Astronomical system of Aryabhatta



AryabhattOne of the important developments in this filed was the theory proved by Aryabhatta that the earth is round in shape unlike the ancient belief that it is flat. The theory of gravity was also promulgated by the astronomers of the Gupta period.

The astronomical system of Aryabhatta was known as the ‘aud Ayaka system’. In this system the days are calculated from dawn. Aryabhatta also proved that the earth revolves around its own axis every day. He was of the opinion that the motion of stars was a result of the motion caused by the rotation of the earth.

This theory of Aryabhatta contradicts the previously believed notion that it is the sky that rotates and not the stars. He believed that the Earth’s orbit is elliptical and not circular. Aryabhatta described a model of the solar system wherein the Sun and the Moon are carried by epicycles.

According to this system, the Sun and the Moon revolve around the Earth. The positions of the various planets in the planetary system were calculated in relation to their moving points. The calculations made by Aryabhatta in reference to the planets movement was believed to have been supported by an underlying heliocentric model.

He scientifically elucidated the reasons for the occurrence of the solar and lunar eclipse. Aryabhatta stated that the lunar eclipse occurs when the moon enters into the shadow of the Earth. He even calculated the sidereal rotation.

Aryabhatta calculated the sidereal year and stated that it takes around 365 days for the earth to complete one revolution around the sun. The development of astronomy in the Gupta period was a source of influence to the next generation astronomers.


Motions of the solar system

 Aryabhata appears to have believed that the earth rotates about its axis. This is made clear in the statement, referring to Lanka , which describes the movement of the stars as a relative motion caused by the rotation of the earth:

Like a man in a boat moving forward sees the stationary objects as moving backward, just so are the stationary stars seen by the people in lankA (i.e. on the equator) as moving exactly towards the West. [achalAni bhAni samapashchimagAni – golapAda.9]

But the next verse describes the motion of the stars and planets as real movements: “The cause of their rising and setting is due to the fact the circle of the asterisms together with the planets driven by the provector wind, constantly moves westwards at Lanka”.

Lanka (lit.SRILANKHA) is here a reference point on the equator, which was taken as the equivalent to the reference meridian for astronomical calculations.

Aryabhata described a “geocentric” model of the solar system, in which the Sun and Moon are each carried by “epicycles” which in turn revolve around the Earth. In this model, which is also found in the Paitāmahasiddhānta (ca. AD 425), the motions of the planets are each governed by two epicycles, a smaller manda (slow) epicycle and a larger sighra (fast) epicycle.The order of the planets in terms of distance from earth are taken as: the Moon, Mercyary, Venus the sun, mars , Jupiter, Saturn and the asterism .

The positions and periods of the planets were calculated relative to uniformly moving points, which in the case of Mercury and Venus, move around the Earth at the same speed as the mean Sun and in the case of Mars, Jupiter, and Saturn move around the Earth at specific speeds representing each planet’s motion through the zodiac. Most historians of astronomy consider that this two epicycle model reflects elements of pre-Ptolemaic Greek Astronomy. Another element in Aryabhata’s model, the śīghrocca, the basic planetary period in relation to the Sun, is seen by some historians as a sign of an underlying heliocentric model



He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogyny where eclipses were caused by pseudo-planetary nodes Rahu and Ketu, he explains eclipses in terms of shadows cast by and falling on earth. Thus the lunar eclipse occurs when the moon enters into the earth-shadow (verse gola.37), and discusses at length the size and extent of this earth-shadow (verses gola.38-48), and then the computation, and the size of the eclipsed part during eclipses. Subsequent Indian astronomers improved on these calculations, but his methods provided the core. This computational paradigm was so accurate that the 18th century scientist Guillaume le Gentil, during a visit to Pondicherry, found the Indian computations of the duration of the lunar eclipse of year 1765 – 08- 30 to be short by 41 seconds, whereas his charts (by Tobias Mayer,1752 were long by 68 seconds.

Aryabhata’s computation of Earth’s circumference as 24,835 miles, which was only 0.2% smaller than the actual value of 24,902 miles. This approximation might have improved on the computation by the Greek mathematician Eratosthenes (c. 200 B.C.), whose exact computation is not known in modern units.

Sidereal Periods

Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referenced the fixed stars) as 23 hours 56 minutes and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days 6 hours 12 minutes 30 seconds is an error of 3 minutes 20 seconds over the length of a year. The notion of sidereal time was known in most other astronomical systems of the time, but this computation was likely the most accurate in the period.


Aryabhata claims that the Earth turns on its own axis and some elements of his planetary epicyclic models rotate at the same speed as the motion of the planet around the Sun. This has suggested to some interpreters that Āryabhata’s calculations were based on an underlying heliocentric model in which the planets orbit the Sun. A detailed rebuttal to this heliocentric interpretation is in a review which describes B.L.Vander ‘s book as “show[ a complete misunderstanding of Indian planetary theory [that] is flatly contradicted by every word of Aryabhata’s description, although some concede that Āryabhata’s system stems from an earlier heliocentric model of which he was unaware It has even been claimed that he considered the planet’s paths to be elliptical, although no primary evidence for this has been cited. Though Aristarchus of samos (3rd century BC) and sometimes Heraclides of Pontus (4th century BC) are usually credited with knowing the heliocentric theory, the version of Greek Astronomy known in ancient India , Paulisa Siddhanta (possibly by a Paul of Alexandria) makes no reference to a Heliocentric theory.


Aryabhata’s work was of great influence in the Indian astronomical tradition, and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic golden Age (CA 820), was particularly influential. Some of his results are cited by Al- Khwarizmi, and he is referred to by the 10th century Arabic scholar Al-Biruni, who states that Āryabhata’s followers believed the Earth to rotate on its axis.

His definitions of sine, as well as cosine (kojya), versine (ukramajya), and inverse sine (otkram jya), influenced the birth of trigonometry. He was also the first to specify sine and versine (1 – cosx) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.

In fact, the modern names “sine” and “cosine“, are a mis-transcription of the words jya and kojya as introduced by Aryabhata. They were transcribed as jiba and kojiba in Arabic. They were then misinterpreted by Gerard of Cremona while translating an Arabic geometry text to Latin; he took jiba to be the Arabic word jaib, which means “fold in a garment”, L. sinus .

Aryabhata’s astronomical calculation methods were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world, and were used to compute many Arbic astronomical tables (zijes). In particular, the astronomical tables in the work of the Arbic Spain scientist Al- Zarqali (11th c.), were translated into Latin as the Table of Toledo (12th c.), and remained the most accurate Ephemeris used in Europe for centuries.

Calendric calculations worked out by Aryabhata and followers have been in continuous use in India for the practical purposes of fixing the Panchanga, or Hindu Calendar, These were also transmitted to the Islamic world, and formed the basis for the Jalali Calendar introduced 1073 by a group of astronomers including Omar Khauuam, versions of which (modified in 1925) are the national calendars in use in Iran and Afghanistan today. The Jalali calendar determines its dates based on actual solar transit, as in Aryabhata (and earlier Siddhanta calendars). This type of calendar requires an Ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were lower in the Jalali Calendar than in the Gregorian calendar.

India’s first satellite Arybhatta, was named after him. The lunar crater Aryabhatta is named in his honour. The interschool Aryabhatta Maths Competiition is named after him.



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