On gravitational orbits and the virial theorem

Abstract

We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)≡−〈E _kin〉/〈E _pot〉.R is calculated as a function of the eccentricity (e) and of the energy (E). Whent→∞, independently ofe andE, R→1/2 for closed orbits (this clearly illustrates the fulfillment of the virial theorem in classical mechanics); whereasR≧1, at any time, for open orbits.