Post-Newtonian Logarithmic Correction Term Effects in Two-Body Dynamics
We use the logarithmic correction to the gravitational potential as introduced by Mucket and Treder, in order to
study the motion of a secondary celestial body under the influence of the corrected gravitational force of the 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
and for the companion star of the pulsar PSR 1913+16 and 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.