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.
Aryabhata was twenty-three when he finished the Aryabhatiya in 499 CE, probably at Kusumapura near modern Patna. It runs to 121 verses, and the first thirteen are a compressed table of astronomical constants written in a letter-numeral code so dense that a single line can take a page of commentary to unpack. One of the numbers is this: Mangala — Mars — completes 2,296,824 revolutions in a mahayuga of 4,320,000 years. The same table gives the Earth 1,582,237,500 rotations across that span; take away one for each of the Sun's 4,320,000 circuits and 1,577,917,500 civil days remain. Divide, and Mars's sidereal period comes out at 686.9997 days. The figure astronomers use now is 686.980. He is out by about half an hour.
The machinery behind that number was not simply borrowed. Indian astronomy had taken in Greek epicycles through Hellenistic intermediaries and the earlier siddhantas, and then rebuilt them. Each planet gets two corrections: the manda, an equation of centre handling the orbit's own lopsidedness, and the shighra, the "fast" correction, whose argument is the planet's elongation from the Sun. In modern terms the shighra is the Earth's orbital motion, folded into a geocentric frame. No Sanskrit text of the period says so. The Earth's motion is in there anyway, doing its work anonymously, exactly as it is in Ptolemy.
One feature is distinctly Indian and genuinely odd: the epicycles are not fixed in size. Aryabhata's tables give epicycle circumferences that vary with the planet's position in its cycle, so the small circle swells and shrinks as it turns. Geometrically it is indefensible — no real sphere behaves that way — but as a curve-fitting device it absorbs errors that a rigid circle cannot. It is a reminder that these systems were built to produce numbers, not pictures.
Aryabhata also argued, in the Gola chapter, that the Earth rotates on its axis and the nightly wheeling of the sky is apparent motion, the stars streaming past the way a riverbank streams past a moving boat. It was rejected. Brahmagupta attacked it directly in 628, later commentators quietly rewrote the verses to save Aryabhata from what they took for an error, and rotation dropped out of mainstream Indian astronomy for centuries. The single boldest idea in the book was the one his successors threw away.
None of it touched Mars as a place. Mangala is a deity — also called Bhauma, son of the Earth — who gives his name to Tuesday, Mangalavara, in Sanskrit and a dozen languages descended from that reckoning. In the mathematics he is a point moving on a circle. Aryabhata could tell you where that point would sit a century later to within a fraction of a degree, and had no way even to frame the question of what it was made of. That required glass.