# The solid angle hidden in polyhedron gravitation formulations

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## Abstract

Formulas of a homogeneous polyhedron’s gravitational potential typically include two arctangent terms for every edge of every face and a special term to eliminate a possible facial singularity. However, the arctangent and singularity terms are equivalent to the face’s solid angle viewed from the field point. A face’s solid angle can be evaluated with a single arctangent, saving computation.

## Keywords

Gravitational potential Polyhedron Solid angle Prism singularity Gore## Supplementary material

## References

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