3. Newtonian motion of the S0-2 star
The possible cusp of the dark matter around the supermassive black hole SgrA* in the Galactic center will deviate the Newtonian gravitational potential from the Coulomb type U = -GMBH /r. In result, the gravitationally bound elliptic orbits would be unclosed. As an representative example we consider this effect for the case of the S0 star which was investigated in most details. The parameters of the Kepler orbit of this star: the eccentricity e = 0.883 ± 0.0034, periapsis rp = 0.585 mpc, apsis ra = 9.419 mpc. The orbital period of the S0-2 star is TS0-2 = 16.17 yrs. The corresponding equation of motion of test particles (stars) in the spherically symmetric Newtonian gravitational field