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Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration
KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
2012 (English)In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 2, no 3, 162-171 p.Article in journal (Refereed) Published
Abstract [en]

We derive computational formulas for determining the Clairaut constant, i.e. the cosine of the maximum latitude of the geodesic arc, from two given points on the oblate ellipsoid of revolution. In all cases the Clairaut constant is unique. The inverse geodetic problem on the ellipsoid is to determine the geodesic arc between and the azimuths of the arc at the given points. We present the solution for the fixed Clairaut constant. If the given points are not(nearly) antipodal, each azimuth and location of the geodesic is unique, while for the fixed points in the ”antipodal region”, roughly within 36”.2 from the antipode, there are two geodesics mirrored in the equator and with complementary azimuths at each point. In the special case with the given points located at the poles of the ellipsoid, all meridians are geodesics. The special role played by the Clairaut constant and the numerical integration make this method different from others available in the literature.

Place, publisher, year, edition, pages
2012. Vol. 2, no 3, 162-171 p.
Keyword [en]
clairaut constant, geodesic, inverse geodetic problem
National Category
Other Engineering and Technologies not elsewhere specified
URN: urn:nbn:se:kth:diva-166676DOI: 10.2478/v10156-011-0037-4OAI: diva2:811796

QC 20150513

Available from: 2015-05-13 Created: 2015-05-13 Last updated: 2015-05-13Bibliographically approved

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Sjöberg, Lars E.
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