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Using post-Newtonian equations of motion for fluid bodies valid to the secondpost-Newtonian order, we derive the equations of motion for binary systems withfinite-sized, non-spinning but arbitrarily shaped bodies. In particular westudy the contributions of the internal structure of the bodies (such asself-gravity) that would diverge if the size of the bodies were to shrink tozero. Using a set of virial relations accurate to the first post-Newtonianorder that reflect the stationarity of each body, and redefining the masses toinclude 1PN and 2PN self-gravity terms, we demonstrate the completecancellation of a class of potentially divergent, structure-dependent termsthat scale as s^{-1} and s^{-5/2}, where s is the characteristic size of thebodies. This is further evidence of the Strong Equivalence Principle, andsupports the use of post-Newtonian approximations to derive equations of motionfor strong-field bodies such as neutron stars and black holes. This extendsearlier work done by Kopeikin.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Post-Newtonian gravitational radiation and equations of motion via  direct integration of the relaxed Einstein equations. V. Evidence for the  strong equivalence principle to second post-Newtonian order