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Aryabhata's Babylonian Contacts
by Manikant Shah

In his article on Planetary constants K D Abhyankar tries to show that certain concepts used by Aryabhata in his treatises on Astronomy and Mathematics were probably influenced by the Babylonian planetary data. In his foreword to the 'Aryabhatiya of Aryabhata' edited by KV Sharma in 1976, B P Pal (the then president of the Indian National Science Academy) wrote that due to his contributions to the fields of Astronomy and Mathematics Aryabhata has rightly been regarded as the founder of scientific astronomy in India. In his introductory remarks in the essay 'Aryabhata- the father of epicyclical astronomy' (History of Science in India vol.2), PC Sengupta states that 'from his own statement made in the Kala Kriya section of his Aryabhatiyam, we know that Aryabhata was born in the year 476 of the Christian Era, that he wrote this famous book (Aryabhatiya) at the age of 23 and that his native place was most probably Kusumapura, Patliputra or the modern city of Patna.' So great was his status in this respect, that whoever differed from Aryabhata was a subject of ridicule. Sengupta further writes that the Indian epicyclic astronomy was constructed by Aryabhata , from whom alone all the later Indian astronomers drew their inspiration.

It is clear that Aryabhata had a wide reputation in India, but Abhyankar shows that the concepts of bhaganas used by Aryabhata were probably derived from the Babylonian planetary data. Before we understand the argument that Abhyankar is making we must take into account certain concepts that are involved. These are the Mahayugas, synodic lunar month, bhaganas, the sidereal revolutions and the solar month.

  • The solar month is One-twelfth of a solar or tropical year.
  • The lunar month is the period of a complete revolution of the moon around the earth.
  • The synodic month is the period between successive new moons equal to 29.531 days.
  • The sidereal month is the period between successive conjunctions with a star equal to 27.322 days.
  • Anomalistic month is the period between successive perigees, equal to 27.555 days.
  • Nodical month or draconic month is the period between successive similar nodes equal to 27.212 days.
  • The Bhaganas relate to the sidereal revolutions of the celestial objects in a Mahayuga.

Abhyankar writes that the Mahayuga of 4.32 x 106 years was found to be adequate for expressing the bhaganas for the short period phenomena in integral numbers. But the slow moving nodes of the planetary orbits required a larger time span. This necessitated the introduction of Kalpa of 4.32 x 109) years equal to 1000 Mahayugas. However, Aryabhata considered both of them as mathematical artifacts for simplifying astronomical computations. He did not associate them with the creation and evolution of the universe as envisaged in the Puranas.

It is well known that the Babylonians were far ahead in astronomical calculations than the Greeks who received the knowledge from the Babylonians. Abhyankar says that the Babylonians had 44528/3600 synodic lunar months in one year arrived at after involved and cumbersome calculations. It is pointed out that what Aryabhata did was to calculate these synodic lunar months in terms of the Mahayuga, which comes to 53433600 synodic lunar months in a Mahayuga. Abhyankar says that by adding 43,20,000 solar bhaganas we get sidereal lunar months in a Mahayuga. Aryabhata gives the value of 53433336 and 57753336 for them, respectively, which are more accurate as they are based on his observations made in 3600 Kali Era.

Abhyankar further writes that the second concept introduced by Aryabhata is the mean superconjunction of all planets at some remote epoch in time. This notion arose from the fact that the periods of synodic phenomena (opposition, conjunction etc.) can be determined more accurately if the observations are separated by a large number of repeated events. Once the period is fairly well known, the discrepancy in actual position of the distant past event will not give rise to large error in the period, provided we have good observations for the current epoch to get error free position in the vicinity of that epoch. Hence there is no harm in assuming that all planets started from one fixed position in the remote past like the beginning of Mahayuga or Kaliyuga. Consequently astronomers had to depend on new data after a reasonable lapse of time. This was the technique devised by Aryabhata and followed later by Siddhantic astronomers.

It is also argued by some that the Indians learned their astronomy form the Greeks but both Sengupta and Abhyankar show that there was an exchange of ideas between Indian and Babylonian astronomers in the pre-Siddhantic period. For example, the Babylonians took the notion of tithi as a time marker from Vedanga-Jyotish while the Indians took the planetary periods from the Babylonians. It is likely that Siddhantic methods were developed through this interaction without the Greek intermediaries. The variable size of epicycles found in the Indian system could be reminiscent of the zigzag functions of the Babylonians.


Abhyankar, K.D. 2000. Babylonian Source of Aryabhata's Planetary Constants. Indian Journal of History of Science 35(3):185-188.

Other References:

Neugebauer,O. 1975. A History of Ancient Mathematical Astronomy. Berlin.