Journal of Geodesy

, Volume 91, Issue 3, pp 307–328 | Cite as

The solid angle hidden in polyhedron gravitation formulations

  • Robert A. Werner
Original Article


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.


Gravitational potential Polyhedron Solid angle Prism singularity Gore 

Supplementary material


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.PasadenaUSA

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