Two-body motion in the post-Newtonian approximation.

Details Two-body motion in the post-Newtonian approximation. Two-body motion in the post-Newtonian approximation.

Mar 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cemec..43..193r&link_type=abstract

Celestial Mechanics, Volume 43, Issue 1-4, pp. 193-210

Physics

Two-Body Problem

Scientific paper

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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