Some years ago I participated in a summer seminar at Yale on "The
Mathematical Sciences in Antiquity," with Prof. Asger Aaboe. If my memory
serves me correctly, he spoke about Ptolemy's late writing moving in the
direction of treating his geocentric picture as a representation of
reality, complete with specific values for the various circle radii and
including the requirement that no two planetary domains would overlap,
thereby excluding the possiibiility of collisions, etc.
Sorry, but I have no references handy at the moment.
Howard Van Till