## 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.

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.

#### Source:

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.