In the Planetary Hypotheses, Ptolemy summarizes the planetary models that he discusses in great detail in the Almagest, but he changes the mean motions to account for more prolonged comparison of observations. He gives the mean motions in two different forms: first, in terms of ‘simple, unmixed’ periods and next, in terms of ‘particular, complex’ periods, which are approximations to linear combinations of the simple periods. As a consequence, all of the epoch values for the Moon and the planets are (...) different at era Philip. This is in part a consequence of the changes in the mean motions and in part due to changes in Ptolemy’s time in the anomaly, but not the longitude or latitude, of the Moon, the mean longitude of Saturn and Jupiter, but not Mars, and the anomaly of Venus and Mercury, the former a large change, the latter a small one. The pattern of parameter changes we see suggests that the analyses that yielded the Planetary Hypotheses parameters were not the elegant trio analyses of the Almagest but some sort of serial determinations of the parameters based on sequences of independent observations. (shrink)

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. (shrink)