While The Institute for Creation Research doesn't take a position in favor of geocentrism, they do have this to say regarding the science involved:
Is anyone able to disprove the claim that geocrentrism is possibly true, due to Einstein’s theory of relativity? I don't believe it is important either way, but it's worth thinking about.
What does modern science say about geocentricity?
The theory of special relativity holds as a basic assumption that the speed of light will always be the same everywhere in the universe irrespective of the relative motion of the source of the light and the observer. The ability of special relativity to successfully explain many non-intuitive physical phenomena which are manifested by atomic particles when moving at speeds greater than about one-tenth the speed of light seems to corroborate this assumption. Thus, the failure of the Michelson-Morley experiment (and all other experiments of similar intent) to detect any motion of the earth through space is understood by modern science in terms of relativity rather than geocentricity.
Einstein's theory of general relativity adds further to the debate. It asserts that it is impossible for a human observer to determine whether any material body is in a state of absolute rest (i.e., immobile in space). It claims that only motion of two material bodies relative to one another can be physically detected. According to this theory the geocentric and heliocentric viewpoints are equally valid representations of reality, and it makes no sense whatsoever scientifically to speak of one as being true and the other false. This shift in emphasis from an either-or argument to a synthesis and acceptance of both viewpoints is summed up by the well-known astronomer, Fred Hoyle, as follows:
The relation of the two pictures [geocentricity and heliocentricity] is reduced to a mere coordinate transformation and 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.... Today we cannot say that the Copernican theory is 'right' and the Ptolemaic theory 'wrong' in any meaningful physical sense.[1]
http://www.icr.org/article/382/
Is anyone able to disprove the claim that geocrentrism is possibly true, due to Einstein’s theory of relativity? I don't believe it is important either way, but it's worth thinking about.