which the ideas both of the precession and of the trepidation of the equinoxes were introduced into India and there interpreted in terms of an older Indian tradition of the position of the solstices relative to the naksatras and in other ways. This example, like that of the planetary model previously discussed in this journal (ii (1971), 80-85), beautifully illustrates the failure of the Greeks to communicate and of the Indians to grasp the full significance of the concepts transmitted.The Jyotisavedanga1 of Lagadha (5/4th century B.c.?) states (Arca 6 = Yâjuca 7): The Sun and the Moon begin their northern [course] at the beginning of aravicthâ [Dhanictha]; the southern [course] of the Sun [begins] in the middle of Sarpa [Aslecâ]. [The beginnings of these two courses occur] always in [the months] Mâgha and aravana [respectively]. One also finds this scheme in, for example, the Parasaratantra cited by Utpala (a.d. 966) on the Brhatsarphita2 of Varahamihira (ca a.d. 550).By the time of Varahamihira a fixed sidereal zodiac was in use in India.3 In this zodiac the beginning of Aries was identified with the beginning of the nakcatra Asvini; in the fifth and sixth centuries the beginning of Aries was further said to be the point of the vernal equinox. Varahamihira recognized the discrepancy with the statement of Lagadha (Brhatsatyhita 3, 1-2):Once, according to what is said in ancient treatises, the southern ayana of the Sun was from the middle of Âelecâ, and the northern began with Dhanicthâ. Now [one] ayana of the Sun begins at the beginning of Cancer, the other at the beginning of Capricorn. This is a negation of what was said; the difference is made manifest by direct observations.In his Pancasiddhantika* (3, 20-2) Varahamihira explains this change by a theory of trepidation over an arc of 46;40°-23;20° (identified with the Sun's maximum declination) to either side of the equinox:When the sum [of the longitudes] of the Sun and Moon is a revolution, it is called Vaidhrta [yoga]; but if it is a revolution plus 10 nakcatras [133 ;20c]. Vyatipata. time is to be ascertained by means of the degrees attained [by the luminaries]. When the return of the Sun was from the middle of Ââlecâ [at 113;20°], then the ayana [-correction] was positive; now the ayana is from Punarvasu [at 90°]. When the falling away [from the mean position] of the ayana is reversed, then the correction [kcepa] for the Sun and Moon [equals] the degrees of the maximum declination [kâcthâ] of the Sun [23;20°]. There is Vyatipata if the sum [of the longitudes] of the Sun and the Moon is 180°.This is the earliest datable reference to a theory of trepidation or precession in India ; unfortunately no rate is given. A theory of trepidation was known to Theon of Alexandria (a.d. 361) and to Proclus (a.d. 410-485), and a theory of precession to Hipparchus (ca -126); Hipparchus's length for a tropical year was used by Sphujidhvaja (a.d. 269/70) in his Yavanajdtaka (79, 34) and in the Romakasiddhanta summarized by VaTahamihira in his Paiicasiddhântikâ (1, 15 and 8, 1). It is not unreasonable to suppose that the idea of trepidation or precession was introduced into India by the Greeks, though the parameters chosen by the Indians are their own, and that the arguments presented in favour of the hypothesis of a motion of the colures are derived from a particular interpretation of the Vedangajyotisa. …