13. Kern E. Kenyon, Kepler's Laws Deduced from a Force Balance

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Volume 7: Pages 464-467, 1994

Kepler's Laws Deduced from a Force Balance

Kern E. Kenyon 1

14632 North Lane, Del Mar, California 920144134 U.S.A.

Kepler's three laws are derived from a force balance without the assistance of either conservation of angular momentum or energy. The force balance occurs for a mass that orbits a much larger mass under the universal law of gravitation. It takes place in the plane of the orbit and in the direction perpendicular to the orbit; the outward centrifugal force balances the inward gravitational force component normal to the orbit. Kepler's first and second laws come directly and together from the force balance equation after introducing a few mathematical (mainly geometrical) relations. Then the force balance is integrated once, from which Kepler's third law is easily obtained with the help of the same mathematical relations and the assumption that the integration constant is zero.

Keywords: Kepler's laws, planetary motion, force balance, centrifugal force

Received: November 4, 1993; Published Online: December 15, 2008