In the Vedas (2nd millennium BC) the need to determine the correct times and the accurate positioning of altars for religious ceremonies led to the development of geometry and astronomy. Much of the mathematics within the Vedas is found in works called Vedangas. Of significance are the Vedangas Jyotish and Kalpa. Jyotish was the name for astronomy; Kalpa included the rules for rituals and ceremonies.
The models and parameters received from external sources were adapted to provide calendars, time-keeping, horoscopes and to predict solar and lunar eclipses and other celestial events. Mathematical astronomy was introduced into India from the West. The earliest source appears to have come from Babylonia via Achaemenid Iran (c.550-331 BC). An intercalation cycle is included in a text called Jyotisavedanga, attributed to Lagadha about whom nothing else is known. Using the Sun and Moon as timekeepers the calendar adds two intercalary months every five years, giving five-year periods each containing a total of sixty-two lunar months. Thus the Vedanga Calendar accumulates the rather large error of four days in five years.
Some important astronomy treatises were written after the invasion by Alexander the Great of Macedon (326 BC). This was followed by Sanskrit translations of Greek texts in western India in the second, third and fourth centuries AD. The earliest of these texts was translated (149/150) near Ujjain by one Yavanesvara (‘Lord of the Greeks’), leader of the Greek colonies in western India under the Saka ruler Rudradaman-I (r.c.130-c.150). In 269/270 Sphujidhvaja versified the now lost translation into the Yavanajataka, which is extant.
From the fourth through to the seventh century various Indian astronomers provided high-level textbooks (siddhantas, or ‘truths’) covering the basics of astronomy. Aryabhata-I (c.476-c.550) wrote the Aryabhatiya (c.499) in which he argues that the planets move in elliptical paths, that the apparent rotation of the heavens is due to Earth’s axial rotation, and that the Moon and planets shine by reflected sunlight. He also explains the causes of solar and lunar eclipses and gives a length for the solar year that is just slightly longer than the value accepted today.
Varahamihira (c.505-c.587) wrote the Pancasiddhantika (‘Five Astronomical Canons’) in c.575. This work is important in itself and it also gives us information about older Indian texts now lost. One of the treatises that Varahamihira summarises is the Romakasiddhanta (probably a translation of some Greek or Roman treatise as it name suggests), which includes an epicycle theory of the motions of the Sun and Moon based on the tropical year and the nineteen-year Metonic cycle. He revised the calendar by updating earlier works to take into account precession since they were written
Brahmagupta (598-668) published his influential text on astronomy, the Brahmasphutasiddhanta, (‘The Opening of the Universe’), in 628. Topics covered are the mean and true longitudes of the planets, lunar and solar eclipses, risings and settings, the Moon’s crescent and shadow, and the conjunctions of the planets with each other and with the fixed stars.
Bhaskara (1114-1185) is also known as Bhaskara II or as Bhaskaracharya, this latter name meaning ‘Bhaskara the Teacher’. He became head of the astronomy observatory at Ujjain. His Siddhantasiromani (1150) is famous because it included everything in Indian astronomy.
Madhava (1340-1425) founded the Kerala School in southwest India. He discovered a procedure to obtain the positions of the Moon every thirty-six minutes and methods to estimate the motions of the planets. Late Kerala school astronomers gave a formulation for the equation of the centre of the planets, i.e. a measure of the difference between the actual position of a planet in its elliptical orbit and its position assuming its motion to be uniform in a circular orbit.
Nilakantha Somayaji (1444-1544) came from a family in Kerala. In his Tantrasangraha (1501) he revised Aryabhata’s model for the planets Mercury and Venus. His equation for the centre of these planets remained the most accurate until Kepler’s time in the seventeenth century.
Observation was little used in Indian astronomy. Astronomy in India was advanced by mathematics rather than by deduction from the facts of nature. Some of their mathematical innovations, however, had profound effects on neighbouring cultures, such as, for example, that of trigonometry on the astronomy of Islam and medieval Western Europe.
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