On the Greek Origin of the Indian Planetary Model Employing a Double Epicycle

Abstract

The development of geometric models to explain the inequalities of planetary motion in terms of combinations of circular motions is characteristic of Greek astronomy, and derives its initial bias from statements of the Pythagoreans, Plato, and Aristotle regarding the structure of the universe and, in the case of Aristotle, the difference between the mechanics of the sublunar centre of the cosmos and that of the celestial spheres. It is hardly necessary to point out here that among the devices invented to account for these inequalities are the eccentric circle and the epicycle, whose properties were investigated by Apollonius of Perge in about 200 b.c.1 The occurrence of these devices in Sanskrit astronomical texts of the fifth century a.d. immediately suggests some Greek influence. And the supposition of such an influence is greatly strengthened by the fact that Greek adaptations of Babylonian linear astronomy2 and Greek treatises on genethlialogy3 were translated into Sanskrit between the second and fourth centuries a.d.; it is virtually confirmed by the fact that the earliest Sanskrit siddhânias to employ epicyclic models, the older Romaka (for the luminaries only4) and Paulisa (for the Sun only5), are largely of Greek or GrecoBabylonian origin. It is my intention here to investigate the Greek background of the common Indian model for the star-planets which involves two concentric epicycles.In the Paitâmahasiddhânta of the Visnudharmottarapurâria,6 which is our earliest extant exponent of the Indian double-epicycle planetary model (it was probably composed in the first half of the fifth century a.d.), the pattern was set for all later texts except for those belonging to or aware of the auduyaka System of the Âryapakca. The orbits of the planets are concentric with the centre of the Earth. The single inequalities recognized in the cases of the two luminaries are explained by manda-cpicycles (corresponding functionally to the Ptolemaic eccentricity of the Sun and lunar epicycle respectively), the two inequalities recognized in the case of each of the five star-planets by a mandaepicycle (corresponding to the Ptolemaic eccentricity) and a .%Arn-epicycle (corresponding to the Ptolemaic epicycle). The further refinements of the Ptolemaic models are unknown to the Indian astronomers.If one tries to imagine the geometric model utilized by the Paitâmahasiddhânta, one immediately realizes that it cannot be cinematic ; the planet cannot ride simultaneously on the circumferences of two epicycles. These two epicycles must be regarded simply as devices for calculating the amounts of the equations by which the mean planet on its concentric orbit is displaced to its true position. This interpretation is confirmed by the explanation offered in early texts of the mechanics of the unequal motions of the planets : demons stationed at the manda and ftghra points on their respective epicycles pull at the planets with chords of wind.7 The computation of the total effect of these two independent forces upon the mean planet varies somewhat from one school (pak$a) of astronomers to another, or even from astronomer to astronomer within a paksa. But the fundamental concept remains clear: the planet is always situated on the ciicumference of a deferent circle concentric with' the centre of the Earth, while two epicycles (one each for the Sun and Moon) revolve about it. As the planet progresses with its mean velocity about this deferent circle, at each instant it is pulled by the two epicycles away from its mean to its true longitude. These instantaneous true longitudes are subject to computation, but a true course of the planet over a period of time can only be conceived of as a series of such instantaneous true longitudes.This is not to deny that the equivalence of an eccentric to an epicyclic model had also been transmitted from Greece to India, though it would seem that the transmission was effected by a different text from that from which the doubleepicycje theory is derived. …