Some good references on this silliness:
Dealing with Creationism in Astronomy: Biblical GeocentrismGeocentrism Debunked
I've had quite a few conversations with geocentrists, and not a one has been able to do any of the math. They are great at saying "according to relativity, X must be true"; but when someone else or I do that math it turns out that X is false. This has been especially true when discussing the role of relativity in GPS. Alas, most of it is gone with the Theology Web crash. But I remember most of it.
Especially I remember Bob Bennet's alleged answer to the issue of "Ether Wind" in relation to the Foucalt pendulum and the fact that rockets launched towards the East get a speed boost. He said there were two ether winds; one electromagnetic blowing wets to east and one inertial blowing west-east. The inertial wind accounts for the rocket, the electromagnetic wind accounts for the pendulum by differences in the wind force between when the pendulum is at the north half of its swing and when it's at the south half of its swing (what happens when the pendulum is swinging in the east-west plane?). (Some geocentrists think that the electromagnet used to keep a Foucalt pendulum swinging is an integral part of the apparatus.) Obviously those are very select winds. It's hard to believe that someone with an earned PhD in physics could actually say something so stupid, but it was secondhand.
Some especially interesting takedowns of geocentrists other than GPS are:
Geocentrism: Flunking the Lagrange Point ChallengeSungenis Followers Double Down
I'd love to have a substantive discussion with someone, but it's pretty unlikely that's going to happen here.