In the first or Vedic period we find attested certain knowledge of stars and constellations, but no astronomical calculation.
In the second period, we find calculations by means of increasing and decreasing arithmetical series, but no trigonometry. The arithmetical methods explained by Varâha-Mihira (an Indian Maga, 6th century A.D.) are just the same as those used in Babylonian cuneiform texts of the second century B.C.
In the third period, the motions of the planets were represented as uniform circular motions on epicycles and eccenters. In this period, planetary positions and eclipses were computed by exact trigonometry.
The first great astronomer of the third period is Aryabhata, born A.D. 476. He proposed the idea of the rotation of the earth about its axis.
The most famous text book of Indian astronomy, the Sûrya-Siddhânta, was written in the fifth century.