  We show that the time-dependent Doppler effect should induce measureable
deviations of the time history of the projected orbit of a star around the
supermassive black hole in the Galactic center (SgrA*) from the expected
Keplerian history. In particular, the line-of-sight acceleration of the star
generates apparent acceleration of its image along its velocity vector on the
sky, even if its actual Keplerian acceleration in this direction vanishes. The
excess apparent acceleration simply results from the transformation of time
between the reference frames of the observer and the star. Although the excess
acceleration averages to zero over a full closed orbit, it could lead to
systematic offsets of a few percent in estimates of the dynamical mass or
position of the black hole that rely on partially sampled orbits with
pericentric distances of ~100AU. Deviations of this magnitude from apparent
Keplerian dynamics of known stars should be detectable by future observations.
