The discrepancy between the Aristotelian and the Ptolemaic astronomies led many medievals to regard the latter (and mathematical astronomy generally) as no more than a calculational device. This was the challenge that Copernicus and Kepler had to meet: How was one to show that a mathematically expressed astronomy could indicate that the earth really moves? Copernicus pointed to features of the planetary motions that he could explain but that Ptolemy could not. Kepler went much further. His account of the planetary system yields a passable theory of why the planets move as they do; the geocentric account (now without the support of carrier spheres) most certainly cannot. The basic hypothesis that the sun is really at the center and the earth really in motion, he claims, is thus likely to be true.
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