  Analyses of absorption from disk winds and atmospheres in accreting compact
objects typically treat the central emitting regions in these systems as point
sources relative to the absorber. This assumption breaks down if the absorbing
gas is located within $few \times 1000\cdot GM/{c}^{2}$, in which case a small
component of the absorber's Keplerian motion contributes to the velocity-width
of absorption lines. Here, we demonstrate how this velocity-broadening effect
can be used to constrain the sizes of central engines in accreting compact
objects via a simple geometric relationship, and develop a method for modeling
this effect. We apply this method on the Chandra/HETG spectra of three
ultra-compact and short period neutron star X-ray binaries in which evidence of
gravitationally redshifted absorption, owing to an inner-disk atmosphere, has
recently been reported. The significance of the redshift is above $5\sigma$ for
XTE J1710$-$281 (this work) and 4U 1916$-$053, and is inconsistent with various
estimates of the relative radial velocity of each binary. For our most
sensitive spectrum (XTE J1710$-$281), we obtain a 1$\sigma$ upper bound of 310
$\text{km}$ $\text{s}^{-1}$ on the magnitude of this geometric effect and a
central engine of size ${R}_{CE} < 60 ~ GM/{c}^{2}$ (or, $< 90 ~ GM/{c}^{2}$ at
the $3\sigma$ level). These initial constraints compare favorably to those
obtained via microlensing in quasars and approach the sensitivity of
constraints via relativistic reflection in neutron stars. This sensitivity will
increase with further exposures, as well as the launch of future
microcalorimeter and grating missions.
