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Accurate Harmonic Series for Inverse and Direct Solutions for the Great Ellipse

Published online by Cambridge University Press:  07 June 2011

Michael A. Earle
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Abstract

In this paper, formulae drawn from the discipline of map projections are applied to provide simple and accurate solutions for the Inverse and Direct problems on the Great Ellipse. Distance along the meridional arc of the spheroid as a function of geodetic latitude is defined in terms of an elliptic integral which will be replaced here with a compact harmonic series approximation possessing simplicity and high accuracy. Latitude as a function of distance along the meridional arc will also be obtained via another equally simple inversion series that also possesses high accuracy. When these two series are applied with their constants modified to suit the section ellipse, they will be shown to provide accurate solutions to the inverse and direct navigation problems pertaining to the Great Ellipse, and thereby provide a complete solution that is also simple to implement.

Keywords

NavigationGreat EllipseGreat CircleInversion
Type
Research Article
Information
The Journal of Navigation , Volume 64 , Issue 3 , July 2011 , pp. 557 - 570
Copyright
Copyright © The Royal Institute of Navigation 2011

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References

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