Surya Siddhanta

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The Surya Siddhanta is one of the earliest doctrines or traditions (siddhanta) in archaeo-astronomy of the Hindus. Its original version is by an unknown author. It describes the archeo-astronomy theories, principles and methods of the ancient Hindus. This siddhanta is supposed to be the knowledge that the Sun god gave to an Asura called Maya. Asuras were enemies of the Deva, the Gods of Hindus. Asuras were believed to be residents of the nether worlds.

Significant coverage is on kinds of time, length of the year of gods and demons, day and night of god Brahma, the elapsed period since creation, how planets move eastwards and sidereal revolution. The lengths of the Earth's diameter, circumference are also given. Eclipses and color of the eclipsed portion of the moon is mentioned. This explains the archeo-astronomical basis for the sequence of days of the week named after the Sun, Moon, etc. Musings that there is no above and below and that movement of the starry sphere is left to right for Asuras makes interesting reading.

Varahamihira in his Panchasiddhantika contrasts it with four other treatises, besides the Paitamaha Siddhantas (which is more similar to the "classical" Vedanga Jyotisha), the Paulisha and Romaka Siddhantas (directly based on Hellenistic astronomy) and the Vasishta Siddhanta. Citation of the Surya Siddhanta is also found in the works of Aryabhata.

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 (1860) 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 version was modified by Bhaskaracharya during the Middle Ages.[citation needed] The present Surya Siddhanta may nevertheless be considered a direct descendant of the text available to Varahamihira.[1] 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 nakshatras and treats the calculation of solar eclipses. as well as solstices eg.summer solstice 21/06


The mean (circular) motion of planets according to the Surya Siddhantha.
The variation of the true position of Mercury around its mean position according to the Surya Siddhantha.

The table of contents in this text are:

  1. The Mean Motions of the Planets[notes 1]
  2. True Places of the Planets
  3. Direction, Place and Time
  4. The Moon and Eclipses
  5. The Sun and Eclipses
  6. The Projection of Eclipses
  7. Planetary Conjunctions
  8. Of the Stars
  9. Risings and Settings
  10. The Moon's Risings and Settings
  11. Certain Malignant Aspects of the Sun and Moon
  12. Cosmogony, Geography, and Dimensions of the Creation
  13. The Gnomon
  14. 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.

Time cycles[edit]

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....

Planetary diameters[edit]

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.[2]


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 [the 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 midday as

s = \frac{g \sin \theta}{\cos \theta} = g \tan \theta

and the hypotenuse of the gnomon at midday as

h = \frac{g r}{\cos \theta} = g r \frac{1}{\cos \theta} = g r \sec \theta

where \ g is the measure of the gnomon, \ r is the radius of the gnomon, \ s is the shadow of the gnomon, and \ h is the hypotenuse of the gnomon.

Calendrical uses[edit]

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.



See also[edit]


Further reading[edit]

  • Victor J. Katz. A History of Mathematics: An Introduction, 1998.