Before Newton proposed his theory of gravitation, a model of planetary motion proposed by Descartes was widely accepted. In Descartes' model the planets were caught in and dragged along by a whirlpool of ether particles centered around the Sun. Newton showed that this vortex scheme contradicted observations because: (a) the speed of an ether particle in the vortex varies inversely as its distance from the Sun; (b) the period of revolution of such a particle varies directly as the square of its distance from the Sun; and (c) this result contradicts Kepler's third law. Prove (a), (b), and (c).
							
Before Newton proposed his theory of gravitation, a model of planetary motion proposed by  Descartes was widely accepted. In Descartes' model the planets were caught in and dragged along by a whirlpool of ether particles centered around the Sun. Newton showed that this vortex scheme contradicted observations because: (a) the speed of an ether particle in the vortex varies inversely as its distance from the Sun; (b) the period of revolution of such a particle varies directly as the square of its distance from the Sun; and (c) this result contradicts Kepler's third law. Prove (a), (b), and (c).