VCAA1: Pingree's Theory Regarding Āryabhaṭa

Pingree maintains that in the late Roman period, the Indian astronomer Aryabhata used a Greek astronomical table based on Ptolemaic calculations to compute parameters for the mean motions of the planets. A planet moves at varying rates in its orbit, but one can define an artificial "average" planet that moves at a steady rate on both its primary cycle and its secondary cycle, if it has one. (Chapter 1 points out that Mercury, Venus, Mars, Jupiter, and Saturn have a secondary cycle, or epicycle.) The motion of this fictitious planet is called mean motion. To define it, two numbers are needed for each cycle: a position at a particular point in time and a rate of uniform motion. These numbers were the parameters needed by Aryabhata.

Pingree proposes that Aryabhata chose noon of March 21, A.D. 499, as the date for his calculations. As Pingree reconstructs it, Aryabhata first used the parameters from an existing Indian astronomical text, the Brahmapaksa, to compute for each planet the whole numbers of revolutions that had already elapsed from the beginning of Kali-yuga to this date.

The Brahmapaksa calculations give not only the whole numbers of revolutions from the start of Kali-yuga, but also fractional parts representing the mean positions of the planets at the chosen date. According to Pingree, Aryabhata knew that these mean positions were wrong. He is convinced that Aryabhata was incapable of making his own observations of mean planetary positions. How then did Aryabhata know that these positions were wrong? Pingree explains that a Greek astronomical table had fallen into Aryabhata's hands, and he had acquired instruction in its use from some person with Greek astronomical knowledge. On the basis of this foreign table, Aryabhata knew the errors in the mean positions computed by his Indian methods, and he desired to correct them in a way that would bring glory to himself and his native India.

Aryabhata's chosen date was exactly 3,600 of his years after the start of Kali-yuga, and he wanted to express his rates of mean motion in Indian style as numbers of revolutions in a yuga cycle, which lasts 4,320,000 years. Since 4,320,000/3,600 is 1,200, all Aryabhata had to do was multiply his total mean motion figures by 1,200 and round them off to integers. (For technical reasons, Aryabhata wanted these integers to be of the form 4n for the seven main planets, and 4n + 2 for Rahu, the ascending node of the moon.)

Pingree maintains that Aryabhata did this and then covered his tracks by neglecting to mention the Greek table in his astronomical writings. He also neglected to mention any of his other Greek source materials. In this way, Aryabhata obtained undying fame as the author of an astronomical system of marvelous accuracy and sophistication.