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Let's go to Mars

Aryabhata fixes Mars's year to within half an hour

The Aryabhatiya assigns Mars 2,296,824 orbits per 4,320,000-year cycle. Work it through with his own day count and the period is 686.9997 days; the modern value is 686.98.

A weathered dark stone lintel carved in deep relief with three standing haloed figures holding small objects, and a large grimacing face with fanned hair at the right-hand end.
A fifth-century lintel from Sarnath carrying the planetary deities in stone — carved in the century Aryabhata spent turning the same planets into arithmetic. · Image: Biswarup Ganguly

Aryabhata finished the Aryabhatiya in 499 CE, aged twenty-three, probably at Kusumapura near modern Patna. Its first thirteen verses, of 121, compress the astronomical constants into a letter-numeral code; a single line can take a page of commentary. Mangala, Mars, is given 2,296,824 revolutions in a mahayuga of 4,320,000 years. The same table gives the Earth 1,582,237,500 rotations over that span; subtract one for each of the Sun's 4,320,000 circuits and 1,577,917,500 civil days remain. Dividing gives Mars a sidereal period of 686.9997 days, against the modern 686.980. The difference is about half an hour.

Indian astronomy took in Greek epicycles through Hellenistic intermediaries and the earlier siddhantas, then rebuilt them. Each planet gets two corrections: the manda, an equation of centre for the orbit's own lopsidedness, and the shighra, the "fast" correction, whose argument is the planet's elongation from the Sun. In modern terms Mars's shighra is the Earth's orbital motion folded into a geocentric frame, which no Sanskrit text of the period states, any more than Ptolemy does.

One feature is distinctly Indian: the epicycles are not fixed in size. Their circumferences vary with the planet's position in its cycle, so the circle swells and shrinks as it turns. No real sphere behaves that way, but the variation absorbs errors a rigid circle cannot.

In the Gola chapter Aryabhata argued that the Earth rotates on its axis and the nightly wheeling of the sky is apparent motion, the stars streaming past like a riverbank past a moving boat. It was rejected: Brahmagupta attacked it in 628, commentators rewrote the verses to correct what they took for an error, and rotation left mainstream Indian astronomy for centuries.

Mangala is a deity, also called Bhauma, son of the Earth, and gives his name to Tuesday, Mangalavara, in Sanskrit and a dozen descended languages. In the mathematics he is a point on a circle, and Aryabhata could place its mean position a century ahead to within a degree and a half.