Relativistic perturbations of planetary orbits in the threeparameter generalized Schwarzschild metric  The case of Mercury
Abstract
Analytical formulas are presented for relativistic perturbations of planetary orbits in the generalized threeparameter Schwarzschild metric, and a semianalytic Newtonian solution combined with the present relativistic corrections for the orbital motion of Mercury is compared with results of numerical integrations. The Lagrangian corresponding to the generalized threeparameter Schwarzschild metric in the first postNewtonian approximation is used to construct a firstorder analytical solution for the postNewtonian corrections to the Newtonian solutions for the orbital motions of the planets in terms of the osculating orbital elements. Comparisons of the Newtonian semianalytical solution of Bretagnon (1980) corrected by the present formulas with the numerical solutions of Oesterwinter and Cohen (1972) and the DE 102 solution of Newhall (1980) are then used to propose new integration constants for the orbit of Mercury fit to the respective numerical orbits.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 July 1981
 Bibcode:
 1981A&A...100..143L
 Keywords:

 Mercury (Planet);
 Orbit Perturbation;
 Orbital Mechanics;
 Relativity;
 Schwarzschild Metric;
 Solar Orbits;
 EulerLagrange Equation;
 Numerical Integration;
 Orbital Elements;
 Astronomy