Edit: Since people don't seem to understand my point, there is more to the theories of celestial mechanics than just path prediction. Our understanding of the path mechanics is derived through our understanding of gravity. To believe that the Sun revolves around the Earth one would have to completely upend our theories of gravity, which have been shown by experiment to agree with predictions in almost all cases.
Unfortunately, I never saw the actual derivation, so that idea is basically hearsay.
But the intuitive view referred to in the article is that the sun revolves around the Earth once per day, as observed from Earth. That you cannot make work by fancy maths, without running into conclusions which contradict other observations.
From:
http://en.wikipedia.org/wiki/Hollow_Earth#Concave_hollow_Ear...
In one chapter of his book On the Wild Side (1992), Martin Gardner discusses the hollow Earth model articulated by Abdelkader. According to Gardner, this hypothesis posits that light rays travel in circular paths, and slow as they approach the center of the spherical star-filled cavern. No energy can reach the center of the cavern, which corresponds to no point a finite distance away from Earth in the widely accepted scientific cosmology. A drill, Gardner says, would lengthen as it traveled away from the cavern and eventually pass through the "point at infinity" corresponding to the center of the Earth in the widely accepted scientific cosmology. Supposedly no experiment can distinguish between the two cosmologies.