  A third post-Newtonian (3 PN) equation of motion for an inspiralling binary
consisting of two spherical compact stars with strong internal gravity is
derived under harmonic coordinate condition using the strong field point
particle limit. The equation of motion is complete in a sense that it is
Lorentz invariant in the post-Newtonian perturbative sense, admits conserved
energy of the orbital motion, and is unambiguous, that is, with no undetermined
coefficient. In this paper, we show explicit expressions of the 3 PN equation
of motion and an energy of the binary orbital motion in case of the circular
orbit (neglecting the 2.5 PN radiation reaction effect) and in the center of
the mass frame. It is argued that the 3 PN equation of motion we obtained is
physically unambiguous. Full details will be reported elsewhere.
