Comment by rcxdude

The Ptolemaic system was already not particularly favored and was well and truly killed in Gallileo's time (in part by his observations). The competition was Tycho Brahe's model, in which the sun revolves around the earth but the planets revolve around the sun. They for the most part make identical predictions as far as astronomical observations, but Brahe's was very slightly simpler and didn't cause the other objections.