Advertisement

New Expressions of the Gravitational Potential and Its Derivatives for the Prism

  • Maria Grazia D’Urso
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 137)

Abstract

We present novel expressions for the gravitational potential and its first derivative induced by a prism, having a constant mass density, at an observation point coincident with a prism vertex. They are obtained as a special case of more general formulas which can be derived for an arbitrary homogeneous polyhedron. Remarkably, the expressions presented in the paper entail a reduced computational burden with respect to alternative ones reported in the specialized literature.

Keywords

Newtonian gravitational field First-order gradient Right rectangular parallelepiped Prism 

References

  1. Banerjee B, DasGupta SP (1977) Gravitational attraction of a rectangular parallelepiped. Geophys 42:1053–1055CrossRefGoogle Scholar
  2. D’Urso MG, Russo P (2002) A new algorithm for point-in polygon tests. Surv Rev 36–284:410–422CrossRefGoogle Scholar
  3. Kellogg OD (1929) Foundations of potential theory. Springer, BerlinGoogle Scholar
  4. MacMillan WD (1930) Theoretical mechanics, vol. 2: the theory of the potential. Mc-Graw-Hill, New YorkGoogle Scholar
  5. Nagy D (1966) The gravitational attraction of a right rectangular prism. Geophys 31:362–371CrossRefGoogle Scholar
  6. Nagy D, Papp G, Benedek J (2000) The gravitational potential and its derivatives for the prism. J Geodesy 74:553–560CrossRefGoogle Scholar
  7. Petrović S (1996) Determination of the potential of homogeneous polyhedral bodies using line integrals. J Geodesy 71:44–52CrossRefGoogle Scholar
  8. Tang KT (2006) Mathematical methods for engineers and scientists. Springer, BerlinGoogle Scholar
  9. Tsoulis D (1999) Analytical and numerical methods in gravity field modelling of ideal and real masses. Deutsche Geodätische Kommission, Reihe C, Heft Nr. 510, MünchenGoogle Scholar
  10. Tsoulis D (2000) A note on the gravitational field of the right rectangular prism. Bollettino di Geodesia e Scienze Affini, LIX-1:21–35Google Scholar
  11. Tsoulis D, Petrović S (2001) On the singularities of the gravity field of a homogeneous polyhedral body. Geophys 66:535–539CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Di.M.S.A.T. - Università di CassinoCassinoItaly

Personalised recommendations