After a discussion of the properties of degenerate fermion balls , we analyze the orbit of the star S0-1 , which has a projected distance of \sim 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 .
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 , 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 .
This could shed some light on the nature of the supermassive compact dark object , or dark matter in general , at the center of our Galaxy .