Galileo was vehemently suspect of heresy. In around 1820 one could read things like "Heliocentrism as now believed is no danger to the faith." Uttered by Pius VII, whom most Catholics (exception the Little Church) took for Pope.
What were the exact stakes that had changed?
1) God's turning the Universe around Earth was by Riccioli denied as a valid proof of God's existence. Riccioli defended God or perhaps rather angels doing that. But to him that - even if done by God - was no proof God existed. Since Epicure was Geocentric but believed Heaven turned around Earth every day by pure chance. Between Riccioli and Pius VII the argument most often associated perhaps with Leibnitz had become the major proof of God's existence, to common culture.
2) Newtonian mechanics had replaced angelic movers.
In Clive Staples Lewis' Perelandra Trilogy, which is Heliocentric, Oyarsa is a word for an angelic being governing the biosphere on Earth, Mars, Venus and having unspecified governing privileges on colder planets like Jupiter and Saturn.
I have studied the author's gleaning activty (if not each source in itself, or even most of them beyond Aquinas) and come to the conclusion that if ever the word ουσιαρχης was used as "one per planet", "angelic being", as CSL or his novel persona concluded about a manuscript of Macrobius where it was misspelled Oyarses, then it meant angelic movers as given in St Thomas Aquinas, more than once.
For a Heliocentric, this concept would seem to have some doctrinal danger. According to him, Earth moves. So, if every planet moving needs an angelic mover, who is that of Earth? I have come across the question "would it be Satan"? And indeed, in the Perelandra Trilogy CSL goes beyond the seeming and does make "the bent Oyarsa" the Oyarsa of Earth.
To a Geocentric, this does very clearly not follow. Earth had no need of one in the first place. If Satan ever was Oyarsa over any planet he moved, he lost that post and got confined to Earth, which does not move.
To CSL, Satan only excluded himself from the cosmic song - which is why the first novel in the series calls, referenced in the title, Earth "the Silent Planet". To a Medieval or Renaissance man, he excluded himself as clearly from the cosmic dance. Earth is the lowest point in univers, not a planet. His domination over Earth - which was meant to be dominated by man - is an usurpation of dominion over man, through the sin of Adam. It is very different from whatever position he could have in relation to any morning star like planet before he fell. On Earth he is clearly not Oyarsa, and its centre is his place of confinement and degradation.
BUT by the time of Pius VII, Newtonian physics was the culture of nearly all the Western World and angelic movers a very forgotten chapter. So, when he said that by then Earth turning around (i e above) the Sun posed no problem for doctrine, he may well have meant that it no longer risked exalting Satan. And it no longer did back then.
Meanwhile, that decision was perhaps a bit hasty. It was also, as being a licence to believe something which nevertheless is untrue if the hitherto believed alternative is the one thing to believe, not an act of magisterial definition. It was pastoral because it was a licence and no definition. This means there may have been an other risk to orthodoxy in Heliocentrism in the Newtonian version. Especially as Riccioli's and Leibnitz' argument for the existence of God is being denied. That other risk would be atheism.
Both directly as in day and night not unequivocally witnessing God is turning Heaven or directing angels turning the Heavens above us. And indirectly, as in giving implications (unforeseen by Pius VII) of very far away stars the light of which would be reaching us after a very long time and thereby implying a universe which is very old. Vastly much older than the history of man as recorded in the Bible. So much that Mark 6:10 becomes hard to understand. So, there was after all a doctrinal problem with Heliocentrism, even as understood by everyone then, unless one is very precise about the "then" part and the "everyone" part so as to exclude what implications have become apparent to the masses only since, though they may have been so to a few specialists already then.
So, we need to avoid one of two propositions, either "Earth moves above the Sun" (or anything implying it!) or "angels move the heavenly bodies that move" (but only not what doesn't move). 1600 years the first of the propositions was avoided, and orthodoxy was fine. 400 years the latter has been very commonly (though not universally I think) forgotten, and that has not really saved the Western World from diverse apostasies and enemies of the Church seeming, oh so credible! Both need not be avoided, only one of them.
Also, the long widely forgotten proposition has not been refuted. When Stephen Tempier condemned "celestial bodies" or "stars" are "animated", probably to agree with De Fide Orthodoxa (which nevertheless says angels direct all our affairs! so St John of Damascus was not attacking angelic movers), he very clearly to those familiar with "intellectual options" of the time avoided condemning angelic movers. Any pretence "angelic movers" have no basis in Scripture as clearly either means that Job 38:7 and a few more are speaking of stars as living (and Jerome was right and John of Damascus wrong among disagreeing saints and Stephen Tempier must be reversed even when St Thomas Aquinas agrees with him, which has not been done) or refuses to see this has been seen as a basis for either of these propositions. Also, Newtonian physics has no basis in Scripture. Not to exclusion of angelic movers at leasts. Wisdom 11:21 (second half of verse)* may have an application to physics (as St Thomas thought, though passage speaks of sth else), but not as in "every cause must be expressible in Newtonian mathematics". Nor as in "angelic movers cannot be accepted as long as there is no Newtonian formula describing how spirit moves matter." These ineptitudes are not what is clearly and unequivocally meant by omnia in mensura, et numero et pondere disposuisti. And what shall we say of those using that to exclude God from doing miracles which they see no Newtonian formula for? The passage is a praise of His Omnipotence!
Hans Georg Lundahl
Nanterre University Library
Feast of Holy Guardian Angels
* Yes, I had to look it up. English translation is thou hast ordered all things in measure, and number, and weight.