  We study the motion of a secondary celestial body under the influence of the
corrected gravitational force of a primary. We study the effect of quantum and
relativistic corrections to the gravitational potential of a primary body
acting on the orbiting body. More specifically, two equations are derived to
approximate the perigee/perihelion/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 quantum as well as
post- Newtonian accelerations. Numerical results have been obtained for the
artificial Earth satellite Molnya, Mercury, and, finally, the for the HW Vir c,
planetary companion.
