Parametrized post-Newtonian equations of motion of N mass monopoles with the SEP violation

Abstract

Post-Newtonian equations of motion of a system of $N$ mass monopoles in the framework of the PPN formalism with two parameters $\beta$ and $\gamma$ are derived for the case when the Strong Equivalence Principle can be violated. The derivation is based on the previously published general framework. The multipole moments of each body are defined as a PPN-generalization of the corresponding Blanchet-Damour multiple moments in a relevant local reference system defined for that body. The classical ten integrals of the derived equations of motion are given. A special version of the equations of motion, for which seven of these integrals are exact, is discussed. The derived equations of motion can be used to test the Strong Equivalence Principle in various solar system experiments.