Both Copernicus heliocentric and the Ptolemaic models agreed on the need for epicycles. These were miniature orbits that the celestial bodies travelled on as well as their normal orbits.
Copernicus still invigaed the bodies orbiting in perfect circles and had to put these in to explain some of the movements of the planets. This may have contributed to his ideas being largely dismissed as it was just as complicated as the already established model. It was not until Kepler proposed elliptical orbits was this problem resolved.

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