Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.

In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer’s frame has an important role. The equations of motion are based on a nonlinear connection modified by the action of an orthogonal tensor which synchronizes the 4-velocities of the considered two bodies. Finally we present periastron shift according to an observer inside the gravitational field, using the orthonormal coordinates. This is different approach than that used in General Relativity where the periastron shift is only given as observed far from the massive bodies.