Velocity-dependent inverse cubic force and solar system gravity tests

Higher mass dimension terms in an effective field theory framework for tests of spacetime symmetries are studied. Using a post-Newtonian expansion method, we derive the spacetime metric and the equations of motion for a binary system. This reveals an effective inverse cubic force correction to post-Newtonian general relativity that depends on the velocity of the bodies in the system. The results are studied in the context of laboratory and space-based tests including the effects on solar-system ephemeris, laser ranging observations, and gravimeter tests. This work reveals the coefficient combinations for mass dimension 5 operators controlling $CPT$ violation for gravity that can be measured using analysis from these tests. Other tests including light propagation can be used to probe these coefficients. Sensitivity estimates are provided and the results are contrasted with the minimal mass dimension 4 terms in the gravity sector.