I remember being taught that geocentric models of the solar system had the other planets simply move in very strange-looking paths around the Earth. This model, while messy, I would think isn't actually inaccurate - the models accurately showed the movement of the cosmos if you treat Earth as stationary. While Galileo proposed a cleaner model, with everything in nice elliptical orbits around the sun, why did the church react so dramatically against the idea?
So two quick misconceptions. First, the idea that space is simply a neutral expanse is a notion that developed in the early modern period, the earth's centrality played a specific and important role in ancient and medieval cosmology. (I wrote a post discussing the development of this idea here.)
Secondly, Galileo's model didn't have elliptical orbits, that was Kepler.
Anyways, you may be interested in some previous answers, by /u/link0007, /u/restricteddata and myself, related to Galileo: 1, 2, 3.