We simulate the astrometric observations of stars moving close to the black hole in the Galactic Center. We show, that for orbits <= 103 AU and position measurements with the accuracy of the Keck Interferometer, the periastron motion of elliptical orbits will be measurable. The models 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 estimate the distance to the Galactic Center. The effects of orbit precession may be visible in some cases. The effects of gravitational radiation are completely negligible as well as the influence of the black hole rotation on the propagation of light.