Paper Title
Post-Newtonian Anomalistic Period Effects of Celestial Bodies due to a Gravitational Law with a Mucket-Treder Correction Term

Abstract
We use a logarithmic correction to the gravitational potential as introduced by Mücket and Treder (1977), in order to study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We derive two equations to approximate the periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period) under the influence of the non-Newtonian radial acceleration. In a kinematic sense, this influence produces apsidal motion. We performed numerical estimations for Mercury, for the companion star of the pulsar PSR 1913+16 and, also, the extra-solar planet b orbiting the star HD 80606 in the constellation of Ursa Major. We also considered the case of the artificial Earth satellite GRACE-A, but the results present a low degree of reliability from a practical standpoint. Keywords - Logarithmic Potential, Gauss’ Planetary Equations, Periastron Time, Anomalistic Period, Keplerian Period.