Aryabhata's amazing astronomical calculations

Aryabhata was born in the year 476 and died in the year 550. And how do we know that? He himself writes in his books about his age and the year he was born. During his lifetime he accomplished much in the field of mathematics and astronomy. His main works were two books - Aryasiddhantam and Aryabhatiyam. Both of them were books in astronomy with the explanation and derivation of mathematics needed to do his calculations. Of them, Aryabhatiyam is the only surviving book from this 5th-century astronomer and mathematician. He was all of 23 years old when he wrote Aryabhatiyam.

In the book, which is a compendium of mathematics and advanced astronomy, he deals with many interesting concepts in geometry, trigonometry, quadratic equations, sums-of-power series and continued fractions among many other subjects. He may have been the first to predict the irrationality of the value of Pi, much before European mathematician Lambert who proved it in 1761.

In the field of astronomy, his genius was no small either. He postulated that the earth was spinning on its own axis and so were the planets in relation to the sun. Though he did not explicitly state the heliocentric theory - that all planets revolve around the sun - many believe all his work on the motions of planets were with a basic assumption that the sun was at the centre of our solar system.

And here is the interesting part. In a simple shloka in his book Aryabhatiya, he presented profound information for those who care to look. In the translated version of his book by William Eugene Clark, Professor of Sanskrit at Harvard University (The University of Chicago Press, 1930) you can find the following translated shloka:

"In a yuga 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 364,224, of Mars 2,296,824 . . . " (page 9).

It is just amazing just to think he not only said all celestial bodies were revolving on their axis, he was able to almost accurately write down the number of times major celestial bodies were revolving, including the Sun. As it can be seen for a quick check that Aryabhata wrote 1,582,237,500 rotations of the Earth equal 57,753,336 lunar orbits. That is a ratio of 27.396… - an extremely accurate figure for the days the moon takes to revolve around the Earth.