Twobody motion in the postNewtonian approximation.
Abstract
The motion of two massive particles is considered within the framework of the first postNewtonian approximation. The system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables. Closedform 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 velocitydependent Legendre transformation. By explicit inversion of this transformation, expressions for the Keplerian elements in the state space are obtained from the Delaunay element solutions.
 Publication:

Celestial Mechanics
 Pub Date:
 January 1988
 DOI:
 10.1007/BF01234566
 Bibcode:
 1988CeMec..43..193R
 Keywords:

 EulerLagrange Equation;
 Gravitational Fields;
 Hamiltonian Functions;
 Particle Mass;
 Two Body Problem;
 Canonical Forms;
 Legendre Functions;
 Newton Theory;
 Astrophysics;
 TwoBody Problem