On Szebehely's equation for the potential of a prescribed family of orbits

Details On Szebehely's equation for the potential of a prescribed family of orbits On Szebehely's equation for the potential of a prescribed family of orbits

Oct 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16..215b&link_type=abstract

Celestial Mechanics, vol. 16, Oct. 1977, p. 215-225.

Physics

41

Orbital Mechanics, Partial Differential Equations, Circular Orbits, Field Theory (Physics), Orbit Calculation

Scientific paper

In the present note we first give a simple proof of the Dainelli formulas for the force field generating a given family of orbits. We also show that the Szebehely partial differential equation for the potential can be derived from the Dainelli formulas if the energy integral is assumed. The Szebehely equation can be solved directly with the method of characteristics or indirectly with the Joukovsky formulas. Several examples are briefly described in the article. In particular we find some rather general potential functions corresponding to circular motion.

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