Prospects for the Determination of Star Orbits near the Galactic Center

We simulate the observations of proper motion of stars very close to theGalactic Center. We show that the speckle interferometry done with the Keck IItelescope is accurate enough to obtain orbital parameters for stars with theperiod P about 10 y during 10 seasons of astrometric observations made once ayear. The determination of a single orbit will give central mass estimate withthe typical uncertainty of the existing mass determinations based on velocitydispersion measurements. A much higher precision orbits will be measured inseveral years when Keck Interferometer becomes operational, and fainter starsare discovered even closer to Sgr A*. Astrometry alone will provide accuratedetermination of the ratio: M/D^3, where M is the black hole mass and D is thedistance to the Galactic Center. If spectroscopic orbits of the stars are alsomeasured then both: M and D will be precisely determined.Comment: 13 pages, 5 figures, accepted by Ap