  In the weak field and slow motion approximation, the general relativistic
field equations are linearized, resembling those of the electromagnetic theory.
In a way analogous to that of a moving charge generating a magnetic field, a
mass energy current can produce a gravitomagnetic field. In this contribution,
the motion of a secondary celestial body is studied under the influence of the
gravitomagnetic force generated by a spherical primary. More specifically, two
equations are derived 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). Kinematically, this influence
results to an apsidal motion. The aforementioned quantities are numerically
estimated for Mercury, the companion star of the pulsar PSR 1913 plus 16, the
companion planet of the star HD 80606 and the artificial Earth satellite GRACE
A. The case of the artificial Earth satellite GRACE A is also considered, but
the results present a low degree of reliability from a practical standpoint.
