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...
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Abraham, G., Cornelius, J.S., David, N.G. (2008). Mean Motions in Indian Astronomy.
In: Selin, H. (eds) Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4425-0_8979