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?
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?