Show mathematically how Kepler’s third law can be derived from Newton’s law of universal gravitation. Hint: use the centripetal force (force directed towards the center) which is equal to the gravitational force in orbital motion.

Show mathematically how Kepler’s third law can be derived from Newton’s law of universal gravitation. Hint: use the centripetal force (force directed towards the center) which is equal to the gravitational force in orbital motion.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter10: Motion In A Noninertial Reference Frame

Section: Chapter Questions

Problem 10.20P: Calculate the effective gravitational field vector g at Earths surface at the poles and the equator....

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Question

Show mathematically how Kepler’s third law can be derived from Newton’s law of universal gravitation. Hint: use the centripetal force (force directed towards the center) which is equal to the gravitational force in orbital motion.

Definition Definition Force on a body along the radial direction. Centripetal force is responsible for the circular motion of a body. The magnitude of centripetal force is given by F C = m v 2 r m = mass of the body in the circular motion v = tangential velocity of the body r = radius of the circular path

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