  The spectral triple approach to noncommutative geometry allows one to develop
the entire standard model (and supersymmetric extensions) of particle physics
from a purely geometry stand point and thus treats both gravity and particle
physics on the same footing. The bosonic sector of the theory contains a
modification to Einstein-Hilbert gravity, involving a nonconformal coupling of
curvature to the Higgs field and conformal Weyl term (in addition to a
nondynamical topological term). In this paper we derive the weak field limit of
this gravitational theory and show that the production and dynamics of
gravitational waves are significantly altered. In particular, we show that the
graviton contains a massive mode that alters the energy lost to gravitational
radiation, in systems with evolving quadrupole moment. We explicitly calculate
the general solution and apply it to systems with periodically varying
quadrupole moments, focusing in particular on the the well know energy loss
formula for circular binaries.
