First-order post-Newtonian analysis of the relativistic tidal effects for satellite gradiometry and the Mashhoon-Theiss anomaly

With continuous advances in technology, future satellite gradiometry missions will be capable of performing precision relativistic experiments and imposing constraints on modern gravity theories. To this end, the full first-order post-Newtonian tidal tensor under inertially guided and Earth-pointing local frames along post-Newtonian orbits is worked out. The physical picture behind the "Mashhoon-Theiss anomaly" is explained at the post-Newtonian level. The relativistic precession of the local frame with respect to the sidereal frame will produce modulations of Newtonian tidal forces along certain bases, which gives rise to two different kinds of secular tidal tensors. The measurements of the secular tidal force from the frame-dragging effect is also discussed.