Ex Cathedra definition that the earth is flat?
Einstien's general theory of relativity is obviously a con. It is best described as magic, not science. Surprisingly though, Newton's theory of gravity is the same way; best described as magic, not science. Finally, the same problem exists with Copernicus; magic not science.
I don't think The Church can base its view of the natural world on magic and retain its legitimacy; it has to base it's views on reason, submitted to divine revelation, in order to maintain its authority.