If I fix the Earth as the center of the solar system, what would this look like? Are there any good images? How complex is this system?
Only for Sun, Earth and Mars, but here's an interactive Flash that illustrates it graphically. Third link from the top "Part I, Equivalence of Hypotheses (Flash)" Note that the planets don't move as you move the mouse over the image, only the circles (the theory) change. http://science.larouchepac.com/kepler/newastronomy/part1/MegaEquivalence.swf for the animation. More generally: http://science.larouchepac.com/kepler/newastronomy/ (And I don't know or care who that LaRouge Pacman is, some rich guy for some reason financed good explanations of what Kepler did, that's what I know about it and that's all very good)
If you move the mouse pointer to the upper left you get the heliocentric system. To the upper right you get the geocentric system. The point is to illustrate how Kepler proved that Ptolemy, Copernicus and Tycho all had the same mathematical model for the solar system. They just used different frames of reference to it, just choosing different fixpoints from where to view it.
Some dots in the illustration represent important points in that ancient model. Some of them are stand-ins for the foci of an ellipse in a model made out of perfect circles. And the Sun was actually not the center of the Copernican model, a point near the Sun was. According to Copernicus the Sun was just a decoration which randomly happened to hang around near the center. Kepler was the first to come up with the thought that maybe there is a relationship between the geometry and the physical existence of stuff. An idea later developed to the theory of gravity by Newton and Einstein, who just added to Kepler's initial formula for describing the movements of the planets.