New Expressions of the Gravitational Potential and Its Derivatives for the Prism
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.
KeywordsNewtonian gravitational field First-order gradient Right rectangular parallelepiped Prism
- Kellogg OD (1929) Foundations of potential theory. Springer, BerlinGoogle Scholar
- MacMillan WD (1930) Theoretical mechanics, vol. 2: the theory of the potential. Mc-Graw-Hill, New YorkGoogle Scholar
- Tang KT (2006) Mathematical methods for engineers and scientists. Springer, BerlinGoogle Scholar
- 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
- 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