Kepler's problem in Einstein's relativistic theories of gravitation. I - Special relativity: Scalar theories

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Einstein Equations, Gravitation Theory, Kepler Laws, Relativity, Computational Astrophysics, Planetary Mass, Planetary Rotation, Relativistic Theory

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Kepler's problem is first analyzed in the framework of special relativity. In this framework the problem is analyzed by making two different assumptions: (1) that the gravitational mass of the planet is constant or (2) that this mass is equal to the relativistic inertial mass. In both cases the models considered predict the rotation of the perihelion of planets. The same problem is then analyzed in the framework of Einstein's scalar theories worked out by Einstein between 1907 and 1911. In this manner, the quantitative result can be improved.

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