Episodes from the Early History of Astronomy

sky with the naked eye, unblinkered by received knowledge, but with curiosity and wit. Chapter 1 deals with the arithmetical astronomy of ancient Mesopotamia where astronomy first was made an exact science. Next are treated Greek geometrical models for planetary motion, culminating in Ptolemy's equant models in his Almagest. Ptolemy does not assign them absolute size in this work, but, as is shown here, if we scale the models properly, they will yield good values, not only of the directions to the planets, but of the distances to them, as well. Thus one can immediately find the dimensions of the Copernican System from parameters in the Almagest - we have evidence that Copernicus did just that. Further, Islamic astronomers' modifications of Ptolemy's models by devices using only uniform circular motion are discussed, as are Copernicus's adoption of some of them. finally, it is made precise which bothersome problem was resolved by the heliocentric hypothesis, as it was by the Tychonic arrangement. Next, the Ptolemaic System, the first cosmological scheme to incorporate quantitative models, is described as Ptolemy himself did it in a recenlty recovered passage from his Planetary Hypotheses. Here he does assign absolute size to his models in order to fit them into the snugly nested spherical shells that made up his universe. This much maligned system was, in fact, a harmonious construct that remained the basis for how educated people thought of their world for a millennium and a half. Finally, after a brief review of the geometry of the ellipse, the author gives an elementary derivation of Kepler's equation, and shows how Kepler solved it, and further proves that a planet moves very nearly uniformly around the empty focus of its orbit. Thus an eccentric circular orbit with the empty focus as the equant point gives a good approximation to Kepler motions. The result of combining two such motions is then shown to be close to Ptolemy's planetary model