  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.

Metric Geometry