Ancient Indian astronomers combined their observational and mathematical skills, and knowledge of celestial mechanics, to accurately calculate Jupiter's orbital period. They have made some remarkable contributions to astronomy,
They relied on meticulous naked-eye observations of celestial bodies, such as Jupiter, and tracked the planet's position relative to the fixed stars in the background, over long periods. They used simple instruments like gnomons (vertical sticks) and armillary spheres to measure angles and positions of celestial objects. (An armillary sphere is a model of the objects in the sky, consisting of a spherical framework of rings, centered on Earth or the Sun, that represent lines of celestial longitude and latitude and the ecliptic.)
Hindu planispheric astrolabe in brass, single plate, made for Raja Ramasimha by Sivalala in 1870. Engraved in Sanskrit with instrument laid out for the latitude of Bundi (25ยบ 28'), Rajasthan, India. Science Museum.
The ancient Indian astronomical texts, known as Siddhantas, provided systematic methods for calculating the positions and motions of the visible planets. The Surya Siddhanta, one of the most famous texts, contains detailed descriptions of planetary motions and methods for calculating their positions. . The Surya Siddhanta includes tables of sine values. Yes, Indian astronomers developed and used trigonometric functions, such as sine and cosine, to perform precise calculations.
By observing Jupiter's position relative to the background stars, ancient Indian astronomers determined its orbital period. They noted that Jupiter takes 12 years to complete one full orbit around the Sun.
