Precession of Fast S0 Stars in the Vicinity of Supermassive Black Hole in the Galactic Center

We elaborate the model of the influence of the diffuse dark matter, invisible stars or stellar mass black holes on the motion of the observed fast moving S0 stars [1–4] around the supermassive black hole SgrA* in the Galactic center with a mass MBH = 4·106. We will call all this invisible mass as a dark matter. The additional mass perturbs the elliptical orbits of the S0 mass resulting in the so called Newtonian precession of the elliptical orbits. The major aim of our research is the fitting of the published dates on the observed orbital positions of the S0 stars by the theoretically modeling orbit with a power-law profile of the additional (dark matter) mass. Nowadays the observational data provide only the upper limit on the additional mass. In the nearest years the observations of the S0 stars may provide the real weighing of the dark matter inside the orbits of these S0 stars in the Galactic center. This method is a very perspective for the elucidation of the formation and evolution of the dark matter in the Galactic nucleus.