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— CH. 1 · ORIGINS AND AUTHORSHIP —

Surya Siddhanta

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  • The Surya Siddhanta is a Sanskrit treatise in Indian astronomy, attributed to Lāta Deva, a student of Aryabhatta I. Scholars date the text to somewhere between the end of the 4th and 9th centuries. A palm-leaf manuscript preserves the work, alongside several newer manuscripts. The text was composed or revised probably around 800 CE from an earlier version also called the Surya Siddhanta. One evidence for this living document status comes from medieval scholar Utpala, who cites ten verses from a version not found in surviving manuscripts. Most scholars place the surviving version variously from the 4th century to the 5th century CE. Kim Plofker states that large portions of the more ancient Sūrya-siddhānta were incorporated into the Pañca-siddhāntikā text. A new version of the Surya Siddhanta was likely revised and probably composed around 800 CE. Some scholars refer to Panca siddhantika as the old Surya Siddhanta and date it to 505 CE.

  • The field of Jyotisha deals with ascertaining time, particularly forecasting auspicious dates and times for Vedic rituals. Ancient Vedic texts describe four measures of time: savana, solar, lunar, and sidereal. They use twenty-seven constellations known as Taras. In the Hindu text Atharvaveda, which dates to about 1000 BCE or older, the idea already appears of twenty-eight constellations. David Pingree suggests influence may have flowed from India to Mesopotamia after the arrival of Darius and the Achaemenid conquest of the Indus Valley about 500 BCE. Yukio Ôhashi considers this proposal incorrect, suggesting instead that Vedic timekeeping efforts began much earlier. Contacts between ancient Indian scholarly tradition and Hellenistic Greece via the Indo-Greek Kingdom explain some similarities. The work of Hipparchus in the 2nd century BCE parallels the table of sines found in the Surya Siddhanta. Alan Cromer states the Greek influence most likely arrived in India by about 100 BCE. The Indians adopted the Hipparchus system, which remained simpler than those made by Ptolemy in the 2nd century CE.

  • The Surya Siddhanta provides methods of calculating sine values in chapter 2. It divides the quadrant of a circle with radius 3438 into 24 equal segments. Each segment has an angle of 3.75 degrees. The first order difference is the value by which each successive sine increases from the previous one. The second order difference is the increment in the first order difference values. Burgess notes that the second order differences increase as the sines do. Each second order difference is about 1/225th part of the corresponding sine. The text uses sexagesimal fractions and includes references to trigonometric functions. The Indians chose 3438 units for the radius and 60 times 360 for the circumference. This calculated ratio of circumference to diameter pi at about 3.1414. The text introduces the versine, which is the difference between the radius and cosine. Various trigonometrical identities were discovered within this framework. These calculations allowed for reasonably accurate predictions of planetary motions.

  • The text treats Earth as a stationary globe around which Sun and other planets orbit. It makes no mention of Uranus, Neptune or Pluto. The calculations use Yojana, a unit estimated as between 8 and 15 kilometers. Surya Siddhanta calculated Earth's diameter to be 1600 Yojana. The known measure being 12756 km, the text estimates range from 12800 to 24000 km. The diameter of the Moon was calculated as 480 Yojana. The known measure being 3475 km, the text estimates range from 3840 to 7200 km. The distance between the Moon and the Earth was set at 51600 Yojana. The elliptical range being 363300 to 405500 km, the text estimates range from 412800 to 774000 km. The text describes formulae with very large numbers for divya-yuga. At the end of this yuga, Earth and all astronomical bodies return to the same starting point. These numbers give reasonably accurate sidereal periods when compared to modern era western calculations.

  • The solar part of the luni-solar Hindu calendar is based on the Surya Siddhanta. Various old and new versions yield the same solar calendar. J. Gordon Melton states both Hindu and Buddhist calendars in South and Southeast Asia are rooted in this text. 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, the lunar month equals 27 days 7 hours 39 minutes 12.63 seconds. It states that the lunar month varies over time. This needs to be factored in for accurate time keeping. Whitney notes the Hindu year is too long by nearly three minutes and a half. The moon's revolution is right within a second. Those of Mercury, Venus and Mars are within a few minutes. That of Jupiter is within six or seven hours. That of Saturn is within six days and a half.

  • The Surya Siddhanta was one of two books in Sanskrit translated into Arabic during the later half of the eighth century. This occurred during the reign of Abbasid caliph Al-Mansur. Muzaffar Iqbal states this translation and that of Aryabhata were of considerable influence on geographic, astronomy and related Islamic scholarship. The tradition of Hellenistic astronomy ended in the West after Late Antiquity. Alan Cromer states the Surya Siddhanta played an important part in the history of science through its translation in Arabic. It stimulated the Arabic sciences. The text reflects the primitive state of Greek science but influenced subsequent developments. A study by Dennis Duke compares Greek models with Indian models based on oldest Indian manuscripts. The Greek influence on Indian astronomy is strongly likely to be pre-Ptolemaic. This transmission preserved knowledge that might otherwise have been lost in Europe.

  • The historical popularity of Surya Siddhanta is attested by at least 26 commentaries plus another 8 anonymous ones. Nearly all commentators re-arranged and modified the text. Mallikarjuna Suri wrote a Telugu language commentary before composing the Sanskrit-language Surya-siddhanta-tika in 1178. Chandeshvara, a Maithila Brahmana, produced the Surya-siddhanta-bhashya in 1185. Maharajadhiraja Madana-pala of Taka family created Vasanarnava around 1375 to 1400. Parameshvara of Kerala published Surya-siddhanta-vivarana in 1432. Yallaya of Andhra-desha wrote Kalpa-valli in 1472. Ramakrishna Aradhya composed Subodhini in 1472. Bhudhara of Kampilya issued another Surya-siddhanta-vivarana in 1572. Tamma Yajvan of Paragipuri created Kamadogdhri in 1599. Ranganatha of Kashi wrote Gudhartha-prakashaka in 1603. Nrsimha of Kashi produced Saura-bhashya in 1611. Vishvanatha of Kashi published Gahanartha-prakasha in 1628. Kamalakara of Kashi wrote Saura-vasana after 1658. Dadabhai, a Chittpavana Brahmana, created Kiranavali in 1719.

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Common questions

Who is the author of the Surya Siddhanta?

The Surya Siddhanta is attributed to Lāta Deva, a student of Aryabhatta I. Scholars date the text to somewhere between the end of the 4th and 9th centuries.

When was the surviving version of the Surya Siddhanta composed?

A new version of the Surya Siddhanta was likely revised and probably composed around 800 CE from an earlier version also called the Surya Siddhanta. Most scholars place the surviving version variously from the 4th century to the 5th century CE.

What trigonometric methods does the Surya Siddhanta use for calculations?

The Surya Siddhanta provides methods of calculating sine values in chapter 2 by dividing the quadrant of a circle with radius 3438 into 24 equal segments. The text uses sexagesimal fractions and includes references to trigonometric functions such as versine.

How accurate are the planetary motion predictions in the Surya Siddhanta compared to modern data?

These numbers give reasonably accurate sidereal periods when compared to modern era western calculations. The moon's revolution is right within a second while that of Saturn is within six days and half.

Who translated the Surya Siddhanta into Arabic and when did this occur?

The Surya Siddhanta was one of two books in Sanskrit translated into Arabic during the later half of the eighth century. This occurred during the reign of Abbasid caliph Al-Mansur.

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All sources

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