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We study the motion of a secondary celestial body under the influence of thelogarithmic corrected gravitational force of a primary one. This kind ofcorrection was introduced by Fabris et al. (2009). We derive two equations tocompute the rate of change of the periastron w.r.t. the eccentric anomaly andits total variation over one revolution, In a kinematical sense, this influenceproduces an apsidal motion. We perform numerical estimations for Mercury andfor the companion star of the pulsar PSR 1913+16. We also consider the case ofthe artificial Earth satellite GRACE-A, but the results present a low degree ofreliability from a practical standpoint

Effects in the Anomalistic Period of Celestial Bodies due to a Logarithmic Correction to the Newtonian Gravitational Potential