Motion of a testing particle in gravitational field of a ring

Abstract

The planar motion of a testing body in the field of gravity of the massive ring is studied. The "perihelion" precession due to non-relativistic reasons is demonstrated on this simple example of planar motion in the radially symmetric (in the plane of motion) situation. The ring as the source of the gravitational field can serve as the toy model for quasi-planar sources of gravity appearing in the galactic dynamics, etc. The results are used to estimate the real perihelion shift of the planet Mercury due to gravitational quadrupole moment of the Sun.