Here is a secular source:
The Church’s ban on reprinting Galileo’s works was lifted in 1718 when permission was granted to publish an edition of his works (excluding the condemned Dialogue) in Florence. In 1741 Pope Benedict XIV authorized the publication of an edition of Galileo’s complete scientific works which included a mildly censored version of the Dialogue. In 1758 the general prohibition against works advocating heliocentrism was removed from the Index of prohibited books, although the specific ban on uncensored versions of the Dialogue and Copernicus’s De Revolutionibus remained. All traces of official opposition to heliocentrism by the Church disappeared in 1835 when these works were finally dropped from the Index.
Pope Urban VIII refused Galileo a stately burial upon his death, though later his bones were interned under a monument at the Church of Santa Croce in Florence. In 1980, Pope John Paul II ordered a re-examination of the evidence against Galileo and formally acquitted him in 1992.
en.wikipedia.org/wiki/Catholic_Church_and_science#Galileo_Galilei
Remember, the issues the Church had with Galeleo had a lot more to do with disobedience and disrespect than it did with scientific or astronomical studies. As you can see the Church embraced heliocentrism by 1741.