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

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Abstract

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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References

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Authors and Affiliations

  1. University of Texas, Austin, Texas, U.S.A.

    R. Broucke

  2. Jet Propulsion Laboratory, Pasadena, California, U.S.A.

    H. Lass

Authors
  1. R. Broucke
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  2. H. Lass
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Broucke, R., Lass, H. On Szebehely's equation for the potential of a prescribed family of orbits. Celestial Mechanics 16, 215–225 (1977). https://doi.org/10.1007/BF01228602

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  • DOI: https://doi.org/10.1007/BF01228602

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