Nīlakantha's Planetary Models

Abstract

(ProQuest: ... denotes formulae omitted.)One of the special qualities of Dan Ingalls' humanism was that he appreciated investigations into all aspects of human intellectual activity, that he recognized that science was an important part of Indian culture as it is of ours. I hope that his magnanimity is shared by the readers of this journal.This paper deals with one occasion when Indian philosophy and astronomy interacted. Philosophy taught an astronomer that perception is a more powerful guide to the real nature of planetary motions than is tradition, even that which claims to be divine revelation. The astronomer, relying on observations, changed both the traditional planetary models and their parameters. However, he failed to justify these changes by showing how his observations made them necessary, and, in the end, he was not radical enough to break completely out of the tradition of geocentrism. Obviously, to notice this limitation is not to criticize the astronomer, but simply to locate him within a particular intellectual tradition wherein what he actually did do was extremely radical.The only Sanskrit work that has so far been found in which are discussed extensively and carefully the role of observations (pratyaksa, panksana) and inference (anumâna) as fundamental to the proper practice of astronomy is the Jyotirnumamsa] of the important Kerala astronomer, NUakantha Somayajin.2 His view, contrary to the frequent assertion that the fundamental siddhantas expressing the eternal rules of jyotihSastra are those alleged to have been composed by deities such as Surya, is that the astronomers must continually make observations and draw logical conclusions from them so that the computed phenomena may agree as closely as possible with contemporary observations. This may be a continuous necessity because models and parameters are not eternally fixed, but change, or because longer periods of observation lead to more accurate determinations of the models and parameters, or because improved techniques of observing and of interpreting the results may lead to superior solutions.As part of his demonstration of the disagreement between the various siddhantas, he computed according to several texts the mean longitudes of each of the seven planets and the lunar apogee for day 1,682,112 since the beginning of the Kaliyuga.3 The calendar equivalent of this ahargana will vary because of the difference in the epoch of the day (sunrise at Lanka) and because of the differences in the lengths of the years in the various paksas. The epoch of the Kaliyuga in the ardharatrika system was midnight at Lanka on 17/18 February in -3101 Julian. The length of a Julian year is 365 1/4 days, so that the ahargana of 1,682,112 corresponds to 4605 years and 135 days. The resulting date in the Julian calendar is 1 August 1504. This date is undoubtedly near the date at which Nllakantha completed the Jyotirmimamsa.In the Jyotirmimamsa, Nllakantha refers to his own Aryabhatiyabhâsya which he had finished after 28 July 1501;4 and in the Aryabhatiyabhâsya he refers to both his Siddhantadarpana5 and his Tantrasahgraha.6 According to the chronograms in the first and the last verses of the Tantrasahgraha the ahargana from the beginning of the Kaliyuga till Nllakantha's beginning to write this book was 1,680,548 (= 20 April 1500), and the ahargana till his completing it was 1,680,553 (= 25 April 1500). In part then, the Jyounnimamsa can be considered a justification for the innovations in siddhaantic astronomy that Nllakantha introduced in the Tantrasahgraha and Siddhantadarpana.And Nllakantha did change many parameters. As examples I will present his mean motions for the planets and his sizes for the epicycles in the Siddhantadarpana and in the Tantrasahgraha? I compare the Siddhantadarpana's parameters with those of the Brahmapaksa.There is no simple relationship between these two columns of numbers. Moreover, although the number of civil days in a Kalpa according to the Siddhantadarpana - 1,577,917,839,500 - is greater than is that of the Brahmapaksa - 1,577,916,450,000, the numbers of rotations are not uniformly more so that the mean daily motions might be reasonably close to each other: instead, a widely differing pattern of changes in mean daily motions occurs. …