A new description of gravitational motion will be proposed. It is part of the proper time formulation of physics as presented on the IARD 2000 conference. According to this formulation the proper time of an object is taken as its fourth coordinate. As a consequence, one obtains a circular space–time diagram where distances are measured with the Euclidean metric. The relativistic factor turns out to be of simple goniometric origin. It further follows that the Lagrangian for gravitational dynamics does not require an interpretation in terms of curvature of space–time. The flat space model for gravitational dynamics leads to the correct predictions for the bending of light, the perihelion shift of Mercury and gravitational red-shift. The new theory is free of singularities. More important, the new formulation of gravitational dynamics restores the validity of the principle of addition of potentials. One therefore can find solutions for static gravitational configurations for which it is difficult to find the solution of the corresponding Einstein equations. The method will be illustrated by means of the orbital precession for non-spherical stellar mass distributions. In case of the bipole mass distribution the agreement with the predictions of the general theory of relativity is very striking. Nevertheless, the new model is far more simple.
Keywordsrelativity gravitation Euclidean space–time orbital precession
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