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arXiv · 1202.2893

Spacetime Symmetries and Kepler's Third Law

Alexandre Le Tiec
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Abstract

The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a simple, covariant condition on the norm of the associated helical Killing vector field. This unusual derivation can be used to illustrate some concepts of prime importance in a general relativity course, including those of Killing field, covariance, coordinate dependence, and gravitational redshift.

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Alexandre Le Tiec. 2012-09-14. Spacetime Symmetries and Kepler's Third Law. https://doi.org/10.1088/0264-9381%2F29%2F21%2F217002

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