Gravitational potential of a homogeneous circular torus: new approach
Abstract
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.
Keywords
Cite
@article{arxiv.1009.4324,
title = {Gravitational potential of a homogeneous circular torus: new approach},
author = {Elena Yu. Bannikova and Victor G. Vakulik and Valery M. Shulga},
journal= {arXiv preprint arXiv:1009.4324},
year = {2015}
}
Comments
10 pages, 9 figures, 1 table; some misprints in formulae were corrected