# Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration

```@inproceedings{Sjberg2012SolutionsTT,
title={Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration},
author={Lars E. Sj{\"o}berg},
year={2012}
}```
Abstract We derive computational formulas for determining the Clairaut constant, i.e. the cosine of the maximum latitude of the geodesic arc, from two given points on the oblate ellipsoid of revolution. In all cases the Clairaut constant is unique. The inverse geodetic problem on the ellipsoid is to determine the geodesic arc between and the azimuths of the arc at the given points. We present the solution for the fixed Clairaut constant. If the given points are not(nearly) antipodal, each…
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