Geodetic Line at Constant Altitude above the Ellipsoid

Details Geodetic Line at Constant Altitude above the Ellipsoid Geodetic Line at Constant Altitude above the Ellipsoid

2007-11-05

arxiv.org/abs/0711.0642v3

Mathematics

Metric Geometry

29 pages, 3 PostScript figures. Corrected eq (78). Added Java program

Scientific paper

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.

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