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arXiv · 1009.4324

Gravitational potential of a homogeneous circular torus: new approach

Elena Yu. Bannikova·Victor G. Vakulik·Valery M. Shulga
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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.

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Elena Yu. Bannikova, Victor G. Vakulik, Valery M. Shulga. 2010-09-22. Gravitational potential of a homogeneous circular torus: new approach. https://doi.org/10.1111/j.1365-2966.2010.17700.x

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