An interesting tangent: At the time of Gallielo, the church used the Tychonian model of the solar system.

In the Tychonian model, the earth is the center and the sun revolves around the earth. But the other planets revolve around the sun! You will notice this is practicallty the same model as the Copernican model except for the arbitrary definition of what is "the center".

The only observable difference was the relation to the firmament which in the Tychonian model revolved around the earth but in the Copernican revolves around the sun. If the Copernican model was correct, some parallax to the stars should be observable. Now we know this is not observable due to the distance to the stars, but this was not known at the time.