2014MNRAS.442.1755K

In this paper, the idea of a single Gaussian elliptical ring on a circular two-dimensional ring or, in the limit, a continuous disc is generalized. Such a ring (hereafter, the R-ring) can consist of identical Keplerian elliptic orbits, of fixed a and e, uniformly portioned on the azimuth angle, or/and filled with orbits that precess around a central star or black hole. The special method of radially averaging the mass of moving bodies is developed. For this wide annulus, we compute the surface density, the two-dimensional and three-dimensional potentials, the mutual gravitational energy and the rotational energy. The surface density has two sharp peaks at the edges of the R-ring and a deep internal minimum. The 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 do not exist. The R-rings can be formed naturally in systems of bodies with a large central mass and play a dynamical role. The model is applied to the assessment of some properties of the clockwise disc in the centre of the Galaxy. For the relation of the rotational energy to the module of mutual gravitational energy, we found τ ~ 0.29. The R-ring model offers an explanation for the existence of sharp local minima on rotation curves, which are observed in many flat galaxies. We discuss the physical sources of apsidal precession, and of the associated time-scales. We have found the relations of time-scales of apsidal precession from the supermassive black hole and the nuclear star cluster for orbits inside and outside the cluster. The apsidal precession rate of stars can largely be determined not to be a relativistic effect from the black hole and the Newtonian gravitational influence of the densest stellar cluster around the supermassive black hole.