Plato proposed that the seemingly chaotic wandering motions of the planets could be explained by combinations of uniform circular motions centered on a spherical Earth, apparently a novel idea in the 4th century.
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Eudoxus of Cnidus, who worked with Plato, developed a less mythical, more mathematical explanation of the planets'motion based on Plato's dictum stating that all phenomena in the heavens can be explained with uniform circular motion.
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Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with uniform circular motion.
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This violated one of the fundamental principles of Aristotelian cosmology namely, that the motions of the planets should be explained in terms of uniform circular motion, and was considered a serious defect by many medieval astronomers.
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However, in the years following publication of " de Revolutionibus ", for leading astronomers such as Erasmus Reinhold, the key attraction of Copernicus's ideas was that they reinstated the idea of uniform circular motion for the planets.
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Using these coordinates, the motion along the path is viewed as a succession of circular paths of ever-changing center, and at each position " s " constitutes non-uniform circular motion at that position with radius " ? ".
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For example, the centripetal force exerted " inwards " by a string on a ball in uniform circular motion " sideways " constrains the ball to circular motion restricting its movement away from the center of the circle.
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Whereas Greek astronomers expressed " prejudice in favor of circles or spheres rotating with uniform motion ", such a preference did not exist for Babylonian astronomers, for whom uniform circular motion was never a requirement for planetary orbits.
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Thanks to his examination of the meticulous observations compiled by astronomer Tycho Brahe, Kepler " was the first to understand the nature of the departures from uniform circular motion that had puzzled astronomers since the time of Plato ."
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The equant solved the last major problem of accounting for the anomalistic motion of the planets but was believed by some to compromise the principles of the ancient Greek philosopher / astronomers, namely uniform circular motion about the Earth.
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