Solutions to the direct and inverse navigation problems on the great ellipse
The Great Ellipse ( GE ) is the curve of intersection between the surface and a plane through the center of an ellipsoid. For arcs within a few thousands of kilometres it agrees within a few metres with the geodesic. As the direct and indirect navigation problems for the GE can be solved almost entirely by closed formulas (in contrast to the corresponding geodetic problems of the geodesic), navigation on the GE is mostly preferred. Here we take advantage of the Clairaut constant on the GE in solving the navigation problems.