Jyotihshastra: Astral and Mathematical Literature c4.38

c4.38

In order to compute the mean longitudes of the planets the Indians adapted the Greek idea of a “great year” which begins and ends with a mean planetary conjunction to the already existing theory of the Kalpa.¹⁷ The choice of the subdivisions of the Kalpa (see Table 1) and of the number of rotations of each of the planets within it (see Table 2) are two of the main features that distinguish one pakṣa or school of astronomy from another, the others being the geometrical models for planetary motion and their parameters (see Table 3). It was demonstrated by R. Billard that the mean longitudes computed by the two systems of Āryabhaṭa converge in accuracy on about 500, and this led him to suggest that Āryabhaṭa founded Indian astronomy in the form which we have called "Greek" on the basis of his own extraordinarily precise observations.¹⁸ However, the same phenomenon is explained in a way that fits better into the known facts of the history of Indian astronomy: that "Greek" astronomy existed in India before Āryabhaṭa; that the geometrical models solve problems faced by Greeks rather than by Indians, and must have been accompanied by means of computing mean longitudes when they were transmitted to India; and that all of the Indian evidence is against the theory of their being able to make accurate observations. This alternate explanation assumes that two procedures were used.¹⁹ One, utilized by the Brāhmapakṣa, consists of an expansion of Babylonian-type period relations to numbers of rotations of the planets in a Kalpa by assuming a fixed time between the beginning of the Kalpa and the beginning of the current Kaliyuga on 18 February - 3101, and a close proximity to a mean conjunction of the planets on the latter date. This problem results in a series of indeterminate equations that can be solved by the kuṭṭaka. Āryabhaṭa could have arrived at his surprising accuracy by using a reasonably accurate set of Greek astronomical tables to compute the mean longitudes of the planets on 21 March 499, and by assuming a true mean conjunction of the planets 3600 years earlier, on 18 February - 3101.