The gravitational properties of a torus are investigated. It is shown that a torus can be formed from test particles orbiting in the gravitational field of a central mass. In this case, a toroidal distribution is achieved because of the significant s
pread of inclinations and eccentricities of the orbits. To investigate the self-gravity of the torus we consider the $N$-body problem for a torus located in the gravitational field of a central mass. It is shown that in the equilibrium state the cross-section of the torus is oval with a Gaussian density distribution. The dependence of the obscuring efficiency on torus inclination is found.
The integral expression for gravitational potential of a homogeneous circular torus composed of infinitely thin rings is obtained. Approximate expressions for torus potential in the outer and inner regions are found. In the outer region a torus poten
tial is shown to be approximately equal to that of an infinitely thin ring of the same mass; it is valid up to the surface of the torus. It is shown in a first approximation, that the inner potential of the torus (inside a torus body) is a quadratic function of coordinates. The method of sewing together the inner and outer potentials is proposed. This method provided a continuous approximate solution for the potential and its derivatives, working throughout the region.
