Surya Siddhanta

The Surya Siddhanta was an astronomical treatise written in India circa 400, which had rules laid down to determine the true motions of the luminaries, which conform to their actual positions in the sky. It is not known who wrote the Surya Siddhanta or when it was first compiled, but the most common dates are usually around the 4th century.

The astronomical time cycles and true positions obtained in the text was remarkably accurate at the time. The Hindu cosmological time cycles explained in the text, which was copied from an earlier work, gives:

• The average length of the tropical year as 365.2421756 days, which is only 2 seconds shorter than the modern value of 365.2421988 days. This estimate remained the most accurate estimate for the length of the tropical year anywhere in the world for another 6 centuries (until Muslim mathematician Omar Khayyam gave a better estimate), and still remains more accurate than the value given by the modern Gregorian calender currently in use around the world, which gives the average length of the year as 365.2425 days.

• The average length of the sidereal year (the length of the Earth's revolution around the Sun) as 365.2563627 days, which is only 1.4 seconds longer than the modern value of 365.2563627 days. This remained the most accurate estimate for the length of the sidereal year anywhere in the world for over a thousand years.

The actual astronomical value stated for the sidereal year however, is not as accurate. The length of the sidereal year is stated to be 365.258756 days, which is longer than the modern value by 3 minutes 27 seconds. This is mostly due to the text using a different method for actual astronomical computation, rather than the Hindu cosmological time cycles copied from an earlier text, possibly because the author didn't fully understand the time cycles. The author instead employed a mean motion for the Sun and a constant of precession inferior to that used in the Hindu cosmological time cycles.

The Surya Siddhanta also contains the roots of modern trignometry. It uses jya (sine), kozya (cosine), and otkram jya (inverse sine). Later Indian mathematicians an astronomers such as Aryabhata made references to this text, while later Arabic and Latin translations were very influential in Europe and the Middle East.

The Indian solar and lunisolar calendars are widely used, with their local variations, in different parts of India. They are important in predicting the dates for the celebration of various festivals, performance of various rites as well as on all astronomical matters. The modern Indian solar and lunisolar calendars are based on close approximations to the true times of the Sun’s entrance into the various rasis.

Conservative "panchang" (calendar) makers still use the formulae and equations found in the Surya Siddhanta to compile and compute their panchangs. The panchang is an annual publication published in all regions and languages in India containing all calendrical information on religious, cultural and astronomical events. It exerts great influence on the religious and social life of the people in India and is found in almost households.

External links

• Surya Siddhanta, Chapter I with Commentary and Illustrations
• Exegesis of Hindu Cosmological Time Cycles