What are the dimensions of Cathedral Terra?
The non-existence of a fact is hard to demonstrate, but I believe this to be the case. I have searched for quite a while and still, the most precise measurement I could find was the mention in Wikia which says:


  The Super Galaxy Gurren Lagann is under half the size of Earth.


It should be possible to calculate a more precise size using the known size of Earth and the visible arc of it in this picture with the relation to Cathedral Terra: