  Using post-Newtonian equations of motion for fluid bodies valid to the second
post-Newtonian order, we derive the equations of motion for binary systems with
finite-sized, non-spinning but arbitrarily shaped bodies. In particular we
study the contributions of the internal structure of the bodies (such as
self-gravity) that would diverge if the size of the bodies were to shrink to
zero. Using a set of virial relations accurate to the first post-Newtonian
order that reflect the stationarity of each body, and redefining the masses to
include 1PN and 2PN self-gravity terms, we demonstrate the complete
cancellation of a class of potentially divergent, structure-dependent terms
that scale as s^{-1} and s^{-5/2}, where s is the characteristic size of the
bodies. This is further evidence of the Strong Equivalence Principle, and
supports the use of post-Newtonian approximations to derive equations of motion
for strong-field bodies such as neutron stars and black holes. This extends
earlier work done by Kopeikin.
