I think that first sentence which includes the phrase "which appeared to attack Pope Urban VIII and thus alienated him and the Jesuits, who had both supported Galileo up until this point" is important and gives a much better setting to the account than is often given, so thank you for that, Sandman.

Now Ptolemy is much misunderstood as well, in my opinion. It is often said that he had an earth-centric model, which is true, but that does not mean he thought the earth was at the centre of the Universe. His writing suggests he understood that movements were relative, and that mathematically speaking whether the Earth or the Sun is taken as the centre has no effect of the 'answers', but it does have a big effect on how hard getting to those answers might be.   But he was not really interested in the question of where the planets were in any absolute sense, because he did understood relative movement. The question he wanted to answer was where the planets were when seen from Earth, because that is where we see them from.   It was really useful to those studying the skies to have information about where the planets would 'appear in the sky' and so forth. It is the usefulness of the model that drove it, much more than a search for whether the Sun moved round the Earth or vice versa.

It is worth reminding ourselves that our language is earth centric, not heliocentric. We talk of sunrise, sunset, the sun being high in the sky, high noon, and many many others: all earth centric.   Describing 'sunrise' with a heliocentric language is clumsy at best and would hardly make good literature. (Saying 'dawn' is really just a synonym for sunrise, so that is not what I mean be describing it in a sun-centred way.)

Even scientifically, I would hazard a guess that when planning a network of GPS or communication satellites the designers use an earth-centric frame of reference, not a sun centred one. "Fitness for the purpose" should be what leads you to selecting a particular model, not a belief that a particular one is 'right.'