The Surya Siddhanta (; ) 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 5th centuries by most modern scholars, and comprises fourteen chapters.Menso Folkerts, Craig G. Fraser, Jeremy John Gray, John L. Berggren, Wilbur R. Knorr (2017), Mathematics, Encyclopaedia Britannica, Quote: "(...) its Hindu inventors as discoverers of things more ingenious than those of the Greeks. Earlier, in the late 4th or early 5th century, the anonymous Hindu author of an astronomical handbook, the Surya Siddhanta, had tabulated the sine function (...)"Plofker, pp. 71–72. 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 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., Quote: "According to Surya Siddhanta the earth is a sphere." It treats Earth as stationary globe around which the classical planets orbit. 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 . The text is known for some of the earliest known discussions of fractions and trigonometric functions., Quote: "c. 350-400: The Surya Siddhanta, an Indian work on astronomy, now uses sexagesimal fractions. It includes references to trigonometric functions. The work is revised during succeeding centuries, taking its final form in the tenth century."
The Surya Siddhanta is one of several astronomy-related Hindu texts. It represents a functional system that made reasonably accurate predictions.David Pingree (1963), Astronomy and Astrology in India and Iran, Isis, Volume 54, Part 2, No. 176, pages 229-235 with footnotes The text was influential on the solar year computations of the luni-solar Hindu calendar., Quote: "The solar calendar is based on the Surya Siddhanta, a text of around 400 CE." 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.
Textual history
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., Quote: "c. 350-400: The Surya Siddhanta, an Indian work on astronomy, now uses sexagesimal fractions. It includes references to trigonometric functions. The work is revised during succeeding centuries, taking its final form in the tenth century."
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.Romesh Chunder Dutt, A History of Civilization in Ancient India, Based on Sanscrit Literature, vol. 3, p. 208. 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 composed or revised around 800 CE from earlier text of the same name and large portions of which were preserved in Varāhamihira's 6th-century text. Some scholars refer to Panca siddhantika as the old Surya Siddhanta and date it to 505 CE.
Vedic influence 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.James Lochtefeld (2002), "Jyotisha" in The Illustrated Encyclopedia of Hinduism, Vol. 1: A–M, Rosen Publishing, , pages 326–327 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.
Kim Plofker states that while a flow of timekeeping ideas from either side is plausible, each may have instead developed independently, because the loan-words typically seen when ideas migrate are missing on both sides as far as words for various time intervals and techniques.
Greek influence It is hypothesized that contacts between the ancient Indian scholarly tradition and Hellenistic Greece via the Indo-Greek Kingdom after the Indian campaign of Alexander the Great, specifically regarding the work of Hipparchus (2nd-century BCE), explain some similarities between Surya Siddhanta and Greek astronomy in the Hellenistic period. For example, Surya Siddhanta provides table of sines function which parallel the Hipparchian table of chords, though the Indian calculations are more accurate and detailed."There are many evident indications of a direct contact of Hindu astronomy with Hellenistic tradition, e.g. the use of epicycles or the use of tables of chords which were transformed by the Hindus into tables of sines. The same mixture of elliptic arcs and declination circles is found with Hipparchus and in the early Siddhantas (note: [...] In the Surya Siddhanta, the zodiacal signs are used in similar fashion to denote arcs on any great circle." Otto Neugebauer, The Exact Sciences in Antiquity, vol. 9 of Acta historica scientiarum naturalium et medicinalium, Courier Dover Publications, 1969, p. 186. According to Alan Cromer, the Greek influence most likely arrived in India by about 100 BCE."The table must be of Greek origin, though written in the Indian number system and in Indian units. It was probably calculated around 100 B.C. by an Indian mathematicisn familiar with the work of Hipparchus." Alan Cromer, Uncommon Sense : The Heretical Nature of Science, Oxford University Press, 1993, p. 111. The Indians adopted the Hipparchus system, according to Cromer, and it remained that simpler system rather than those made by Ptolemy in the 2nd century."The epicyclic model in the Siddnahta Surya is much simpler than Ptolemy's and supports the hypothesis that the Indians learned the original system of Hipparchus when they had contact with the West." Alan Cromer, Uncommon Sense : The Heretical Nature of Science, Oxford University Press, 1993, p. 111.
The influence of Greek ideas on early medieval era Indian astronomical theories, particularly zodiac symbols (astrology), is broadly accepted by the Western scholars. According to Pingree, the 2nd-century CE cave inscriptions of Nasik mention sun, moon and five planets in the same order as found in Babylon, but "there is no hint, however, that the Indian had learned a method of computing planetary positions in this period".David Pingree (1963), Astronomy and Astrology in India and Iran, Isis, Volume 54, Part 2, No. 176, pages 233-238 with footnotes In the 2nd-century CE, a scholar named Yavanesvara translated a Greek astrological text, and another unknown individual translated a second Greek text into Sanskrit. Thereafter started the diffusion of Greek and Babylonian ideas on astronomy and astrology into India. The other evidence of European influential on the Indian thought is Romaka Siddhanta, a title of one of the Siddhanta texts contemporary to Surya Siddhanta, a name that betrays its origin and probably was derived from a translation of a European text by Indian scholars in Ujjain, then the capital of an influential central Indian large kingdom.
According to mathematician and historian of measurement John Roche, the astronomical and mathematical methods developed by Greeks related arcs to chords of spherical trigonometry. The Indian mathematical astronomers, in their texts such as the Surya Siddhanta, developed other linear measures of angles, made their calculations differently, "introduced the versine, which is the difference between the radius and cosine, and discovered various trigonometrical identities". For instance "where the Greeks had adopted 60 relative units for the radius, and 360 for circumference", the Indians chose 3,438 units and 60x360 for the circumference thereby calculating the "ratio of circumference to diameter [pi, π] of about 3.1414". The Surya Siddhanta was one of the two books in Sanskrit that were translated into Arabic in the later half of the eighth century during the reign of Abbasid caliph Al-Mansur.
Importance in history of science