This article is a follow‐up of a very important contribution to the understanding of Indian astronomy by Billard (Billard 1971, 1977; van der Waerden 1980, 1988) who has calculated the mean longitudes of the sun, moon, moon's apogee and node, and those of the five known planets, from the numerical data in the main astronomical texts. The errors of these longitudes are determined by comparing them with the results of the modern formulae.
Billard uses the methods of mathematical statistics to find the most probable dates of the observations. His graphs, in which the errors of the longitudes are plotted against time from BCE 500 to AD 1900, illustrate his most important conclusions. For example, the Āryabhaṭa graph, Fig. 1, of this article, (Fig. 6 in Billard's book) shows that he made accurate observations at about AD 510. The error lines are for the Sun (☼), Moon (☾), Moon's apogee and node (ω, θ), Mercury (☿), Venus (♀), Mars (♂), Jupiter (♆), and Saturn (♄). There are large errors on...
References
Abraham, G. and Samuel Cornelius, J. Observational Astronomy. Indian Journal of History of Science 38.4 (2003): 367–76.
Google Scholar
Billard, R. L'Astronomie Indiènne, Paris: École française d'Extrême‐Orient, 1971.
Google Scholar
Billard, R. Aryabhata and Indian Astronomy. Indian Journal of History of Science 2.2 (1977) 207–24.
Google Scholar
Dikshit, S. B. History of Indian Astronomy, Part II. Calcutta: Government of India Press, 1985.
Google Scholar
Mercier, R. The Date of the Mahasiddhanta. Ganita Bharati 15.1–4 (1993): 1–13.
Google Scholar
Neugebauer, O. History of Ancient Mathematical Astronomy. New York: Springer‐Verlag, 1975. 390.
Google Scholar
Pingree, D. History of Mathematical Astronomy in India. Dictionary of Scientific Biography. Vol. 15. Ed. Charles G. Gillispie. New York: Scribners, 1987. 533–633.
Google Scholar
Simon, J. L., et al. Numerical Expressions for Precession Formulae and Mean Elements for the Moon and the Planets. Astronomy and Astrophysics 282 (1994): 663–83.
Google Scholar
van der Waerden, B. L. Two Treatises on Indian Astronomy. Journal for the History of Astronomy 11 (1980): 50–8.
Google Scholar
van derWaerden, B. L. A Summary of Roger Billard's L'Astronomie Indienne. Ganita Bharati 10 (1988): 21–30.
Google Scholar
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Hampshire College, 893 West Street, 01002, Amherst, MA, USA
Helaine Selin
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