"In The Logical Leap, Objectivist physicist and philosopher David Harriman denigrates medieval science. In Chapter 3 "The Mathematical Universe" under the subhead "The Birth of Celestial Physics" on page 85 (ppb), Harriman says that with the Ptolemaic Model, the relative sizes of the orbits of the planets could not be calculated. That leads to an interesting contradiction. If it is true that the Geocentric model prevents such calcuations, then they must have used some other model, because the relative sizes of the orbits were known. On the other hand, perhaps the geometry and observations of the time did, indeed, allow them to make those calculations, even assuming the Geocentric model. My reference for that is Astronomies and Cultures in Early Medieval Europe by Stephen McCluskey (Cambridge, 1998). In fact, because of the religious viewpoint, the very scale of the measurable universe and the comparatively small size of the (spherical; not flat) Earth, were substantiating evidence to the relative unimportance of Earthly affairs. Saturn's orbit was estimated to be 72 million miles from Earth. (McCluskey, page 203)."