They are equivalent.... as coordinate systems.
Gravity on the other hand dictates that the small mass of the Earth is in orbit around the many orders of magnitude larger mass of the Sun.
Why do you continue to deny that you think God’s words have weighed in on the subject and that you DO NOT think the two are actually equivalent at all - that accepting one means you are putting ‘man’s words above the Word of God’ or some such nonsense?
Again, admitting equivalence as CS admits physical equivalence.
“... it is the main tenet of the Einstein theory that any two ways of looking at the world which are related to each other by a coordinate transformation are entirely equivalent from a physical point of view.... “
Hoyle, Fred. Nicolaus Copernicus. London: Heinemann Educational Books Ltd., 1973.
Again, geokineticists always ignore the mass of the rest of the universe, while geocentrists always include it.
Again, “So why continue to imply that the two systems are not equivalent under GR when the quotes of learned men have been provided to you?”