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.

(2014). Gravity effects of polyhedral bodies with linearly varying density [journal article - articolo]. In CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. Retrieved from http://hdl.handle.net/10446/157817

Gravity effects of polyhedral bodies with linearly varying density

D'Urso, Maria Grazia
2014-01-01

Abstract

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.
articolo
2014
D'Urso, Maria Grazia
(2014). Gravity effects of polyhedral bodies with linearly varying density [journal article - articolo]. In CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. Retrieved from http://hdl.handle.net/10446/157817
File allegato/i alla scheda:
File Dimensione del file Formato  
Celestial Mechanics_published.pdf

Solo gestori di archivio

Versione: publisher's version - versione editoriale
Licenza: Licenza default Aisberg
Dimensione del file 1.31 MB
Formato Adobe PDF
1.31 MB Adobe PDF   Visualizza/Apri
Pubblicazioni consigliate

Aisberg ©2008 Servizi bibliotecari, Università degli studi di Bergamo | Terms of use/Condizioni di utilizzo

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/157817
Citazioni
  • Scopus 59
  • ???jsp.display-item.citation.isi??? 57
social impact