What common belief was shared between Ptolemy's and Copernicus's models?

The shared belief between Ptolemy's and Copernicus's models is that uniform circular motion is fundamental to planetary movement. Both astronomers proposed that celestial objects, including planets, move in circular paths at constant speeds. In Ptolemy's geocentric model, planets were thought to move in a series of circular orbits around Earth, while Copernicus, in his heliocentric model, maintained that planets orbit the Sun in circular paths.

This concept was grounded in the ancient understanding of astronomy, where circles were viewed as the perfect shape, thus making circular motion the most logical choice for describing the heavens. It wasn’t until later that Kepler introduced the idea of elliptical orbits to better fit observational data, which departed from the earlier belief in uniform circular motion.