  We use the Effective Field Theory (EFT) framework to compute the mass
quadrupole moment, the equation of motion, and the power loss of inspiralling
compact binaries at the second order in the Post-Newtonian (PN) approximation.
We present expressions for the stress-energy pseudo-tensor components of the
binary system in higher PN orders. The 2PN correction to the mass quadrupole
moment as well as to the acceleration computed in the linearized harmonic gauge
presented here are the ingredients needed for the calculation of the
next-to-next-to leading order radiation reaction force, which will be presented
elsewhere. While this paper reproduces known results, it supplies the building
blocks necessary for future higher order calculations in the EFT methodology.
