Hamiltonian equations of the planetary Nbody problem in the postNewtonian approximation
Abstract
The canonical equations in the planetary problem of N bodies having a spherical symmetry in the postNewtonian approximation of the general relativity theory are obtained. It is ascertained that the influence of the rotational motion of planets in the solar system on the translational one has the same order as the primary components of relativistic effects. The influence of the postNewtonian term in the Hamiltonian function on the secular changes of the orbital elements is considered. The relativistic correction is shown to have a value and an analytical structure such that it is possible to apply the KAM theory conclusions on the existence of nearlyperiodic solutions of the planetary Nbody problem quite as much in the postNewtonian case as in the classical one.
 Publication:

Astronomicheskii Zhurnal
 Pub Date:
 April 1986
 Bibcode:
 1986AZh....63..371K
 Keywords:

 Approximation;
 Celestial Mechanics;
 Hamiltonian Functions;
 Many Body Problem;
 Newton Theory;
 Planetary Rotation;
 Relativity;
 Solar System;
 Translational Motion;
 Astrophysics