Eclipse Prediction and the Length of the Saros in Babylonian Astronomy

Abstract

The Saros cycle of 223 synodic months played an important role in Late Babylonian astronomy. It was used to predict the dates of future eclipse possibilities together with the times of those eclipses and underpinned the development of mathematical lunar theories. The excess length of the Saros over a whole number of days varies due to solar and lunar anomaly between about 6 and 9 h. We here investigate two functions which model the length of the Saros found in Babylonian sources: a simple zigzag function with an 18-year period presented on the tablet BM 45861 and a function which varies with the month of the year constructed from rules found on the important procedure text TU 11. These functions are shown to model nature very well and to be closely related. We further conclude that these functions are the likely source of the Saros lengths used to calculate the times of predicted eclipses and were probably known by at latest the mid-sixth-century BC. 1. Eclipse Prediction and the Saros Throughout most, perhaps all, of the Late Babylonian period, the basic method of predict- ing eclipses of the sun and moon in Babylonia was based upon the so-called Saros cycle (SC) of 223 synodic months. This method was not restricted to simply identifying dates 1 or more Saroi after a visible eclipse but could be used to identify the dates of all eclipse possibilities (EPs). It almost certainly originated with lunar eclipses and was then applied to solar eclipses. Indeed, it is most likely that all Babylonian eclipse theories—for want of a better term—were developed from lunar eclipse observations and used for predicting lunar eclipses and then applied by analogy to solar eclipses. The method for predicting lunar eclipses itself arises by combining the Saros with the realization that EPs generally occur every 6 months but occasionally after only 5 months. Therefore, if within a Saros of 223 months, there are a eclipses at a 6-month interval and b eclipses at a 5-month in- terval, simple mathematics shows from 6a + 5b = 223 that a = 33 and b = 5. Within a Saros of 223 months, there are therefore 38 EPs, of which 33 are at a 6-month interval and the remaining 5 are at a 5-month interval. Distributing the 5-month intervals as evenly as possible, we obtain five groups of eclipses in which the first eclipse of each group