  After a discussion of the properties of degenerate fermion balls, we analyze
the orbits of the stars S0-1 and S0-2, which have the smallest projected
distances to Sgr A*, in the supermassive black hole as well as in the fermion
ball scenarios of the Galactic center. It is shown that both scenarios are
consistent with the data, as measured during the last six years by Genzel et
al. and Ghez et al. The free parameters of the projected orbit of a star are
the unknown components of its velocity v_z and distance z to Sgr A* in 1995.4,
with the z-axis being in the line of sight. We show, in the case of S0-1 and
S0-2, that the z-v_z phase-space which fits the data, is much larger for the
fermion ball than for the black hole scenario. Future measurements of the
positions or radial velocities of S0-1 and S0-2 could reduce this allowed
phase-space and eventually rule out one of the currently acceptable scenarios.
This may shed some light into the nature of the supermassive compact dark
object, or dark matter in general at the center of our Galaxy.
