ИСТИНА

In this study, the idea of a single Gaussian elliptical ring on a circular two-dimensional ring, or in the limit – a continuous disk is generalized. Such ring (here the R-ring) may be consists of identical Keplerian elliptic orbits, of fixed and , uniformly portioned on azimuth angle, or/and filled with orbits that precess around central star or black hole. The special method of radial averaging mass of moving bodies is developed. We compute for this wide annulus the surface density, 2D and 3D potentials, the mutual gravitational energy and the rotational energy. The surface density has two sharp peaks at the edges of the R-ring and deep internal minimum. Newtonian potential of the R-ring is carefully studied and the spatial equipotential surfaces are calculated. The force of attraction at the edges of the R-ring strives for infinity, and in cavity the circular orbits don't exist. The R-rings naturally can be formed in systems of bodies with a big central mass and to play there dynamical role. The model is applied to the assessment of some properties of the clockwise disk in the center of Galaxy. For relation of the rotational energy to the module of mutual gravitational energy we found The R-ring model offers an explanation of an riddle of existence of sharp local minima on the rotation curves, which are observed in many flat galaxies. We discuss the physical sources of apsidal precession, and of the associated timescales. Found the relations of timescales of apsidal precession from the SMBH and the NSC for cases orbits inside and out of the cluster. Apsidal precession rate of stars can largely be determined not relativistic effect from the black hole, and the Newtonian gravitational influence of a densest stellar cluster around the SMBH.