I was under the impression that Copernicus definitively established the idea of the heliocentric universe. However:
In Kepler's day three models existed to explain the observed motions of the "wandering stars." However, no clear criteria of physical "truthfulness" existed to discern which of these models corresponded to the actual, physical universe. Each model could be used to predict the future longitude and latitude of planets in the sky for a few years out. All of them became less accurate as time progressed.Copernicus's model was no more accurate than Ptolemy's because he built his system on Ptolemy's 1,500-year old data!
It was Kepler who painstakingly, over the course of 10 years, worked out the orbits and orbital planes of Mars and Earth and thus established a system for accurate measurement of the movements of the planets solar system.
What was the key to Kepler's intellectual rigor? The "difference between the straight and the curved" or the importance of "incommensurable magnitudes." Now, if we assume, "for simplicities sake" that a line is as good as a curve, we might be able to make short-term predictions, but we're going to miss something essential.