  After discussion of the properties of degenerate fermion balls, we analyze
the orbit of the star S0-1, which has a projected distance of ~5 light-days 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 6 years by Genzel and coworkers and by Ghez
and coworkers. We show 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, which
could be orbiting within such a fermion ball, may reduce this allowed phase
space and eventually rule out one of the currently acceptable scenarios.
