Greek angles from Babylonian numbers

Abstract

Models of planetary motion as observed from Earth must account for two principal anomalies: the nonuniform speed of the planet as it circles the zodiac, and the correlation of the planet’s position with the position of the Sun. In the context of the geometrical models used by the Greeks, the practical difficulty is to somehow isolate the motion of the epicycle center on the deferent from the motion of the planet on its epicycle. One way to isolate the motion of the epicycle center is to determine the longitude and time of oppositions of the planet with the mean Sun. A Greek astronomer might have realized that the predictions of mean oppositions by Babylonian models could serve as useful proxies for real empirical observations. It is shown that a Greek astronomer with a reasonable understanding of Babylonian System A models for the outer planets and the Sun–Moon could have used those models to estimate approximate values for the eccentricity e and longitude of apogee A required for geometrical models. The same method would work for the inner planets if conjunctions were observable, but they are not, and the variation of the observable synodic events—first and last morning and evening visibilities—is dominated more by the motion of the planet in latitude than the nonuniform motion of the epicycle center.