Geodetic Line at Constant Altitude above the Ellipsoid
Abstract
The two-dimensional surface of a bi-axial ellipsoid is characterized by the lengths of its major and minor axes. Longitude and latitude span an angular coordinate system across. We consider the egg-shaped surface of constant altitude above (or below) the ellipsoid surface, and compute the geodetic lines - lines of minimum Euclidean length - within this surface which connect two points of fixed coordinates. This addresses the common "inverse" problem of geodesics generalized to non-zero elevations. The system of differential equations which couples the two angular coordinates along the trajectory is reduced to a single integral, which is handled by Taylor expansion up to fourth power in the eccentricity.
Keywords
Cite
@article{arxiv.0711.0642,
title = {Geodetic Line at Constant Altitude above the Ellipsoid},
author = {Richard J. Mathar},
journal= {arXiv preprint arXiv:0711.0642},
year = {2022}
}
Comments
Version 4: with 4th order Taylor approximation for the predictors in the FEM program