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It didn't, at first. Copernicus was no better at predicting the exact position of the planets relative to Earth than was Ptolemy. This was because Copernicus was still relying on circular, uniform motion. Only when Kepler threw out circles for Ellipses with varying speeds did the predictions work.

Still, this was too subtle and mathematical for many Geocentric believers. The nail in the coffin was Gaileo's telescope, which showed "flaws" in the moon's surface, other moons orbiting Jupiter (not Earth), and Venus having phases that could only be explained by a sun-centered orbit.

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