[antognini]

This is a really good overview. However:

> It actually needed more cycles to explain than the geocentric version of the model!

This part is not true. The main advantage of Copernicus's model was that it reduced the number of epicycles needed. In the Ptolemaic system every planet (except the Moon and Sun) required an epicycle with a period of one year, which we now know was needed in order to account for the relative motion of the Earth on its own orbit. In a heliocentric system these epicycles could be eliminated. Copernicus presented his model more in terms of it requiring fewer calculations.

[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.