This is a very insightful comment -- in the sense of making something "click" for me that hadn't done so before. Namely:

After 1610 or so, if one had a decent understanding of astronomy, one accepted that Ptolemy was wrong and that heliocentrism was now not about overthrowing the Greeks' astronomy, but their mechanics

So, thank you.

(Cf. Douglas Knight's comment, which also implies that Galilean relativity was central to the argument.)