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Mercury in a Quantum-Gravitational Field

Paul R. Gerber

A scalar field theory of gravitation yields the correct perihelion precession of Mercury’s orbit around the sun. We present the corresponding theory and numerical calculations for the relativistic Kepler problem. Furthermore, it turns out that the concept of gravitational potential cannot be maintained in the relativistic case because acceleration becomes velocity-dependent. In addition, in extreme cases, like large distances from a gravitational center or for high velocities of a body, the gravitational forces become also dependent on the direction of the body’s velocity.