If Galileo had noted that Mars increased and diminished in size during its orbit, then this could have been a good clue, although perhaps not a proof, that planets orbited the sun. The Church wished him to just say that he only had a hypothesis, not a truth. (Parallax measurements were not yet known.)
The real concern of the Earth not being the center of all was that perhaps Hell was not to be found within the bowels of the no longer so important Earth, as well as the concentric crystalline spheres surrounding it not being so, although this notion was really only proposed by Dante. And, too, for some reason, the notion of the universe being infinite.
It was also a time of challenge from the Protestant reformation and thus the necessary Catholic counter-reformation. Galileo was in the right mind at the wrong time.
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