ಸೂರ್ಯ ಸಿದ್ಧಾಂತ ಗ್ರಂಥ | The Surya Siddhanta

The Surya Siddhanta is among the oldest astronomical texts in continuous use anywhere. Its surviving recension dates to roughly the fourth or fifth century, though it presents itself as considerably older, revealed by a messenger of the sun to the asura Maya at the end of a previous age.

It runs to about five hundred verses across fourteen chapters, covering mean and true planetary motion, the three problems of diurnal astronomy, eclipses, planetary conjunctions, the phases of the moon, risings and settings, cosmography and instruments.

How it computes a position

The method is systematic and needs nothing but arithmetic and a table.

First, the ahargana: the count of days elapsed since the beginning of the Kali era, taken as mean midnight at Ujjain on 18 February 3102 BCE. Today that number is a little over 1.87 million.

Second, the mean longitude: each body is assigned a number of revolutions completed in a mahayuga of 4,320,000 years, against 1,577,917,828 civil days. The sun has 4,320,000, the moon 57,753,336, the moon’s apogee 488,203 and its node 232,238. Multiply, divide, and the mean position follows.

Third, the manda correction: the equation of centre, applied through an epicycle whose circumference is itself made to vary between quadrants. This is where the text is cleverest: a fixed epicycle would be a cruder approximation, and the variation is a real refinement.

The sines used are not modern sines but the text’s own table of twenty-four values at intervals of three and three-quarter degrees, with a radius of 3438, which is the number of minutes of arc in a radian. Anudina uses that table rather than a modern sine function, because a panchanga computed by hand from the text would use it.

How accurate it turns out to be

Compared against modern computation over the years 500 to 2026, the Surya Siddhanta’s sun drifts slowly: about three degrees ahead in the sixth century, crossing zero around 1800, and about a third of a degree behind today. Its periodic behaviour is excellent, with a swing of only about a quarter of a degree.

Its moon is within about two degrees. The residual is what one would expect from a model that includes the equation of centre but not the evection or the variation, the two large periodic terms in the moon’s motion that were not isolated until much later.

Two degrees of lunar longitude corresponds to about four hours in a tithi boundary, which is the practical scale of the disagreement between a siddhantic and a drik panchanga.

One detail worth recording

A naive implementation puts the moon’s apogee and node at zero at the Kali epoch. The text does not: the apogee stands at three signs and the node at six. Getting this wrong puts the moon out by up to nine degrees, five times the true error of the system, and is the most common mistake in modern reimplementations. Anudina’s Surya Siddhanta mode, computed with the correct epoch positions, matches the Sringeri Math’s own printed panchangam to within about two minutes.