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