On gravitational orbits and the virial theorem
Abstract
We emphasize the sharp distinctions between different onebody 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.
 Publication:

Celestial Mechanics
 Pub Date:
 December 1988
 DOI:
 10.1007/BF01245760
 Bibcode:
 1988CeMec..45..395B