Celestial Mechanics and Dynamical Astronomy

, Volume 120, Issue 4, pp 349–372 | Cite as

Gravity effects of polyhedral bodies with linearly varying density

  • M. G. D’Urso
Original Article


We extend a recent approach for computing the gravity effects of polyhedral bodies with uniform density by the case of bodies with linearly varying density and by consistently taking into account the relevant singularities. We show in particular that the potential and the gravity vector can be given an expression in which singularities are ruled out, thus avoiding the introduction of small positive numbers advocated by some authors in order to circumvent undefined operations. We also prove that the entries of the second derivative exhibit a singularity if and only if the observation point is aligned with an edge of a face of the polyhedron. The formulas presented in the paper have been numerically checked with alternative ones derived on the basis of different approaches, already established in the literature, and intensively tested by computing the gravity effects induced by real asteroids with arbitrarily assigned density variations.


Gravitational potential Gradient Singularities Polyhedra Eros 



The author wishes to express its deep gratitude to the Associate Editor, prof. Erricos C. Pavlis, and to the anonymous reviewers for careful suggestions and useful comments which resulted in an improved version of the original manuscript.

Supplementary material

10569_2014_9578_MOESM1_ESM.pdf (42 kb)
ESM 1 (PDF 43 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

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

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