On the Origin of the Anomalous Precession of Mercury’s Perihelion

Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post–Newtonian physics. As a result, the differential equations of motion in Newtonian physics are replaced by functional differential equations, where the delay associated with the finite propagation speed is taken into account. Newtonian equations of motion, with post–Newtonian corrections, are often used to approximate the functional differential equations. In [12] a simple atomic model based on a functional differential equation which reproduces the quantized Bohr atomic model was presented. The unique assumption was that the electrodynamic interaction has a finite propagation speed. In [13] a simple gravitational model based on a functional differential equation which gives a gravitational quantification and an explanation of the modified Titius–Bode law is described. Firstly, in this work, we recall the calculations made by Einstein to arrive at the explanation of the anomalous precession of Mercury’s perihelion. Secondly, we recover an ancient work of Gerber in 1898 as a precursor of the retarded theories, see [9]. In this paper Gerber gave an explanation of the anomalous precession of the Mercury’s perihelion in terms of a velocity–dependent potential. In this paper an explanation of the anomalous precession of Mercury’s perihelion is given in terms of a simple retarded potential, which, at first order, coincides with Gerber’s potential, and which agrees with the author’s previous works [12, 13].