In 1623 Galileo publishes The Assayer and this book goes into Galileo's theories about Physics. It is not to be confused with The Dialogues which appears in 1632 and is about astronomy. I cannot find a copy of Assayer on the net.
However, there is a book by Pietro Redondi(non-cath) published by Einstiens Princeton U called Galileo Heretic.
This work is an evaluation of the Assayer's physical theories.
Galileo was an 'atomic materialist' of the kind that originates with Pythagoras--everything can be defined as a number(and they both thought the Sun was stationary). This is sometimes called Quantum Physics--based on a quantity. Senor Einstien was of this type and we all know where he has gotten us.
Aristotle was a 'Qualitative' physicist and although he made an astronmical error, as a physicist he is of much greater value than an enemy of the Catholic Church like Einstien.
At any rate, Galileo Heretic explains that what began to upset the Church was that while The Assayer didn't actually say it in so many words, what was being suggested by Galileo's physical theories conflicted with with the Doctrine Of The Real Presence in the Sacrifice of the Mass. This is one of the first things heretics(Luther, Calvin, Wycliff etc) do. So it appears that the allegation of Galileo's association with Sarpi may be true.
How the book got by Urban VIII is not one of the high points of his Papacy and unless I am mistaken, the Pope had a left leaning reputation until he woke up(he practically collaborated openly with Richelieu in the latters alliance with Gustavus.)
Now it is true that Galileo's condemnation in 1633 is again in astronomical terms, however I believe it to be symbolic and the real problem to be as described by Redondi(while as Catholics, we will of course disagree with a good portion of the conclusions that the author reaches.) It is unique how the physics of Aristotle are compatable with the Mass and those of the others are not.
A couple of quotes:Fr Parsons--Some Lies and Errors of History pg86. "To a tribunal, a denunciation was made that Galileo or his deciples had asserted that God Was an accident, and not a substance, a personal being: that miracles are not miracles at all. Then the Pontiff declared that for the end of the scandal, Galileo should be indicted."
Prof Pastor v29 where he quotes Urban as follows--"Galileo has dared to meddle with matters beyond his competence and with the most important as well as the most dangerous which it is possible to discuss in these days. ..........it was an injury to religion as grievous as ever there was and of a perversion as bad as could be encountered." It sounds to me a little more important than if two rocks in space have an attraction of some sort to each other.
Prof Pastor expresses his wonderment that the Pope is being so harsh on Galileo, but then the former makes no mention at all in his coverage of the Galileo case of anything other than astronomy--albeit the best and most thorough coverage at least on the major points and their relationship to Holy Church.