Did or did not the RCC accept and build on Aquinas's geocentric cosmology?
Let me be blunt, Petronius. You don't know what you are talking about. That's not an insult. It's simply a fact. You throw around phrases like Aquinas's cosmology. If by cosmology you mean the Ptolemaic view of the universe, then the answer is no, because that was a scientific theory and no doctrinal or dogmatic Church statement ever enshrined the Ptolemaic or Newtonian scientific theories as dogma--for the simple reason that science and philosophy/theology do different things.
If by Aquinas's cosmology you meant belief that God created the heavens and the earth and actively sustained them, then the Church of course dogmatically asserts that--but Ptolemy and Aristotle wouldn't have touched that with a ten-foot pole and Aquinas knew that and dealt extensively with the differences between Christian belief in creation and ancient Greek belief in the eternal existence of the universe etc.
Your assumption that Aquinas was taken in by a "false" cosmology and that the Church foollishly endorsed it shows that you don't know the first thing either about the philosophy of science or theology or how the two both relate and differ from each other.
The Ptolemaic theory was the best theory anyone had come up with based on the data they had. It was as "true" as any scientific explanatory model ever is. All scientific theories or explanatory models are by their very nature temporary, ripe for revision--unlike eternal truths of philosophy and theology. The Church did not endorse the Ptolemaic model because the Church does not do science in her doctrinal teaching. Most Christians before Copernicus accepted the Ptolemaic model of explanation because it was the one that made the most sense. The time of transition between reigning scientific paradigms is always a time of controversy and confusion. The Galileo case and the debate over the shift from Ptolemy to Copernicus/Kepler would have been just another scientific debate if scientists and philosophers on both sides of the issue had not been foolish--Galileo in claiming philosophical implications for the scientific theory he had embraced that were not within the province of science and Galileo's opponents (many of whom were scientists who were also philosophers and theologians) who likewise did not keep the proper distinctions between the two forms of knowledge clear. But give them a break--it was a time of momentous philosophical and scientific change and it would be surprising if no confusion between theology, philosophy, and science had taken place.
In disciplining Galileo the Church was making a disciplinary action, not a dogmatic doctrinal teaching. And the officials erred in some aspects of their discipline of Galileo, even as he erred in some aspects of his behavior toward the Church. That is what the JPII commision findings essentially boil down to. There was a miscarriage of justice, not a miscarriage of doctrine.
Yet, in the courts of the Papal States and the Roman Inquisition at that time you received a far fairer trial, had more opportunity to know the accusations against you and defend yourself than you had in any of the courts of the kings of Europe of that day. In England there was the Star Chamber court where you had no rights whatever and the Carthusian martyrs under Henry VIII were left to starve to death without even a trial of any sort. Philip II of Spain, the Swedes, and so on down the line were far more arbitrary and unjust in their legal systems and failure to provide due process than the Papal States were at the time. That is the consensus of a wide variety of secular historians of the Inquisition: Henry Kamen, John Tedeschi, Edward Peters. Yet it is only right to say, as the JPII commission did, that Galileo was the victim of injustice in his trial. Scientists and anti-Christian philosophers who embrace scientism have used the Galileo case to make philosophical and theological points for which it is not relevant. And by employing it the way you have employed it, you too are blurring the boundaries between scientific knowledge (always temporary, based on always increasing, changing data that eventually forces a paradigm shift in explanatory models) and theological and philosophical knowledge that has to do with "perennial things," eternal truths.
And it also suggests that you get your information about the Catholic Church from modern scientistic sources that have it in for the Catholic Church, have distorted her record on matters of science and faith to support the "big bad Church and poor innocent persecuted scientists" myth, a myth that Protestants have taken a major part in perpetuating because they thought it served their anti-Catholic purposes, not realizing that it turns around to bite them in the form of scientistic attacks on Bible-believing Protestants.
You anti-Catholic, you live with a chip on your shoulder against Catholics, despite all your "let's just be friends" rhetoric, and in this case it has led you to accept some very bad science and very lousy history.