Analytical solution of Newton's Integral in terms of polar spherical coordinates

Robert Tenzer, P. Moore, O. Nesvadba

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

2 Citations (Scopus)

Abstract

In association with precise modelling of the Earth's gravity field, analytical integration can be used as an alternative to numerical integration, particularly for the intermediate neighbourhood of the computation point. Accordingly, closed analytical formulae for the gravitational potential and attraction are derived after expressing Newton's integral in terms of polar spherical coordinates. As the elemental volume for the integration element is defined by finite changes of the polar spherical coordinates, the actual mass density distribution is discretized so that each integration element is represented by a constant value of density.
Original languageEnglish
Title of host publicationDynamic Planet
Subtitle of host publicationMonitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools - lAG Symposium
Pages410-415
Number of pages6
Volume130
DOIs
Publication statusPublished - 1 Dec 2007
Externally publishedYes
EventIAG Symposium on Dynamic Planet: Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools - Cairns, QLD, Australia
Duration: 22 Aug 200526 Aug 2005

Conference

ConferenceIAG Symposium on Dynamic Planet: Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools
CountryAustralia
CityCairns, QLD
Period22/08/0526/08/05

Keywords

  • Gravity
  • Newton's integral
  • Potential
  • Tesseroid

ASJC Scopus subject areas

  • Computers in Earth Sciences
  • Geophysics

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