Exploring the Mysteries of Babylonian Astronomy with Maple

Modern scholarship asserts that the Babylonians were able to determine the synodic periods (discussed below) of the outer planets with exceptional accuracy. We experimented with a simple Maple mathematical software model to see if we could mathematically re-create the synodic cycles of Mars determined by Babylonian astronomers starting from around 400 BC. We sought first to understand whether unique planetary cycles known as Goal-Year periods which the Babylonians gleaned from centuries of observation were mathematically inevitable. We wanted to determine their accuracy quantitatively and find out if other plausible Goal-Year choices were available to them. The Babylonians also invented a method of using Goal-Years in error-canceling combinations to create long-term ‘exact’ periods that markedly improved the accuracy of their planetary predictions for centuries ahead. We tested whether the mathematical method surmised by scholars made sense in terms of our own program and whether we could replicate it. This paper is a report on the success of those efforts.