The total 2pN net shifts per orbit and the orbital precessions are calculated as the sum of two contributions: the direct ones due to the 2pN acceleration and the mixed, or indirect, ones caused by the 1pN instantaneous shifts during the orbital revolution. A comparison with other approaches existing in the literature is made.

The total 1pN gravitoelectric mass quadrupole orbital precessions of the Keplerian orbital elements are calculated in their full generality for an arbitrary orientation of the primary’s spin axis and a general orbital configuration of the test particle. Both the direct effects, due to the 1pN gravitoelectric mass quadrupole acceleration, and the mixed effects, due to the simultaneous action of the 1pN gravitoelectric mass monopole and Newtonian quadrupole accelerations, are calculated.

The orbital precessions of the Keplerian orbital elements induced by the 1pN gravitomagnetic spin octupole moment of a rigidly rotating oblate spheroid are calculated in their full generality for an arbitrary orientation of the primary’s spin axis and a general orbital configuration of the test particle.