arXiv:1102.1215physics.geo-ph
Geodesics on an ellipsoid of revolution
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Abstract
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems involving geodesics (triangulation, projections, maritime boundaries, and polygonal areas) are investigated.
Indeed, computing the geodesic is not that simple... the geodesics are not even closed in general on Earth. I always just use GeographicLib (https://geographiclib.sourceforge.io/) for this. https://arxiv.org/abs/1102.1215 is a paper by the author on geodesics.
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