Surya Siddhanta

The Surya Siddhanta (IAST: Sūrya Siddhānta; lit. 'Sun Treatise') is a Sanskrit treatise in Indian astronomy, attributed to Lāṭadeva, a student of Aryabhatta I, and dated to somewhere between the end of the 4th and 9th centuries, and comprises fourteen chapters. The Surya Siddhanta describes the author's rules, within a geocentric model, to calculate the motions of the Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn, along with his estimate of their diameters, and the circumference of their assumed circular orbits around the Earth. The text is known from a 15th-century CE palm-leaf manuscript, and several newer manuscripts. It was composed or revised probably c. 800 CE from an earlier text also called the Surya Siddhanta. The Surya Siddhanta text is composed of verses made up of two lines, each broken into two halves, or pãds, of eight syllables each.

The second verse of the first chapter of the Surya Siddhanta attributes the words to an emissary of the solar deity of Hindu god, Surya, as recounted to an asura called Maya at the end of Satya Yuga, the first golden age from Hindu texts, around two million years ago.

The text asserts, according to Markanday and Srivatsava, that the Earth is of a spherical shape. It treats Earth as stationary globe around which then Sun and other planets orbit, and makes no mention of Uranus, Neptune and Pluto. The calculations uses Yojana, a unit estimated as between 8 – 15 km. Though astronomical dimensions had already been estimated with more accuracy by ancient Greek astronomers such as Aristarchus (c. 310–230 BCE) and Eratosthenes (c. 276–194 BCE), Surya Siddhanta calculated the Earth's diameter to be 1,600 Yojana (12,800 - 24,000 km, the known measure being 12,756 km), the diameter of the Moon as 480 Yojana (3,840 - 7,200 km, the known measure being 3,475 km), the diameter of the Sun as 6,500 Yojana (52,000 - 97,509 km, the known measure being ~ 1,392,000 km) and the distance between the Moon and the Earth to be 51,600 Yojana (412,800 - 774,000 km, the known elliptical range being 221,500–252,700 miles (356,500–406,700 kilometres). The text is known for some of the earliest known discussions of fractions and trigonometric functions.

The Surya Siddhanta is one of several astronomy-related Hindu texts. It represents a functional system that made reasonably accurate predictions. The text was influential on the solar year computations of the luni-solar Hindu calendar. The text was translated into Arabic and was influential in medieval Islamic geography. The Surya Siddhanta has the largest number of commentators among all the astronomical texts written in India. It includes information about the mean orbital parameters of the planets, such as the number of mean revolutions per Mahayuga, the longitudinal changes of the orbits, and also includes supporting evidence and calculation methods.

In a work called the Pañca-siddhāntikā composed in the sixth century by Varāhamihira, five astronomical treatises are named and summarised: Paulīśa-siddhānta, Romaka-siddhānta, Vasiṣṭha-siddhānta, Sūrya-siddhānta, and Paitāmaha-siddhānta. Most scholars place the surviving version of the text variously from the 4th century to the 5th century CE.

According to John Bowman, the version of the text existed between 350 and 400 CE wherein it referenced fractions and trigonometric functions, but the text was a living document and revised through about the 10th century. One of the evidence for the Surya Siddhanta being a living text is the work of medieval Indian scholar Utpala, who cites and then quotes ten verses from a version of Surya Siddhanta, but these ten verses are not found in any surviving manuscripts of the text. According to Kim Plofker, large portions of the more ancient Sūrya-siddhānta was incorporated into the Panca siddhantika text, and 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 Surya Siddhanta is a text on astronomy and time keeping, an idea that appears much earlier as the field of Jyotisha (Vedanga) of the Vedic period. The field of Jyotisha deals with ascertaining time, particularly forecasting auspicious dates and times for Vedic rituals. Vedic sacrifices state that the ancient Vedic texts describe four measures of time – savana, solar, lunar and sidereal, as well as twenty seven constellations using Taras (stars). According to mathematician and classicist David Pingree, in the Hindu text Atharvaveda (~1000 BCE or older) the idea already appears of twenty eight constellations and movement of astronomical bodies.

According to Pingree, the influence may have flowed the other way initially, then flowed into India after the arrival of Darius and the Achaemenid conquest of the Indus Valley about 500 BCE. The mathematics and devices for time keeping mentioned in these ancient Sanskrit texts, proposes Pingree, such as the water clock may also have thereafter arrived in India from Mesopotamia. However, Yukio Ôhashi considers this proposal as incorrect, suggesting instead that the Vedic timekeeping efforts, for forecasting appropriate time for rituals, must have begun much earlier and the influence may have flowed from India to Mesopotamia. Ôhashi states that it is incorrect to assume that the number of civil days in a year equal 365 in both Indian (Hindu) and Egyptian–Persian year. Further, adds Ôhashi, the Mesopotamian formula is different than Indian formula for calculating time, each can only work for their respective latitude, and either would make major errors in predicting time and calendar in the other region.