Relative geocentrism holds to general relativity, so any point in the universe could be made the center. This is not an exciting claim because you could make a fly the center, if you wanted. When you do this, you get terms in the metric equation that only show up when you are in a rotating frame of reference. These terms go away if you go in a non-rotating frame of reference (such as off of the earth). However, if one wanted, one could understand those terms as being weird gravitational forces that appear and disappear depending on your frame of reference; these are usually understood to be fictitious forces, even by general relativists; but I see nothing in the math that prevents us from taking them to be real. This point of view is WEIRD from a physics standpoint, but if there are reasons for preferring the earth frame, then that must be ultimately how it is, and the simpler frames are just simpler for calculation. What is the reason for preferring the earth frame? The basic answer is that this is how God has revealed the universe to us in the Scriptures, but it goes deeper than that, which I wish I would love to explore more at some point.
One should be careful to distinguish from interpretation and working out what statements mean according to scientific theories though. The relative geocentrist position allows us to say that the sun really moves....when we are in the reference frame of the earth, which allows consistency with the Scriptures' statement:
https://www.puritanboard.com/thread...nterpreting-special.78565/page-2#post-1012032
I think John Byl also holds to a relative geocentrism, though I don't recall for sure.
See Sean Caroll's admission (he wrote a famed General Relativity textbook):
https://www.preposterousuniverse.com/blog/2005/10/03/does-the-earth-move-around-the-sun/
See the reference to Weinberg in this thread (actually, the whole discussion I had with MW is very revealing; but unless I misunderstood his appropriation of Mach at one point, it should be noted that Mach's principle has almost decisively been disproven):
https://www.puritanboard.com/threads/another-article-against-geocentrism.90800/page-6
Also, see the article from CMI in the above thread, which makes the distinction
Plenty of googling can be found where relative geocentrism is allowed but absolute is denied by secular scientists.