The Planetary Theory of Ibn al-Shāṭir

A recent paper' has discussed the solar and lunar kinematic models described by the fourteenth-century Damascene astronomer known as Ibn al-Sht the planet is at the terminal point of the last. Thus Ibn al-Shatir abandoned the eccentric orbits and the equants which so strongly characterize the work of Ptolemy. For all the outer planets and Venus the number of component vectors is the same, and the models differ only in the lengths and angular velocities of the components. It is therefore possible to dispose of all four planets together, and this has been done in ? 2 below. The highly eccentric behavior of Mercury demands special treatment, and the model worked out for it is described in the following section, ? 3. The paper referred to above contains the statement that the planetary machinery of Ibn al-Sh&tir is quite different from that of Copernicus. It is now clear that this assertion is valid only to the extent that the universes of the two individuals are geostatic and heliostatic respectively. In all other respects, particularly in the case of Mercury and Venus, the solutions worked out in Copernicus' De revolutionibus2 for corresponding planets show a remarkable similarity to those of our source. In Copernicus' shorter work, the Commentariolus,a generally speaking, the order in which vectors have been inserted varies widely from that utilized by Ibn al-Sh&tir. A comparison of the three sets of models is made in ? 5 below. A reader who is not familiar with the leading concepts of the Ptolemaic planetary theory will find expositions by 0. Neugebauer4 and D. J. Price,5 both readily available.