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Advanced MechanicsFrom Euler's Determinism to Arnold's Chaos$
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S. G. Rajeev

Print publication date: 2013

Print ISBN-13: 9780199670857

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199670857.001.0001

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The Kepler problem

The Kepler problem

Chapter:
(p.21) 4 The Kepler problem
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0004

The often unstated zero-th law of Kepler is that a planetary orbit lies in a plane. This follows from the conservation of the direction of orbital angular momentum. The next in logical order is the law of areas, saying that the normal component of angular momentum is conserved as well. That the orbits are ellipses is a special feature of the inverse square law force. The third law can be thought of as the inspiration for this hypothesis.

Keywords:   kepler, planetary orbit, law of areas, angular momentum, inverse square law force

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