We know that the Catholic church has a troubled history with the idea of heliocentrism, but when did this history become history? What year would Galileo have gotten away with publishing his book?
In 1632, Galileo and the Catholic Church had a little spat. You may have heard about it. It was partly because he had evidence that contradicted the prevailing geocentric worldview, and partly because, while presenting that evidence, he called the pope a dummy. While it's doubtful that any pope would have warmed to the second offense, few people know when the church changed its opinion on the first offense.
The answer is, 'when it had to,' which turned out to be in 1822. For the centuries beforehand, heliocentrism became a battle ground for different religions and religious factions. As Protestantism and Catholicism battled it out for religious supremacy, whichever religion gave ground on the geocentric model of the universe was accused by the other of turning away from the scriptures. As a result, both stood firm on an immobile Earth.
In schools, things made a bit more progress. For much of the 1700s, people insisted that both models should be taught to students. (Sound familiar?) Once both models were being taught, with both professional and amateur astronomers proliferating, the geocentric model continuously lost ground. It simply didn't support the growing body of data that scientists were accumulating. As astronomers stopped believing in geocentrism, schools stopped teaching it, and it was good and dead, academically, by the 1800s.
So when the Catholic church convened a college of cardinals and let people know that the books about the heliocentric model of the universe would now be "permitted," there was some public amusement. Amazingly, there were still strict Protestant sects that forbade the teaching of the heliocentric model. The dates on which they relented (if they ever did) are unrecorded.