2007/11/05 by Richard J. Mathar, Mathar, Richard J.
Social Sciences · #53A05 (Secondary) #86A22 (Primary) 86-08 #FOS: Mathematics #Historical Geography and Cartography #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.0711.0642
openalex publication_date 2007/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.