  The rate of gravitational-wave energy loss from inspiralling binary systems
of compact objects of arbitrary mass is derived through second post-Newtonian
(2PN) order $O[(Gm/rc^2)^2]$ beyond the quadrupole approximation. The result
has been derived by two independent calculations of the (source) multipole
moments. The 2PN terms, and in particular the finite mass contribution therein
(which cannot be obtained in perturbation calculations of black hole
spacetimes), are shown to make a significant contribution to the accumulated
phase of theoretical templates to be used in matched filtering of the data from
future gravitational-wave detectors.
