The
Surya Siddhanta is a treatise of Indian astronomy. It is a more than a thousand year old text book of Indian Astronomy.
Later
Indian mathematiciansIndian mathematics is the mathematics that emerged in South Asia from ancient times until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today ...
and astronomers such as
AryabhataAryabhata was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy...
and
VarahamihiraDaivajna Varāhamihira , also called Varaha, or Mihira was an Indian astronomer, mathematician, and astrologer who lived in Ujjain. He is considered to be one of the nine jewels of the court of legendary king Vikramaditya...
made references to this text.
Varahamihira in his
Panchasiddhantika contrasts it with four other treatises, besides the Paitamaha Siddhantas (which is more similar to the "classical"
Vedanga JyotishaThe Vedanga Jyotisha, is an Indian text on Jyotisha , redacted by Lagadha .The text is foundational to the Jyotisha discipline of Vedanga, and is dated to the final centuries BCE. The text describes rules for tracking the motions of the sun and the moon...
), the Paulisha and
RomakaThe Romaka Siddhanta is an Indian astronomical treatise, based on the works of the ancient Romans. "Siddhanta" literally means "Doctrine" or "Tradition".-Content:...
Siddhantas (directly based on Hellenistic astronomy) and the Vasishta Siddhanta.
The work referred to by the title
Surya Siddhanta has been repeatedly recast.
The
Surya Siddhanta is a treatise of Indian astronomy. It is a more than a thousand year old text book of Indian Astronomy.
Later
Indian mathematiciansIndian mathematics is the mathematics that emerged in South Asia from ancient times until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today ...
and astronomers such as
AryabhataAryabhata was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy...
and
VarahamihiraDaivajna Varāhamihira , also called Varaha, or Mihira was an Indian astronomer, mathematician, and astrologer who lived in Ujjain. He is considered to be one of the nine jewels of the court of legendary king Vikramaditya...
made references to this text.
Varahamihira in his
Panchasiddhantika contrasts it with four other treatises, besides the Paitamaha Siddhantas (which is more similar to the "classical"
Vedanga JyotishaThe Vedanga Jyotisha, is an Indian text on Jyotisha , redacted by Lagadha .The text is foundational to the Jyotisha discipline of Vedanga, and is dated to the final centuries BCE. The text describes rules for tracking the motions of the sun and the moon...
), the Paulisha and
RomakaThe Romaka Siddhanta is an Indian astronomical treatise, based on the works of the ancient Romans. "Siddhanta" literally means "Doctrine" or "Tradition".-Content:...
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.
UtpalaUtpala or ' is the name of a 10th century Indian commentator of Vārāha Mihira's Brihat Samhitā. Brihat Samhitā is a Samhitā text of . Samhitā is one of three branches of Utpala or ' is the name of a 10th century Indian commentator of Vārāha Mihira's Brihat Samhitā. Brihat Samhitā is a...
, 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. 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
nakshatraNakshatra or lunar mansion is one of the 27 divisions of the sky, identified by the prominent star in them, used in Jyotisha.-Overview:...
s and treats the calculation of
solar eclipseA solar eclipse occurs when the moon passes between the Sun and the Earth so that the Sun is fully or partially covered. This can only happen during a new moon, when the Sun and Moon are in conjunction as seen from the Earth. At least two and up to five solar eclipses can occur each year on Earth,...
s.
Astronomy
The table of contents in this text are:
- The Motions of the Planet
A planet , is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
s
- The Places of the Planets
- Direction, Place and Time
- The Moon
The Moon is Earth's only natural satellite and the fifth largest satellite in the Solar System. The average centre-to-centre distance from the Earth to the Moon is , about thirty times the diameter of the Earth. The common centre of mass of the system is located at about —a quarter the Earth's...
and EclipseAn eclipse is an astronomical event that occurs when one celestial object moves into the shadow of another. The term is derived from the ancient Greek noun , which is derived from the verb , "to cease to exist," a combination of prefix , from preposition , "out," and of verb , "to be absent"...
s
- The Sun
The Sun is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 99.86% of the Solar System's mass....
and Eclipses
- The Projection of Eclipses
- Planetary Conjunctions
- Of the Star
A star is a massive, luminous ball of plasma that is held together by gravity. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth. Other stars are visible in the night sky, when they are not outshone by the Sun...
s
- Rising
Rising may refer to:*Rising , the last novel of R. C. Hutchinson*The following albums:**Rising **Rising **Rising **Rising **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 gnomon is the part of a sundial that casts the shadow. Gnomon is an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."It has come to be used for a variety of purposes in mathematics and other fields....
- The Movement of the Heavens and Human Activity
Methods for accurately calculating the shadow cast by a
gnomonThe gnomon is the part of a sundial that casts the shadow. Gnomon is an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."It has come to be used for a variety of purposes in mathematics and other fields....
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 average length of the tropical year
A tropical year is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.A tropical year can equivalently be defined as the time taken...
as 365.2421756 days, which is only 1.4 seconds shorter than the modern value of 365.2421904 days (J2000). This estimate remained the most accurate approximation for the length of the tropical year anywhere in the world for at least another six centuries, until Muslim mathematicianIn the history of mathematics, mathematics in medieval Islam, sometimes termed Islamic mathematics, is the mathematics developed in the Islamic world between 622 and 1600, during what is known as the Islamic Golden Age...
Omar KhayyamOmar Khayyám , , was a Persian polymath, mathematician, philosopher, astronomer and poet. He also wrote treatises on mechanics, geography, music and was a physicist....
gave a better approximation, though it still remains more accurate than the value given by the modern Gregorian calendarThe Gregorian calendar is the internationally accepted civil calendar. It was first proposed by the Calabrian doctor Aloysius Lilius, and decreed by Pope Gregory XIII, after whom the calendar was named, on 24 February 1582 by the papal bull Inter gravissimas...
currently in use around the world, which gives the average length of the yearA year is the amount of time it takes the Earth to make one revolution around the Sun...
as 365.2425 days.
- The average length of the sidereal year
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It was equal to at noon 1 January...
, the actual length of the Earth's revolution around the SunThe Sun is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 99.86% of the Solar System's mass....
, as 365.2563627 days, which is virtually the same as the modern value of 365.25636305 days (J2000). This remained the most accurate estimate for the length of the sidereal year anywhere in the world for over a thousand years.
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 motionMean motion, , is a measure of how fast a satellite progresses around its orbit. Unless the orbit is circular, the mean motion is only an average value, and does not represent the instantaneous angular rate....
for the Sun and a constant of
precessionPrecession refers to a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
inferior to that used in the Hindu cosmological time cycles.
Trigonometry
The
Surya Siddhanta contains the roots of modern
trigonometryTrigonometry is a branch of mathematics that deals with triangles, particularly those plane triangles in which one angle has 90 degrees...
. It uses
sineMaurice Sinet, known as Siné is a French cartoonist.As a young man he studied drawing and graphic arts, while earning a living as a cabaret singer. After his military service he started publishing his drawings and also worked as a photo-retoucher for porn magazines. His first published drawing...
(
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
secantSecant is a term in mathematics. It comes from the Latin secare . It can refer to:* a secant line, in geometry* the secant method, a root-finding algorithm in numerical analysis, based on secant lines to graphs of functions...
when discussing the shadow cast by a
gnomonThe gnomon is the part of a sundial that casts the shadow. Gnomon is an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."It has come to be used for a variety of purposes in mathematics and other fields....
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 hypotenuseA hypotenuse is the longest side of a right triangle , the side opposite the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the...
at mid-day.
In modern notation, this gives the shadow of the
gnomonThe gnomon is the part of a sundial that casts the shadow. Gnomon is an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."It has come to be used for a variety of purposes in mathematics and other fields....
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
solarA solar calendar is a calendar whose dates indicate the position of the earth on its revolution around the sun .-Tropical solar calendars:...
and
lunisolar calendarA lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will...
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" (
almanacAn almanac is an annual publication containing tabular information in a particular field or fields often arranged according to the calendar...
) 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
- Hindu Time Cycles
- Indian science and technology
- Indian mathematics
Indian mathematics is the mathematics that emerged in South Asia from ancient times until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today ...
- Hindu astronomy
Indian astronomy—the earliest textual mention of which is given in the religious literature of India —became an established tradition by the 1st millennium BCE, when and other ancillary branches of learning called Vedangas began to take shape...
- Vedanga Jyotisha
The Vedanga Jyotisha, is an Indian text on Jyotisha , redacted by Lagadha .The text is foundational to the Jyotisha discipline of Vedanga, and is dated to the final centuries BCE. The text describes rules for tracking the motions of the sun and the moon...
External links