This is a very difficult topic to make any headway in. We are so indoctrinated by the current scientific beliefs that it is nearly impossible to think against them. The concept of a geocentric universe is entirely impossible to understand in the universe we live in. What I mean is that given the way we perceive the world, i.e. the main foundation stones of science, we are logically driven to the conclusions and facts that science presents us with. And those conclusions are proven, given that the intial facts are correct.
For example, Gravity is a pretty fundamental scientific concept that nearly everyone takes for granted as fact. If you believe that matter attracts matter with a force relative to its mass, and that the world is limited to three dimensions, and only a known number of forces play in nature, it is impossible to believe that the large Sun does not swing the small Earth about itself in an orbit.
However, once you stop taking these things for granted the possibilities are only limited by the limitations of the next scientific “foundation stone”. For example, there are alternative theories to Gravity. All of them are laughed at by the scientific community of today. But how do we know that gravity exists and is what we think of it? These are difficult questions to even think about. It is hard to challenge the fundamentals, but they are based only on popular beliefs about un-provable realities. We know that we “stick” to the ground, but we only assume it is due to gravity. It has not been proven; it has only been deemed more likely than its competing theories.
It is not necessary to actually challenge the “fact” of gravity – it would only frustrate you – but any intelligent person will be able to accept that it is only a theory and that it could theoretically be challenged. I am not aware of a Chazal that defines gravity as a real force in this world, either. If gravity is not real, it is possible that we live in a heliocentric universe. I am not saying that we are required to believe that gravity is or is not real – nor am I saying that we are required to believe in a geo/heliocentric universe – I am only saying that since it is NOT defined clearly (by Chazal) what our belief about this should be (nor are we taught any reason to think of this as an important question) we can believe what is popular today if we accept that it is not as solid a belief as scientists would have us think.
Einstein’s theory of relativity cannot be proven. It too, is flawed in that its premise is based on these “foundation stones” of science. Remove the foundation and even the theories that are safely relagated to the top of the ivory towers will fall. We know nothing about our universe.
In summary, our only certainties in this world are what we learn from Torah. But we do not have the abilities to glean all the answers we would like from the Torah. We can satisfy our curiosity with present day science as long as we understand its limitations (which are great). Simply put, do not accord science any more credence than it deserves.