Spacetime Symmetries and Kepler's Third Law
arXiv:1202.2893 · doi:10.1088/0264-9381/29/21/217002
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.
11 pages, 3 figures; minor changes and text improvements; matches version to appear in Class. Quant. Grav