  We present an analytic frequency-domain gravitational waveform model for an
inspiraling binary whose center-of-mass undergoes a small acceleration, assumed
to be constant during the detection, such as when it orbits a distant tertiary
mass. The center-of-mass acceleration along the line of sight is incorporated
as a new parameter that perturbs the standard TaylorF2 model. We calculate the
wave phase to 3rd post-Newtonian order and first order in the acceleration. It
is shown that acceleration most significantly modifies the wave phase in the
low frequency portion of the signal, so ground-based detectors with a good
sensitivity at low frequencies are the most effective at detecting this effect.
We present a Fisher information calculation to quantify the detectability of
this effect at advanced LIGO A Plus, Cosmic Explorer, and Einstein Telescope
over the mass range of neutron stars and stellar-mass black holes, and discuss
degeneracy between acceleration and other parameters. We also determine the
parameter space where the acceleration is large enough that the wave phase
model would have to be extended to nonlinear orders in the acceleration.
