Surya Siddhanta
The Surya Siddhanta is the name of a Sanskrit treatise in Indian astronomy from 6th Century BCE.[1][3] The text survives in several versions, was cited and extensively quoted in a 6th-century BCE text, was likely revised for several centuries under the same title.[4][3] It has fourteen chapters.[5] A 12th-century manuscript of the text was translated by Burgess in 1860.[2]
The Surya Siddhanta describes rules to calculate the motions of various planets and the moon relative to various constellations, diameters of various planets, and calculates the orbits of various astronomical bodies.[6][7] The text asserts that the universe is of a spherical shape.[5] It treats the earth as a stationary plane above which the sun orbits, and makes no mention of Uranus, Neptune or Pluto.[8] It calculates the earth's diameter to be 8,000 miles (modern: 7,928 miles), diameter of moon as 2,400 miles (actual ~2,160) and the distance between moon and earth to be 258,000 miles (actual ~238,000).[6] The text is known for some of earliest known discussion of sexagesimal fractions and trigonometric functions.[1][3][9]
It represents a functional system that made reasonably accurate predictions.[10][11][12] The text was influential on the solar year computations of the luni-solar Hindu calendar.[13]
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.[14]: 50 The surviving version of the text is dated to about the 6th-century BC by Markandaya and Srivastava.[3][15]
According to John Bowman, the earliest version of the text existed between 350-400 CE wherein it referenced sexagesimal fractions and trigonometric functions, but the text was a living document and revised through about the 10th-century.[3] 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.[16] 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 composed around 800 CE.[4] Some scholars refer to Panca siddhantika as the old Surya Siddhanta and date it to 505 CE.[17]
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 day and time for Vedic rituals.[18] Max Muller, quoting passages by Garga and others for Vedic sacrifices, states that the ancient Vedic texts describe four measures of time – savana, solar, lunar and sidereal, as well as twenty seven constellations using Taras (stars).[19] The idea of twenty eight constellations and movement of astronomical bodies already appears, states David Pingree – a professor of History of Mathematics and Classics, in the Hindu text Atharvaveda (~1000 BCE).[10] Scholars have speculated that this may have entered India from Mesopotamia. However, states Pingree, this hypothesis has not been proven because no cuneiform tablet or evidence from Mesopotamian antiquity has yet been deciphered that even presents this theory or calculations.[10]
According to Pingree, the influence may have flowed the other way initially, then flowed into India after the arrival of Darius in 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 Ohashi considers this proposal as incorrect,[20] 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.[21] Ohashi states that it is incorrect to assume that the number of civil days in a year equal 365 in both Hindu and Egyptian–Persian year.[22] Further, adds Ohashi, 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.[23]
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.[24][25]
Greek influence
It is hypothesized that there were cultural contacts between the Indian and Greek astronomers via cultural contact with Hellenistic Greece, specifically the work of Hipparchus (2nd-century BCE). There were some similarities between Suryasiddhanta and Greek astronomy in Hellenistic period. For example, Suryasiddhanta provides table of sines function which parallel the Hipparchus table of chords, though the Indian calculations are more accurate and detailed.[26] [27] 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.[28]
Planet | Surya Siddhanta | Ptolemy | 20th-century | ||||||||||||||||||||||||||||||||||||||||||||||||||
Mangala (Mars) | 686 days, 23 hours, 56 mins, 23.5 secs | 686 days, 23 hours, 31 mins, 56.1 secs | 686 days, 23 hours, 30 mins, 41.4 secs | ||||||||||||||||||||||||||||||||||||||||||||||||||
Budha (Mercury) | 87 days, 23 hours, 16 mins, 22.3 secs | 87 days, 23 hours, 16 mins, 42.9 secs | 87 days, 23 hours, 15 mins, 43.9 secs | ||||||||||||||||||||||||||||||||||||||||||||||||||
Bṛhaspati (Jupiter) | 4,332 days, 7 hours, 41 mins, 44.4 secs | 4,332 days, 18 hours, 9 mins, 10.5 secs | 4,332 days, 14 hours, 2 mins, 8.6 secs | ||||||||||||||||||||||||||||||||||||||||||||||||||
Shukra (Venus) | 224 days, 16 hours, 45 mins, 56.2 secs | 224 days, 16 hours, 51 mins, 56.8 secs | 224 days, 16 hours, 49 mins, 8.0 secs | ||||||||||||||||||||||||||||||||||||||||||||||||||
Shani (Saturn) | 10,765 days, 18 hours, 33 mins, 13.6 secs | 10,758 days, 17 hours, 48 mins, 14.9 secs | 10,759 days, 5 hours, 16 mins, 32.2 secs | [30][20][31][32] their zodiac signs being nearly identical.[18]
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".[33][33] 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.[33] According to John Roche – a professor of Mathematics with publications on the history of measurement, the astronomical and mathematical methods developed by Greeks related arcs to chords of spherical trigonometry.[34] The Indian mathematical astronomers, in their texts such as 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".[34] For instance, states Roche, "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".[34] Cite error: A The Surya Siddhanta was one of the two books in Sanskrit translated into Arabic in the later half of the eighth century during the reign of Abbasid caliph Al-Mansur. According to Muzaffar Iqbal, this translation and that of Aryabhatta was of considerable influence on geographic, astronomy and related Islamic scholarship.[35] ContentsThe 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.[36][37] This method of expressing and sharing knowledge made it easier to remember, recall, transmit and preserve knowledge. However, this method also meant secondary rules of interpretation, because numbers don’t have rhyming synonyms. The creative approach adopted in the Surya Siddhanta was to use symbolic language with double meanings. For example, instead of one, the text uses a word that means moon because there is one moon. To the skilled reader, the word moon means the number one.[36] 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.[36][38] 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.[15][37] The text has 14 chapters and 500 shlokas.[37] It is one of the eighteen astronomical siddhanta (treatises), but thirteen of the eighteen are believed to be lost to history. The Surya Siddhanta text has survived since the ancient times, has been the best known and the most referred astronomical text in the Indian tradition.[37][7] The fourteen chapters of the Surya Siddhanta are as follows, per the much cited Burgess translation:[5][39]
The methods for computing time using the shadow cast by a gnomon are discussed in both Chapters 3 and 13. Planets and their characteristics
—Surya Siddhanta, XII.53 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.[55] 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. However, unlike modern heliocentric model for the solar system, the Surya Siddhanta relies on a geocentric point of view.[55] The text describes some of its formulae with the use of very large numbers for divya yuga, stating that at the end of this yuga earth and all astronomical bodies return to the same starting point and the cycle of existence repeats again.[56] 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.[56] For example, the Surya Siddhanta states that the sidereal period of moon is 27.322 which compares to 27.32166 in modern calculations. For Mercury it states the period to be 87.97 (modern W: 87.969), Venus 224.7 (W: 224.701), Mars as 687 (W: 686.98), Jupiter as 4,332.3 (W: 4,332.587) and Saturn to be 10,765.77 days (W: 10,759.202).[56] The Surya Siddhanta also estimates the diameters of the planets. The estimate for the diameter of Mercury is 3,008 miles, an error of less than 1% from the currently accepted diameter of 3,032 miles. It also estimates the diameter of Saturn as 73,882 miles, which again has an error of less than 1% from the currently accepted diameter of 74,580. Its estimate for the diameter of Mars is 3,772 miles, which has an error within 11% of the currently accepted diameter of 4,218 miles. It also estimated the diameter of Venus as 4,011 miles and Jupiter as 41,624 miles, which are roughly half the currently accepted values, 7,523 miles and 88,748 miles, respectively.[57] CalendarThe solar part of the luni-solar Hindu calendar is based on the Surya Siddhanta.[58] The various old and new versions of Surya Siddhanta manuscripts yield the same solar calendar.[59] According to J. Gordon Melton, both the Hindu and Buddhist calendars in use in South and Southeast Asia are rooted in this text, but the regional calendars adapted and modified them over time.[60][61] The Surya Siddhanta calculates the solar year to be 365 days 6 hours 12 minutes and 36.56 seconds.[62][63] 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.[64] According to Whitney, the Surya Siddhanta calculations were tolerably accurate and achieved predictive usefulness. In Chapter 1 of Surya Siddhanta, states Whitney, "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".[65] Trigonometry
The Surya Siddhanta contains the roots of modern trigonometry. Its trigonometric functions jyā and koti-jyā (reflecting the chords of Hipparchus) are the direct source (via Arabic transmission) of the terms sine and cosine. It also contains the earliest use of the tangent and secant when discussing the shadow cast by a gnomon in verses 21–22 of Chapter 3:
In modern notation, this gives the shadow of the gnomon at midday as
and the hypotenuse of the gnomon at midday as
where is the measure of the gnomon, is the radius of the gnomon, is the shadow of the gnomon, and is the hypotenuse of the gnomon. Calendrical uses
The Indian solar and lunisolar calendars are widely used, with their local variations, in different parts of India. They are important in predicting the dates for the celebration of various festivals, performance of various rites as well as on all astronomical matters. The modern Indian solar and lunisolar calendars are based on close approximations to the true times of the Sun’s entrance into the various rasis. Conservative "panchang" (almanac) makers still use the formulae and equations found in the Surya Siddhanta to compile and compute their panchangs. The panchang is an annual publication published in all regions and languages in India containing all calendrical information on religious, cultural and astronomical events. It exerts great influence on the religious and social life of the people in India and is found in most Hindu households. Editions
See alsoReferences
Bibliography
Further reading
External linksSanskrit Wikisource has original text related to this article:
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