Post-Newtonian direct and mixed orbital effects due to the oblateness of the central body

Abstract

The orbital dynamics of a test particle moving in the nonspherically symmetric field of a rotating oblate primary is impacted also by certain indirect, mixed effects arising from the interplay of the different Newtonian and post-Newtonian accelerations which induce known direct perturbations. We systematically calculate the indirect gravitoelectromagnetic shifts per orbit of the Keplerian orbital elements of the test particle arising from the crossing among the first even zonal harmonic J2 of the central body and the post-Newtonian static and stationary components of its gravitational field. We also work out the Newtonian shifts per orbit of order [Formula: see text], and the direct post-Newtonian gravitoelectric effects of order J2c-2 arising from the equations of motion. In the case of both the indirect and direct gravitoelectric J2c-2 shifts, our calculation holds for an arbitrary orientation of the symmetry axis of the central body. We yield numerical estimates of their relative magnitudes for systems ranging from Earth's artificial satellites to stars orbiting supermassive black holes. As far as their measurability is concerned, highly elliptical orbital configuration are desirable.