The contents of the
Surya Siddhanta is written in
classical Indian poetry tradition, where complex ideas are expressed lyrically with a rhyming meter in the form of a terse
shloka. The entire table of trigonometric functions, sine tables, steps to calculate complex orbits, predict eclipses and keep time are thus provided by the text in a poetic form. This cryptic approach offers greater flexibility for poetic construction. The
Surya Siddhanta thus consists of cryptic rules in Sanskrit verse. It is a compendium of astronomy that is easier to remember, transmit and use as reference or aid for the experienced, but does not aim to offer commentary, explanation or proof. The fourteen chapters of the
Surya Siddhanta are as follows, per the much cited Burgess translation: • Of the Mean Motions of the
Planets • On the True Places of the Planets • Of Direction, Place and Time • Of Eclipses, and Especially of Lunar Eclipses • Of Parallax in a Solar Eclipse • The Projection of Eclipses • Of Planetary Conjunctions • Of the Asterisms • Of Heliacal (Sun) Risings and Settings • The Moon's Risings and Settings, Her Cusps • On Certain Malignant Aspects of the Sun and Moon • Cosmogony, Geography, and Dimensions of the Creation • Of the Armillary Sphere and other Instruments • Of the Different Modes of Reckoning Time The methods for computing time using the shadow cast by a
gnomon are discussed in both Chapters 3 and 13.
Description of Time The author of
Surya Siddhanta defines time as of two types: the first which is continuous and endless, destroys all animate and inanimate objects and second is time which can be known. This latter type is further defined as having two types: the first is
Murta (Measureable) and
Amurta (immeasureable because it is too small or too big). The time
Amurta is a time that begins with an infinitesimal portion of time (
Truti) and
Murta is a time that begins with 4-second time pulses called
Prana as described in the table below. The further description of
Amurta time is found in
Puranas where as
Surya Siddhanta sticks with measurable time. The text measures a
savana day from sunrise to sunrise. Thirty of these
savana days make a
savana month. A solar (
saura) month starts with the entrance of the sun into a
zodiac sign, thus twelve months make a year.
North pole star and South pole star Surya Siddhanta asserts that there are two pole stars, one each at north and south
celestial pole.
Surya Siddhanta chapter 12 verse 43 description is as following: मेरोरुभयतो मध्ये ध्रुवतारे नभ:स्थिते। निरक्षदेशसंस्थानामुभये क्षितिजाश्रिये॥१२:४३॥ This translates as "On both sides of the Meru (i.e. the north and south poles of the earth) the two polar stars are situated in the heaven at their zenith. These two stars are in the horizon of the cities situated on the equinoctial regions".
The Sine table The
Surya Siddhanta provides methods of calculating the sine values in chapter 2. It divides the quadrant of a circle with radius 3438 into 24 equal segments or sines as described in the table. In modern-day terms, each of these 24 segments has angle of 3.75°. The 1st order difference is the value by which each successive sine increases from the previous and similarly the 2nd order difference is the increment in the 1st order difference values.
Burgess says, it is remarkable to see that the 2nd order differences increase as the sines and each, in fact, is about 1/225th part of the corresponding sine. Following the sine tables and methods of calculating the sines,
Surya Siddhanta also attempts to calculate the Earth's tilt of contemporary times as described in chapter 2 and verse 28, the obliquity of the
Earth's axis, the verse says "The sine of greatest declination is 1397; by this multiply any sine, and divide by radius; the arc corresponding to the result is said to be the declination". The greatest declination is the inclination of the plane of the ecliptic. With radius of 3438 and sine of 1397, the corresponding angle is 23.975° or 23° 58' 30.65" which is approximated to be 24°.
Planets and their characteristics The text treats earth as a stationary globe around which sun, moon and five planets orbit. It makes no mention of Uranus, Neptune and Pluto. It presents mathematical formulae to calculate the orbits, diameters, predict their future locations and cautions that the minor corrections are necessary over time to the formulae for the various astronomical bodies. These very large numbers based on
divya-yuga, when divided and converted into decimal numbers for each planet, give reasonably accurate
sidereal periods when compared to modern era western calculations. The various old and new versions of
Surya Siddhanta manuscripts yield the same solar calendar. According to J. Gordon Melton, both the Hindu and Buddhist calendars that are in use in South and Southeast Asia are rooted in this text, but the regional calendars adapted and modified them over time. The
Surya Siddhanta calculates the solar year to be 365 days 6 hours 12 minutes and 36.56 seconds. On average, according to the text, the lunar month equals 27 days 7 hours 39 minutes 12.63 seconds. It states that the lunar month varies over time, and this needs to be factored in for accurate time keeping. According to Whitney, the Surya Siddhanta calculations were tolerably accurate and achieved predictive usefulness. In Chapter 1 of
Surya Siddhanta, "the Hindu year is too long by nearly three minutes and a half; but the moon's revolution is right within a second; those of Mercury, Venus and Mars within a few minutes; that of Jupiter within six or seven hours; that of Saturn within six days and a half". The
Surya Siddhanta was one of the two books in Sanskrit translated into
Arabic during the reign of
'Abbasid caliph
al-Mansur (). According to
Muzaffar Iqbal, this translation and that of
Aryabhata was of considerable influence on geographic, astronomy and related Islamic scholarship. ==Editions==