Some of it is well documented, other parts are a bit hit and miss. There isn't enough documentation on what happened with Copernicus (who was studying to become a priest at one stage), but it's generally believed that during his life when he raised his theories the church didn't care much. It wasn't until long after Copernicus was dead and his theories started raising scientific schools that the church acted against it and attempted to ban his work. The major one being Galileo who was tried for Herasy because he studied Copernicus theory and talked about heliocentricity which the Catholic Church didn't like and until this day they still refuse to apologise for imprisoning Galileo and effectively killing him for studying science. Although some church leaders have hinted that what the church did was wrong.
One other interesting facts in the context of it. Even though people would have you believe that the church believed the earth was flat, it's quite the opposite. Since the dawn of the Catholic Church they have always supported the belief that the earth is round. The conjecture was over whether the earth was the centre of the Universe. Based on descriptions in Psalms and Genesis the Catholic Church believed that the Universe revolved around the Earth and to suggest otherwise was considered Heresy (Hence Galileo's incarceration)
