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Journal of Geodesy

, Volume 88, Issue 1, pp 13–29 | Cite as

Analytical computation of gravity effects for polyhedral bodies

  • M. G. D’UrsoEmail author
Original Article

Abstract

On the basis of recent analytical results we derive new formulas for computing the gravity effects of polyhedral bodies which are expressed solely as function of the coordinates of the vertices of the relevant faces. We thus prove that such formulas exhibit no singularity whenever the position of the observation point is not aligned with an edge of a face. In the opposite case, the contribution of the edge to the potential to its first-order derivative and to the diagonal entries of the second-order derivative is deemed to be zero on the basis of some claims which still require a rigorous mathematical proof. In contrast with a common statement in the literature, it is proved that only the off-diagonal entries of the second-order derivative of the potential do exhibit a noneliminable singularity when the observation point is aligned with an edge of a face. The analytical provisions on the range of validity of the derived formulas have been fully confirmed by the Matlab\(^{\textregistered }\) program which has been coded and thoroughly tested by computing the gravity effects induced by real asteroids at arbitrarily placed observation points.

Keywords

Gravitational potential Singularities Polyhedron  Numerical computation 

Notes

Acknowledgments

The author wishes to express his deep gratitude to the Editor-in-Chief, prof. Roland Klees, to the Associate Editor, prof. Christopher Jekeli, and to the three anonymous reviewers for careful suggestions and useful comments which resulted in an improved version of the original manuscript.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.DICeM, Università di Cassino e del Lazio MeridionaleCassinoItaly

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