Roman Catholic Church does accept heliocentric model of universe. In fact pope John Paul II accepted heliocentric model in april of 1993. He also apologised for many of Churchs wrongdoings including the ones Church did to Galileo Galilei. Even the current pope Benedict XVI praised Galileo's astronomy (see http://news.bbc.co.uk/2/hi/europe/7794668.stm).
There is even an astronomical observatory in Vatican today.
Modern Catholic Church now accepts many scientific theories it rejected before including even evolution which is not the case for protestant denominations.
As you can see the Church is not so conservative towards the science as it used to be and that is largely the credit of John Paul II.
Catholic Church did not accept theories of Galileo, Bruno, Copernicus and others because they thought their model of space is in contradiction with teachings of Bible even thou the Bible says nothing about Earth being center of universe. That is simply some model (Ptolemaic system) previous popes accepted earlier and when pope says something it is almost equivalent as if God has said it because the pope is direct representative of God on Earth.