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

Robert Tenzer; P. Moore; O. Nesvadba

doi:10.1007/978-3-540-49350-1_60

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

Robert Tenzer, P. Moore, O. Nesvadba

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

3 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 language	English
Title of host publication	Dynamic Planet
Subtitle of host publication	Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools - lAG Symposium
Pages	410-415
Number of pages	6
Volume	130
DOIs	https://doi.org/10.1007/978-3-540-49350-1_60
Publication status	Published - 1 Dec 2007
Externally published	Yes
Event	IAG Symposium on Dynamic Planet: Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools - Cairns, QLD, Australia Duration: 22 Aug 2005 → 26 Aug 2005

Conference

Conference	IAG Symposium on Dynamic Planet: Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools
Country/Territory	Australia
City	Cairns, QLD
Period	22/08/05 → 26/08/05

Keywords

Gravity
Newton's integral
Potential
Tesseroid

ASJC Scopus subject areas

Computers in Earth Sciences
Geophysics

More information

10.1007/978-3-540-49350-1_60

Cite this

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Tenzer, R, Moore, P & Nesvadba, O 2007, Analytical solution of Newton's Integral in terms of polar spherical coordinates. in Dynamic Planet: Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools - lAG Symposium. vol. 130, pp. 410-415, IAG Symposium on Dynamic Planet: Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools, Cairns, QLD, Australia, 22/08/05. https://doi.org/10.1007/978-3-540-49350-1_60

Analytical solution of Newton's Integral in terms of polar spherical coordinates. / Tenzer, Robert; Moore, P.; Nesvadba, O.
Dynamic Planet: Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools - lAG Symposium. Vol. 130 2007. p. 410-415.

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

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

Abstract

Conference

Keywords

ASJC Scopus subject areas

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