Apparent Deviations from Keplerian Acceleration for Stars Around the Supermassive Black Hole at the Galactic Center

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.