On the dynamics of the relativistic restricted three-body problem.

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Celestial Mechanics, Relativity

Scientific paper

The equations of motion for the relativistic restricted three-body problem are derived using the post-Newtonian approximation of relativity. It turns out that they obey the same symmetry relations as the classical eqations and that they depend - as second parameter besides the mass ratio μ - on (M)/(R), on the ratio of the total mass of the system and the separation of the primaries. This parameter (M)/(R) is thus a kind of measure for the role of relativistic effects in the system (the classical case is (M)/(R)=0). Finally, the model is applied to the computation of the advance of Mercury's perihelion in the Solar system and leads to results compatible with published data.

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