Anyone who is slightly familiar with Hindu mythology or Hindu cosmology knows that ancient Indians were fond of extremely large time periods. According to traditionalists the war of Mahabharata happened more than 5000 years ago (3102 BCE). A Yuga is supposed to last for 1.08 million years. A Yuga cycle, consisting of 4 Yugas, is 4.32 million years long. Who came up with these numbers ?
The story behind these numbers is quite interesting. Although the word Yuga goes back to Vedic age, Vedic texts do not mention these numbers. The specific numbers were first introduced by Aryabhata, who was born in 476 CE. According to his definition a new Yuga begins whenever all five visible planets along with the Sun and the Moon have zero celestial longitude (we are using the current terminology here, Aryabhata used the word Yugapda to denote a Yuga). The first verse of Aryabhatia, his only surviving work, states the following :
Aryabhatia 1.1 : In a yuga cycle the revolutions of the Sun are 4,320,000, of the Moon 57,753,336, of the Earth eastward 1,582,237,500, of Saturn 146,564, of Jupiter 364224, of Mars 2,296,824, of Mercury and Venus the same as those of the Sun.
The accuracy levels of these estimates are reasonably high, ranging from 99.9 percent (period of Saturn) to 99.999 percent (period of Earth’s rotation). It is possible to get this level of accuracy from 20-30 years of naked eye observations. Not surprisingly, the exact numbers are all wrong. Assuming an error margin of 0.3 degrees for an observation, one needs 3600 years of sky watching to count the exact numbers of revolutions in 1.08 million years. Aryabhata definitely knew this but he also accepted the traditional view that the current Yuga started during the war of Mahabharata (Aryabhatia 1.3). Seven astronomical objects having celestial longitudes close to zero is a very strong condition, and the initial estimates he obtained from 20-30 years of observations were good enough to rule out all years in the past few thousand years except 3102 BCE. So he concluded that the beginning of the current Yuga and Mahabharata war happened in in 3102 BCE.
Aryabhatia 3.10 : When three Yugas and sixty times sixty years had elapsed (from the beginning of the Yuga cycle) then twenty three years of my life had passed.
Since he could directly see the positions of the celestial objects during 499 CE vernal equinox, the assumption that they all had zero longitude in 3102 BCE meant having observations separated by 3600 years. This allowed him to make extremely precise claims about their periods. At the same time he was forced to increase the length of a Yuga to 1.08 million years to ensure that all the celestial objects make complete revolutions.
Why did he come up with the concept of Yuga cycle and how did he know that we are in the fourth Yuga of the current Yuga cycle ? This is related to two abstract points corresponding to apsidal and nodal precession of Moon’s orbit. Aryabhata wanted to include them in the list of celestial objects but his initial estimates showed that their celestial longitudes were closer to -270 degrees and 180 degrees in 3102 BCE. So he introduced a 4.32 million years long Yuga cycle and assumed that we are in the fourth Yuga.
How do we know all these details ? As remarked earlier, Aryabhata’s model was not accurate enough to go 3600 years in the past and detect a Yuga changing moment. However if we calculate the positions during 499 CE equinox using modern technology and apply Aryabhata’s model to go back another 3600 years, then celestial longitudes of the first seven objects become close to zero. The probability of this being a pure coincidence is less than one in a billion. The only logical conclusion is that Aryabhata was born in 476 CE and his definitions and methods were as described above.