On gravitational orbits and the virial theorem

Details On gravitational orbits and the virial theorem On gravitational orbits and the virial theorem

Dec 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988cemec..45..395b&link_type=abstract

Celestial Mechanics, Volume 45, Issue 4, pp.395-400

Physics

Scientific paper

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