Equating the Sun: Geometry, Models, and Practical Computing in Greek Astronomy

Summary

Introduction

Ancient Greek planetary theory was geometrical in spirit. Each planet was deemed to ride on a circle, or combination of circles. Greek planetary theory, conceived in this way, originated late in the third century B.C. with the work of Apollonios of Perga. At first, such theories offered only a broad explanation of planetary phenomena: each planet generally travels eastward around the zodiac, but occasionally reverses direction and travels in retrograde motion toward the west for a few weeks or months (depending on the planet), before reverting to its normal eastward motion. Apollonius's geometrical models were under-girded by Aristotle's philosophy of nature, which postulated the centrality of the Earth and the primacy of circular motion for celestial bodies.

In the middle of the second century b.c., Hipparchos, who had been strongly influenced by his contact with quantitative Babylonian astronomy, insisted on the importance of having geometrical theories that also reproduce the phenomena in a quantitative sense. But Hipparchos was able to achieve this only for the Sun and the Moon. The Greek theory of the planets was brought into its final, very successful form by Ptolemy only in the second century a.d. Now it became possible to calculate positions for the planets (as well as the Sun and Moon) from geometrical models based on circular motion. Thus, by Ptolemy's day, Greek planetary theory offered not merely a broad, explanatory view of how the universe works: it also provided a tool for practical, predictive calculation of planetary phenomena. Moreover, Ptolemy's planetary theories are usually pretty accurate.