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Two-body motion in the post-Newtonian approximation

  • Long Term Evolution of Planetary Systems
  • Session on General Dynamical Systems
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Abstract

The motion of two massive particles is considered within the framework of the first post-Newtonian approximation. The system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables. Closed-form solutions for the Delaunay elements in the phase space are obtained. The bridge between the phase space and the state space of the Lagrangian of the motion is provided by a velocity-dependent Legendre transformation. By explicit inversion of this transformation, expressions for the Keplerian elements in the state space are obtained from the Delaunay element solutions.

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Authors and Affiliations

  1. Dept. of Aerospace Engineering, University of Cincinnati, 45221, Cincinnati, OH, USA

    D. L. Richardson & T. J. Kelly

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  1. D. L. Richardson
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  2. T. J. Kelly
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Richardson, D.L., Kelly, T.J. Two-body motion in the post-Newtonian approximation. Celestial Mechanics 43, 193–210 (1987). https://doi.org/10.1007/BF01234566

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  • DOI: https://doi.org/10.1007/BF01234566

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