Relativistic effects in proper motions of stars surrounding the Galactic center

We simulate the astrometric observations of stars moving close to the black hole in the Galactic center. We show that for orbits less than or equal to 10(3) AU and position measurements with the accuracy of the Keck Interfero meter, the periastron motion of elliptical orbits will be measurable. The m odels of star trajectories neglecting the periastron motion will be easy to reject with the high confidence level. The measurement of orbital elements and the periastron motion can be effectively used as an independent estima te the distance to the Galactic center. The effects of orbit precession may be visible in some cases. The effects of gravitational radiation are compl etely negligible as well as influence of the black hole rotation on the pro pagation of light.