The geocentric model required the addition of several epicycle adjustments with no observable cause. Re-framing the local system with the sun at the center eliminated most of the epicycles.

(... and the remaining errors in the heliocentric model relative to the observed motion led to the discovery of the moons and, eventually, Newton's gravitational theory. The driving function, overall, is simplification of the model by removing special cases and the need for acausal "I don't know why; this is what we observe" rules).