Sūrya Siddhānta

The Sūrya Siddhānta, or Saura Siddhanta (Sanskrit for Solar Tenets), was one of the eighteen famous Indian works on astronomy known as the Siddhāntas.

History
The origins of the Surya Siddhanta are uncertain. It has been revised over the centuries, incorporating new knowledge as time passed. Varāhamihira produced a version of it circa 505 AD. In fact, it is one of the five siddhānta that he recommends as required knowledge for an astronomer. The latest version probably formed some time between the 500s and the 1100s AD. . It has been particularly used in northern India.

The Surya Siddhanta itself begins with a description of itself as having been a textbook promulgated by the Sun God, after appeals from Maya.

Contents
The newest version of the work contains 14 chapters.

The topics covered include, at least, the following:


 * The planets
 * mean motion of
 * true position of
 * conjuctions of
 * helical rising and setting of
 * eclipses of the sun and moon
 * cosmogony
 * time
 * astronomical instruments

The precession of the equinoxes is also described in the Sūrya Siddhānta. It puts the rate at 600 oscillations per mahāyuga (4,320,000 years). This works out to a rate of 54 arcseconds per year, which is close to the modern number of about 50.

The work continued the previous notion of the Pravaha, or celestial wind, as the cause of planetary motion.

Time and the Ages
The Sūrya Siddhānta contains the Sāṅkhya as well as it's own version of Yuga.

The four Ages within a single Mahāyuga were described as follows:

Dawn and twilight made up 1/6th of an age.

The Sūrya describes units larger than caturyuga:


 * Seventy one ages made a manvantara, or 'patriarchate'.
 * Fourteen manvantara (or manu) made a kalpa
 * kalpas have an extra 'dawn' on the end, as long as the Golden age
 * kalpas have 1,000 yugas
 * Brahmā's day and night are each one kalpa.
 * A day of Brahmā "brings about the destruction of all that exists"

It goes on to describe where in all this the current time fits:


 * Brahmā is 100, and half his life is gone.
 * Within the current kalpa, six manu have passed + twilights
 * The current age is the 28th age.

Divine time

The Sūrya also describes time as it exists for the gods and demons.


 * 360 divine days were in one divine year.
 * 12,000 divine years made a caturyuga
 * caturyuga was 10,000 * 432 solar years

Early Use of Trigonometry
The Surya Siddhanta contains the roots of modern trigonometry. It uses sine (jya), cosine (kojya or "perpendicular sine") and inverse sine (otkram jya) for the first time, and also contains the earliest use of the tangent and secant when discussing the shadow cast by a gnomon.

Online versions

 * An English translation from 1860, by Ebenezer Burgess and the American Oriental Society, is available in full from Google Books, at this link: books.google.com id=jpE7AAAAcAAJ