Sagittarius A*: A supermassive black hole or a spatially extended object?

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