Gravitational potential of a homogeneous circular torus: new approach

Details Gravitational potential of a homogeneous circular torus: new approach Gravitational potential of a homogeneous circular torus: new approach

2010-09-22

arxiv.org/abs/1009.4324v1

Astronomy and Astrophysics

Astrophysics

Galaxy Astrophysics

10 pages, 9 figures, 1 table, accepted for publication in MNRAS

Scientific paper

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 potential 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.

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