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Surya Siddhanta is the first of the tradition or doctrine ( *Siddhanta* ) in archaeo-astronomy Vedic era.

In fact, it is the oldest book in the world that describes the *earth as a ball (not flat)* , gravity being the reason objects fall on the earth, etc.

This is the knowledge that the Sun god gave to an Asura named Maya in Treta Yuga. Maya

this is the father-in-law of Ravana, the villain of the first epic poem, the Ramayana. According to Yugas' calculations, the first version of Surya Siddhanta must have been known about 2 million years ago. However, the version currently available is believed to be over 2500 years old, which still makes it the oldest Astronomy book on earth.

This book covers the various times, the length of the year of gods and demons, the day and night of the god Brahma, the period that has passed since creation, how the planets move east and sidereal revolutions. The length of the diameter of the earth, the circumference is also given. The eclipse and the color of the lunar eclipse section are mentioned.

It explains the archeo-astronomical basis for the order of the days of the week named the Sun, Moon, etc. The reflection that there is no above and below and that the movement of the starry ball from left to right for Asuras (demons) makes for an interesting read.

Quotations of Surya Siddhanta are also found in the works of Aryabhata.

The work preserved and edited by Burgess (1860) dates back to the Middle Ages.

Utpala, a 10th-century commentator on Varahamihira, quotes six shlokas of Surya Siddhanta of his day, none of which can be found in the text now known as Surya Siddhanta. The present version has been modified by Bhaskaracharya during the Middle Ages.

Surya Siddhanta today can be considered a direct descendant of the texts available to Varahamihira (who lived between 505–587 AD)

#### Quotes from Surya Siddhanta

- The average length of a tropical year is 365.2421756 days, which is only 1.4 seconds shorter than the modern value of 365.2421904 days!
- The average length of the sidereal year, the true length of the Earth's revolution around the Sun, was 365.2563627 days, which is about the same as the modern value of 365.25636305 days. This remains the most accurate estimate of the length of a sidereal year anywhere in the world for more than a thousand years!
- Not content to limit measurements to Earth, Surya Siddhanta also stated the motions, and diameters of the planets! For example, the approximate diameter of Mercury is 3,008 miles, an error of less than 1% of the currently accepted diameter of 3,032 miles. It also estimates Saturn's diameter as 73,882 miles, which again has an error of less than 1% of the currently accepted diameter of 74,580.
- Apart from inventing the decimal system, zero and standard notation (giving the ancient Indians the ability to count trillions when the rest of the world struggled with 120), Surya Siddhanta also contains Trigonometric roots.
- It uses sine (jya), cosine (kojya or "perpendicular sine") and inverted sine (otkram jya) for the first time!
- Objects fall to the earth because of the gravitational force of the earth. therefore, the earth, the planets, the constellations, the moon and the sun are held in orbit because of this attraction”. (this is also discussed in the Prasnopanishad
- It wasn't until the late 17th century in 1687 that Isaac Newton rediscovered the Law of Gravity.
- Surya Siddhanta also discusses in detail about the cycles of time and time flows differently under different circumstances, the root of relativity. Here we have a perfect example of the Indian philosophical belief that science and religion are not mutually exclusive. Unlike, Abrahamic religions, one does not have to dig and try all means to impose scientific truths from scriptures. Instead it is expressed in cold hard figures by the Sun God, Surya.
- This work shows that spirituality is all about seeking the Truth (Satya) and that Science is a valid path to God like living in a monastery. It is the search for one's own personal Truth that will lead one ultimately to God.

**The astronomical time cycle contained in the text is very accurate.**

- What begins with breathing (prana) is called real…. Six breaths make vinadi, sixty of which are nadi
- And sixty pulses make sidereal day and night. Of the thirty sidereal days it consists of one month; civil moon (savanna) consists of many sunrises
- Lunar months, as many as lunar days (tithi); the solar moon (saura) is determined by the entry of the sun into the zodiac sign; twelve months to one year. This is called the day of the gods. (Day at the North Pole)
- Day and night gods and demons contradict each other. Six times sixty of them are the year of the gods, as well as the year of the devil. (Day and Night are six months each at the South Pole)
- These twelve thousand divine years are called chaturyuga; ten thousand times four hundred and thirty-two solar years
- It consists of the chaturyuga, with its dawn and dusk. The difference between kritayuga and other yugas as measured by the difference in the number of Righteous feet in each is as follows:

- The tenth part of the chaturyuga, multiplied by four, three, two, and one, respectively, gives the length of another krita and yuga: the sixth part belongs to dawn and dusk, respectively.
- One and seventy chaturyuga make manu; at its end is the twilight which has the number of years of kritayuga, and which is the flood.
- In one kalpa are counted fourteen manus with each twilight; at the beginning of a kalpa is the fifteenth dawn, has the length of kritayuga.
- The kalpa, which consists of a thousand chaturyugas, and which causes the destruction of all that exists, is the day of Brahma; the night is the same length.
- His extreme age was a hundred, according to this day and night judgment. Half of his life had passed; of the rest, this is the first kalpa.
- And from this eon, six sages have passed, with their respective twilights; and from Manu son of Vivasvant twenty-seven chaturyugas have passed;
- From this moment, the twenty-eighth, this chaturyuga, kritayuga is past.

#### Diameter of the Planet in the Sun Siddhanta

Surya Siddhanta also estimated the diameters of the planets. Mercury's estimated diameter is 3,008 miles, an error of less than 1% of the currently accepted diameter of 3,032 miles. It also estimates Saturn's diameter as 73,882 miles, which again has an error of less than 1% of the currently accepted diameter of 74,580. 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 estimates the diameter of Venus as 4,011 miles and Jupiter as 41,624 miles, which is roughly half of the currently accepted values, respectively. 7,523 miles and 88,748 miles.#### Trigonometry at Surya Siddhanta

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 tangents and secant when discussing the shadow cast by gnomons in verses 21–22 from Chapter 3:

From [peak distance of the solar meridian] find jya ("basic sine") and kojya (cosine or "perpendicular sine"). If then jya and radius are multiplied respectively by the size of the gnomon in numbers, and divided by kojya , the result is the shadow and hypotenuse at midday. In modern notation, this gives the shadow of the gnomon at midday as:

Even today many astrologers in India use Surya Siddhanta as the basis for calculating their Panchang (Almanac) in many languages.

The diagram below shows a variation of the standard positional triangle which first appeared in Sanskrit astronomical texts sometime before the 12th century. The most famous is (Surya Siddhanta).

The Sanskrit word for bow is (CAPA). It is also the name given to a circular arc. The Sanskrit word for bowstring is (jya). This is also the name given to circle chords. At some point, Indian astronomers discovered that knowing the size of half a chord was more useful than knowing the size of the whole chord. The half chord in Sanskrit is (jya ardh). The term became so popular that the modifier ( ardh ) was dropped and the word ( jya ) or a similar word ( jiva ) meant half a chord by itself.

Arabic scholars transliterated ( jiva ) to ( Jiba ). They basically make up a new word in Arabic. European scholars did not know that it was a new word, so they read it as an existing word. This kind of thing is easy to do because vowels are never written in Arabic. The letters may represent Jiba (they may not know) or they may represent jaib (they may know). Latin scholars went with the latter. The Arabic word (jaib) is an English word dada is the Latin word sinus. The bowstring becomes the chest into a sinus. You can't make up stories like that. It must be true.

In old Sanskrit texts, the half chord is called (jya). The line that cuts the chord in half is called ( Koti-jya ) on one side and (untukrama-jya ) on the other. You can think of them as "complementary chords" and "counter chords." When ( jya ) becomes sine to sine, ( Koti-jya ) or ( kojya ) becomes cosine to become cosine. Sine and cosine have the same value for complementary angles. This concept is reused for other cofunctional pairs — tangents have cotangents, secants have cosecants.

The remainder of the diagram, ( forrama-jya ), is compared to sine in Latin to sine or versine in English. The experienced part relates to the Latin word versus in the sense of opposing something else, but I don't quite get it. There is a large family of co-, ver-, cover-, ha-, oat-, cohaver, hacover, and ex-functions that are not widely used anymore. I will not discuss them.

Which leaves us with tangents and intersections. The diagram below shows another variation of the standard position triangle with three additional line segments that form a triangle outside the circle — one starting at the center of the circle and intersecting an arc like an arrow waiting to be fired, the second leaning against the circle touching it just at the point where the finger -finger ends, and a third at right angles to the first that also intersects the circle.

The line segment touching the circle gives us the tangent and cotangent slices (one to the right and one to the left of the point touching the circle). The English word tangent comes from the Latin tangens — to touch. The line segment that intersects the circle gives us the intersection of the secant and cosecant (one intersects the circle horizontally and the other intersects the circle vertically). The English word secant comes from the Latin word secans cutting. The words tangens and secant were given their mathematical meaning by the Danish mathematician Thomas Fincke in 1583. Earlier Arabic, Hindu, Roman, Greek, and Babylonian mathematicians may have known these concepts, but their words do not seem to have made their way into many modern languages ( Modern Greece being the main exception).