Surya Siddhanta - Unravelling The Marvels of Ancient Indian Astronomy


Staff member
Image for post

Palm leaf inscriptions of Surya Siddhanta written in Tamil | Source: Wikimedia
The distinguished writer Mark Twain once told the world,

“India is the cradle of the human race, the birthplace of human speech, the mother of history, the grandmother of legend and the great grandmother of tradition. Our most valuable and constructive materials in the history of man-kind are treasured up in India only.”
Standing as a testimony to this declaration, great works in the annals of the history of Mathematics and Astronomy trace their roots to Ancient India, the motherland to the development of myriad scientific notions. The vast achievements of Indian astronomy are scattered through a multitude of articles and books. Sacred texts and scriptures written by Indian philosophers contain descriptions about the functioning of the universe. While the Western world was busy debating about the authenticity of the heliocentric model, the Indian minds were lucrative in gauging the mammoth distances between Earth and other celestial bodies. When the rest of the world proposed various ideas about the working of the cosmos based on ‘Seeing is Believing’, the scientific temperament of Indians could successfully explain various celestial phenomena.

The ancient Indian texts on Astronomy are classified broadly into two main types:

  • Works of distinguished pioneers of astronomy like Aryabhata, Brahmagupta, etc. whose compilations are well known around the world and most popular in the field of astronomical sciences.
  • Works of authors, who preferred anonymity with a definite motive of representing these as a direct transmission from their Supreme Gods. These were called Siddhantas.
The word Siddhanta, which literally means ‘established (Siddh) in the end (Anta)’, comprises eighteen texts of which thirteen couldn’t stand against the ravaging time. The reason behind this was that knowledge was passed orally. The astronomical concepts were usually memorized and seldom recorded. Very often, a text falls into oblivion or maybe precariously holding on to its presence and identity when quoted in other texts as fragments.

The rest five were compiled and presented as Pañca-siddhāntikā or ‘The Compendium of the Five Astronomies’ in the sixth century by Varāhamihira, a polymath known for defining the algebraic properties of zero. These treatises are named as: Paulīśa-siddhānta, Romaka-siddhānta, Vasiṣṭha-siddhānta, Sūrya-siddhānta, and Paitāmaha-siddhānta. These are regarded as ganitas or treatises on astronomy. The Surya Siddhanta (Surya — sun) rests at the top of these revelations. Notably, it is the oldest book in astronomy in existence and has been the best known and the most referred astronomical text in the Indian tradition.

According to mythology, this sacred text is believed to have been given to Mayasura, the father-in-law of Ravana, by Lord Surya himself.

The second and third verse of Surya Siddhanta states that:

“Sometime during the end of Krita Yuga, a great demon named Maya, being desirous of obtaining the sound, secret, excellent, sacred and complete knowledge of Astronomy, which is the best of the six sciences subordinate to the Veda, practiced the most difficult penance, the worship of the Sun.”
Historians believe that this highly specific knowledge of the cosmos was passed on to allow the people of Earth to better worship the Sun God. This revelation dates back to Treta Yuga, as observed by Rev. Burgess, a skilled linguist who had translated a 12th century version of the text in English in 1860.

As earlier mentioned, there isn’t any direct evidence about the original text. It managed to find a place in history due to the extensive quoting and citation of it in the 6th century CE texts, notably by Rev. Ebenezer Burgess. Citations of the Surya Siddhanta are also found in the works of Aryabhata. 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.

The present Surya Siddhanta may nevertheless be considered a direct descendant of the text available to Varahamihira (who lived between 505–587 CE)

There are three distinct growths of this text:

  • The original work as it existed before Varahamira.
  • Varahamira’s redaction with the epicycle theory (a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets) in it.
  • Later additions and alterations.
The contents of the Surya Siddhanta are written in classical Indian poetry tradition, where complex ideas are expressed lyrically with a rhyming meter in the form of a verse or shloka.

This method of expressing and sharing knowledge made it easier to remember, recollect, 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 dual meanings. For example, instead of one, the text uses a word that means moon because there is only one moon and for a skilled reader, the word ‘moon’ means the number one. The entire table of trigonometric functions, sine tables, and 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.

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.

This anthropology consists of five hundred shlokas or terse verses, compiled in 14 chapters as given below:

Image for post

Image for post

Source: Wikipedia
Stay tuned for the second part of Surya Siddhanta as we decode various shlokas and expound the scientific principles behind it!

Image for post

Image for post

The first shloka of the compilation is written in praise of Lord Brahma, Lord Shiva and Lord Vishnu. | Source : Wikipedia


Staff member
Decoding the scientific findings

Following the glimpse into the colossal magnificence of this ancient wonder of Indian Astronomy, we shall now attempt decipher the nuances of the lapidary verses in this article.

Surya Siddhanta is enriched by the language and has ample scientific facts in the form of verses. The text asserts, according to Markanday and Srivatsava, that the earth is of a spherical shape. This book covers 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 metrics of the Earth’s diameter and circumference are also given. Eclipses and colour of the eclipsed portion of the moon is mentioned.

Given below highlights and interprets few slokas from the 14 chapters:

Chapter 12, verse 12.53 states that:

Thus everywhere on [the surface of] the terrestrial globe, people suppose their own place higher [than that of the others], yet this globe is in space where there is no one above or below.
Using that there is no above and below and that movement of the starry sphere is left to right for Asuras (demons) makes interesting reading. This indicates that ancient Indians had a considerable knowledge about outer space.

Chapter 12, verse 12.43 and 12.44, which provides stunning evidences for pole stars, is as follows

There are two pole stars, one each, near Northern Celestial point and near Southern Celestial point. From equatorial locations, these stars are seen along the horizon.
The pole stars are seen along the horizon, from these places, and thus the place latitude is close to zero, while the declination of Northern Celestial Pole and Southern Celestial Pole is 90 degrees.
Considering the age of the text, it’s worthy to note here that pole stars aren’t constant and vary over thousands of years. Researchers say that at around 1200BC (the time when Surya Siddhanta was probably scripted), there was indeed a Northern and Southern pole star, Canopus (Agastya) and Vega (Abhijit) respectively, contrary to Polaris (Northern pole star) and absence of Southern pole star.

Further, sloka 12:45 and 12:46 predicts periapsis and apoapsis and provides direct evidence to Kepler’s laws.

In the half revolution beginning with Aries, the Sun, being in the hemisphere of the gods, is visible to the gods: but while in that beginning with Libra, he is visible to the demons, moving in their hemisphere.
Hence, owing to these exceeding nearness, the rays of sun are hot in the hemisphere of gods in summer, but in that of the demons in winter: in the contrary season, they are sluggish
Verse 12.68 of Surya Siddhanta has stated that the inclination of Earth along its axis is 24 degrees, a value close enough to the modern revelations of 23.4366 degrees. But, astronomers do believe the value provided by Surya Siddhanta can actually state the fact that Earth’s obliquity oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle, considering the age of the sacred text.

The sun during his northern and southern progresses (ayana) revolves directly over a fifteenth part of the Earth’s circumference, on the side both of the gods and demons.
Objects fall on earth due to a force of attraction by the earth, therefore the earth, the planets, constellations, the moon and the sun are held in orbit due to this attraction
This sloka shows that people at those times had formulated the presence of an invisible force (now called gravity) that is behind objects falling back on Earth.

For each planet, the orbital circumference is a constant multiple of its time period. This comes about because of the following rule in the Surya Siddhanta for computing the orbital circumferences:

If the stated number of revolutions of the moon in an Aeon (kalpa) be multiplied by the moon’s orbit, the result is to be known as the orbit of the ether: so far do the sun’s rays penetrate. [12.81]
If this be divided by the number of revolutions of any planet in an Aeon (kalpa), the result will be the orbit of that planet: divide this by the number of terrestrial days, and the result is the daily eastward motion of them all
. [12.82]
The idea behind this rule is that all of the planets move at the same mean rate in their geocentric orbits. Since the Surya Siddhanta gives accurate figures for the revolutions of each planet in a kalpa, this rule results in orbital circumferences proportional to the modern geocentric periods of the planets. (According to modern astronomy, the period squared should be proportional to the orbital circumference cubed.)

The Surya Siddhanta says that there are 15 yojanas per minute of the arc at the distance of the moon. Thus, the mean angular diameters of the planets can be computed by dividing the diameters upon the moon’s orbit by 15. If we analyse the data transcribed about the angular diameters of various celestial bodies in Surya Siddhanta, we can find all the values on the higher side as juxtaposed to the modern era calculations. But, considering the fact that a small, distant light source looks larger to the naked eye than it really is, this shows that all the measurements were made by naked eye!

Surya Siddhanta follows a model based on precession of equinoxes. It makes use of the zodiac signs to make calculations on astronomical distances.

  • The text asserts that the average length of the tropical year is 365.2421756 days, which is only 1.4 seconds shorter than the modern value of 365.2421904 days!
  • Not content to limit measurements to Earth, the Surya Siddhanta also states the motion, and diameters of the planets too! 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 estimates the diameter of Saturn as 73,882 miles, which is just short by 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.
  • The most fascinating revelation is the sidereal period of the moon as 27.322 , compared to 27.32166 in modern calculations. For Mercury it states the period to be 87.97 (modern result: 87.969), Venus as 224.7 (modern: 224.701), Mars as 687 (modern: 686.98), Jupiter as 4,332.3 (modern: 4,332.587) and Saturn to be 10,765.77 days (modern: 10,759.202).
  • The Surya Siddhanta also goes into a detailed discussion about time cycles and that time flows differently in different circumstances, the roots of relativity. Here we have a perfect example of Indian philosophy’s belief that science and religion are not mutually exclusive.
  • It has described rules to calculate the motions of various planets and the moon relative to various constellations, diameters of various planets, and the orbits of various astronomical bodies. The text asserts that the universe is of a spherical shape.
All the shlokas stand as an incredible testimony of the advanced thinking of the Ancient Indians.

One possible hypothesis is that at some time in the past, ancient astronomers possessed realistic values for the diameters of the planets. One can suppose that they might have acquired this knowledge during a forgotten period in which astronomy reached a high level of sophistication and planets were observed using telescopes or other advanced instruments. Later on, much of this knowledge was lost, but fragmentary remnants were preserved and eventually incorporated into texts such as the Surya Siddhanta.

Surya Siddhanta
also explains about a myriad of mathematical concepts like Trigonometry functions and sexagesimal fractions.

It contains the roots of modern trigonometry. This is evident from the use of trigonometric ratios like 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.
Image for post

Image for post

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.

The solar part of the luni-solar Hindu calendar is based on the Surya Siddhanta. The various old and new versions of Surya Siddhanta manuscripts yield the same solar calendar. Both the Hindu and Buddhist calendars used in South and Southeast Asia are rooted in this text, but the regional calendars have adapted and modified them over time.

“Panchang” (almanac) makers still use the formulae and equations found in the “Surya Siddhanta” to compile and compute their panchangas. It exerts great influence on the religious and the social life of people in India and is found in most Hindu households. On an 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.

The entire collection of Surya Siddhanta has well substantiated asseverations on scientific notions, a clear indication that Indians were at the forefront of moving towards the understanding of the reality that was hidden behind the illusionary ideas prevalent in those times. It’s high time for us to develop a sense of understanding about the greatness of ancient texts and the prowess that we had possessed. People, especially youth, should be encouraged to turn back to the forgotten pages of Indian history and restore the glory of our culture and tradition.