Abstract
We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)≡−〈Ekin〉/〈Epot〉.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.
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