Indian astronomy has a rich history, right up to modern times.1 The Vedic religion, from which modern Hinduism has developed, is one of the earliest religions recorded in written form (the language being Sanskrit) and the Vedic literature contains many references to the heavens and their divine qualities. The earliest astronomical text-the VedangaJyotisa-dates backto around 1200 BC. It is clear from the use of numerical periods determined by the Babylonians that the two civilizations were in contact and, from the use of epicyclic mechanisms, that at some time between Hipparchus and Ptolemy aspects of Greek astronomy were transmitted to India, though the precise mechanism is uncertain. That this happened before Ptolemy can be deduced from the fact that the lunar theories of the Hindus show no evidence of Ptolemy's modifications to Hipparchus' theory.
Two different approaches are evident in early Hindu astronomy. First, there were arithmetical methods similar to those developed by the Babylonians and, second, there were the trigonometric methods based on Greek geometrical constructions. Examples of the former type can be found in the Panca Siddhantika, written in about AD 550 by the Indian philosopher, astronomer and mathematician Varaha Mihira. Just as in Babylonian astronomy, these Hindu models could be used to compute longitudes at discrete times and underlying the techniques were zigzag functions, but the actual formulation was quite distinctive. In order to illustrate these Indian arithmetic models we will consider the motion of the
1 A detailed account of the history of mathematical astronomy in India from its beginnings through to the sixteenth century is given in Pingree (1975) and Balachandra Rao (2000) provides a comprehensive summary of the algorithms that were actually used to determine the positions of the Sun, Moon, and planets.
For further details, including theories for Jupiter and Saturn, see Abraham (1982).
The anomalistic month (the average time it takes for the Moon to return to the same speed) was taken to be 248 padas (apada being one-ninth of a day). This value is extremely accurate (see Table 1.1, p. 7) and was also used by Babylonian astronomers. This month was divided into two equal parts, with the Moon's speed increasing during the first half and decreasing during the second. For the first half, the longitude of the Moon after each pada was given (in degrees) by the quadratic formula
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