Relativistic perturbations of planetary orbits in the three-parameter generalized Schwarzschild metric - The case of Mercury

Details Relativistic perturbations of planetary orbits in the three-parameter generalized Schwarzschild metric - The case of Mercury Relativistic perturbations of planetary orbits in the three-parameter generalized Schwarzschild metric - The case of Mercury

Jul 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981a%26a...100..143l&link_type=abstract

Astronomy and Astrophysics, vol. 100, no. 1, July 1981, p. 143-155. In French.

Astronomy and Astrophysics

Astrophysics

6

Mercury (Planet), Orbit Perturbation, Orbital Mechanics, Relativity, Schwarzschild Metric, Solar Orbits, Euler-Lagrange Equation, Numerical Integration, Orbital Elements

Scientific paper

Analytical formulas are presented for relativistic perturbations of planetary orbits in the generalized three-parameter 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 three-parameter Schwarzschild metric in the first post-Newtonian approximation is used to construct a first-order analytical solution for the post-Newtonian 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.

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