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The Surya Siddhanta is a treatise of Indian Astronomy . Later Indian Mathematicians and astronomers such as Aryabhata and Varahamihira made references to this text. Varahamihira in his ''Panchasiddhantika'' contrasts it with four other treatises, besides the Paitamaha Siddhanta s (which is more similar to the "classical" Vedanga Jyotisha ), the Paulisha and Romaka Siddhantas (directly based on Hellenistic astronomy) and the Vasishta Siddhanta . The work referred to by the title ''Surya Siddhanta'' has been repeatedly recast. There may have been an early work under that title dating back to the Buddhist Age of India (3rd century BC). The work as preserved and edited by Burgess (1858) dates to the Middle Ages. Utpala , a 10th century commentator of Varahamihira, quotes six shlokas of the Surya Siddhanta of his day, not one of which is to be found in the text now known as the Surya Siddhanta. The present Surya Siddhanta may nevertheless be considered a direct descendant of the text available to Varahamihira.Romesh Chunder Dutt, A History of Civilization in Ancient India, Based on Sanscrit Literature, vol. 3, ISBN 0543929396 p. 208. This article discusses the text as edited by Burgess. For what evidence we have of the Gupta Period text, see Pancha-Siddhantika . It has rules laid down to determine the true motions of the luminaries, which conform to their actual positions in the sky. It gives the locations of several stars other than the lunar Nakshatra s and treats the calculation of Solar Eclipse s. ASTRONOMY The table of contents in this text are: #The Motions of the Planet s #The Places of the Planets #Direction, Place and Time #The Moon and Eclipse s #The Sun and Eclipses #The Projection of Eclipses #Planetary Conjunctions #Of the Star s # Rising s and Settings #The Moon's Risings and Settings #Certain Malignant Aspects of the Sun and Moon #Cosmogony, Geography, and Dimensions of the Creation #The Gnomon #The Movement of the Heavens and Human Activity Methods for accurately calculating the shadow cast by a Gnomon are discussed in both Chapters 3 and 13. The astronomical time cycles contained in the text were remarkably accurate at the time. The Hindu Time Cycles , copied from an earlier work, are described in verses 11–23 of Chapter 1: :11. That which begins with respirations (prana) is called real.... Six respirations make a vinadi, sixty of these a nadi; :12. And sixty nadis make a sidereal day and night. Of thirty of these sidereal days is composed a month; a civil (savana) month consists of as many sunrises; :13. A lunar month, of as many lunar days (tithi); a solar (saura) month is determined by the entrance of the sun into a sign of the zodiac; twelve months make a year. This is called a day of the gods. :14. The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise of the demons. :15. Twelve thousand of these divine years are denominated a caturyuga; of ten thousand times four hundred and thirty-two solar years :16. Is composed that caturyuga, with its dawn and twilight. The difference of the krtayuga and the other yugas, as measured by the difference in the number of the feet of Virtue in each, is as follows: :17. The tenth part of a caturyuga, multiplied successively by four, three, two, and one, gives the length of the krta and the other yugas: the sixth part of each belongs to its dawn and twilight. :18. One and seventy caturyugas make a manu; at its end is a twilight which has the number of years of a krtayuga, and which is a deluge. :19. In a kalpa are reckoned fourteen manus with their respective twilights; at the commencement of the kalpa is a fifteenth dawn, having the length of a krtayuga. :20. The kalpa, thus composed of a thousand caturyugas, and which brings about the destruction of all that exists, is a day of Brahma; his night is of the same length. :21. His extreme age is a hundred, according to this valuation of a day and a night. The half of his life is past; of the remainder, this is the first kalpa. :22. And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvant, twenty-seven caturyugas are past; :23. Of the present, the twenty-eighth, caturyuga, this krtayuga is past.... When computed, this astronomical time cycle would give the following results:
The actual astronomical value stated for the sidereal year however, is not as accurate. The length of the sidereal year is stated to be 365.258756 days, which is longer than the modern value by 3 minutes 27 seconds. This is due to the text using a different method for actual astronomical computation, rather than the Hindu cosmological time cycles copied from an earlier text, probably because the author didn't understand how to compute the complex time cycles. The author instead employed a Mean Motion for the Sun and a constant of Precession inferior to that used in the Hindu cosmological time cycles. TRIGONOMETRY The ''Surya Siddhanta'' contains the roots of modern Trigonometry . It uses Sine (''jya''), Cosine (''kojya'' or "perpendicular sine") and Inverse Sine (''otkram jya'') for the first time, and 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: Of sun's meridian zenith distance find the ''jya'' ("base sine") and ''kojya'' (cosine or "perpendicular sine"). If then the ''jya'' and radius be multiplied respectively by the measure of the gnomon in digits, and divided by the ''kojya'', the results are the shadow and Hypotenuse at mid-day. In modern notation, this gives the shadow of the Gnomon at mid-day as and the hypotenuse of the gnomon at mid-day 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 Calendar s 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. REFERENCES
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