  We report here on a calculation of possible orbits of the fast moving
infrared source S1 which has been recently observed by Eckart and Genzel (1997)
near the Galactic center. It is shown that tracking of the orbit of S1 or any
other fast moving star near Sgr A^* offers a possibility of distinguishing
between the supermassive black hole and extended object scenarios of Sgr A^*.
In our calculations we assumed that the extended object at the Galactic center
is a non-baryonic ball made of degenerate, self-gravitating heavy neutrino
matter, as it has been recently proposed by Tsiklauri & Viollier (1998a,b).
