The conflict between geocentrism and heliocentrism with regards to the solar system goes back to Nicholas Copernicus around 1514 A.D. This was not out of any religious conflict but out of conflict with intellectuals of his day that insisted on Aristotle’s geocentric system. To some degree this conflict still continues today as there are some who still strongly hold to an absolute geocentric model.
The irony is that there is no need for any kind of conflict because under General Relativity both models are actually just a choice of a frame of reference. In other words there is no actual conflict between the two, each one is just a result of a choice of coordinate systems.
The only reason there is any degree of controversy or ever has been the insistence on the false notion of absolute motion or an absolute frame of reference. Once you eliminate the need for an absolute frame of reference then any and all conflict between the two goes away.
In conclusion, any conflict between geocentrism and heliocentrism that exists or has ever existed is based entirely on the notion of an absolute frame of reference producing absolute motion. If you are insisting on either geocentrism or heliocentrism you are assuming absolute motion. The reality thanks to General Relativity is that absolute motion does not exist and consequently geocentrism and heliocentrism are nothing but arbitrary choices of a frame of reference from which to look at the solar system.
