  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.
