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Non-singular expressions for the vector and gradient tensor of gravitation in a geocentric spherical frame
KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatics (closed 20110301).
2008 (English)In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 34, no 12, 1762-1768 p.Article in journal (Refereed) Published
Abstract [en]

The traditional expressions of the gravitational vector (GV) and gravitational gradient tensor (GGT) have complicated forms depending on the first and second order derivatives of associated Legendre functions (ALF), and also singular terms when approaching the poles. The article presents alternative expressions for the GV and GGT, which are independent of the derivatives, and are also non-singular. By using such expressions, it suffices to compute the ALF to two additional degrees and orders, instead of computing the first and second derivatives of all the ALF.  Therefore the formulas are suitable for computer programming. Matlab software as well as an output of a numerical computation around the North Pole is also presented based on the derived formulas.

Place, publisher, year, edition, pages
2008. Vol. 34, no 12, 1762-1768 p.
Keyword [en]
Non-singularity, Accociated Legendre functions, Normalization
National Category
Earth and Related Environmental Sciences
URN: urn:nbn:se:kth:diva-11513DOI: 10.1016/j.cageo.2008.02.022ISI: 000261632000010ScopusID: 2-s2.0-52049091469OAI: diva2:277448
Project no.63:07:1 funded by the Swedish National Space Board (SNSB)
QC 20100709Available from: 2010-07-09 Created: 2009-11-18 Last updated: 2011-11-09Bibliographically approved

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Eshagh, Mehdi
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