There's a guy named Bob Sungenis and his sidekick Robert Bennett who have some Catholic Apologetics website where they advocate geocentrism. Strictly kooks. Bennett is the "scientist" of the group. Whereas in the past a kook would be ignored by normal people, now every kook can have his own website!! The number of Catholics with an education past fourth grade who believe in geocentrism could be counted on one hand, probably. These guys are like "Pope Michael" and other sedevacantists. Sungenis used to say that the moon landings were a hoax. They cannot be reasoned with. They know the TRUTH, and probably not even God Himself appearing in a cloud and telling them they are idiots would shake their belief in their own infallibility. Basically, Sungenis still has the fundamentalist Protestant mindset:
it's me and my bible.