  It has been recently shown (Munyaneza, Tsiklauri and Viollier 1998) that the
analysis of the orbits of the fast moving stars close to Sgr A$^{*}$ (Eckart
and Genzel 1997) provides a valuable tool to probe the gravitational potential
near the Galactic center. As an example, we present here the results on a
calculation of possible orbits of the star S0-1 in both, the black hole and
degenerate neutrino ball scenarios of the central mass, based on the recent
measurements of stellar proper motions at the Galactic center by Ghez et al.
1998. Taking into account the error bars of their analysis, it is shown that
within a few years time, the orbit of S0-1 may indeed reveal the nature of the
supermassive compact dark object at the Galactic center.
