Not a physicist so my answer may be totally wrong, but my first _guess_ would be that geocentrism necessitates unequally valid reference frames. You would need

Not a physicist so my answer may be totally wrong, but my first _guess_ would be that geocentrism necessitates unequally valid reference frames. You would need different equations to represent the movements of Venus and Mars relative to Earth as you would need to represent their movements relative to each other. Or at least it certainly seems to me like you would at first guess. Perhaps you could use matrix algebra to apply geocentric laws of motion to all reference frames, and then simply translate them into a reference frame where Earth is the "actual" center of things? But then you're just admitting that Earth isn't the "actual" center of things.