# 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…

## 18 Citations

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## References

SHOWING 1-10 OF 11 REFERENCES

Precise Determination of the Clairaut Constant in Ellipsoidal Geodesy

- Mathematics
- 2007

Abstract The Clairaut constant, the cosine of the maximum latitude of the geodesic, is used in a number of applications in ellipsoidal geodesy. This study provides formulas to precisely determine the…

DIRECT AND INVERSE SOLUTIONS OF GEODESICS

- Physics
- 1963

Abstract : This Technical Report supersedes TR No. 7 entitled: INVERSE COMPUTATION FOR LONG LINES: A NON-ITERATIVE METHOD BASED ON THE TRUE GEODESIC, which is out of print. It contains the material…

New solutions to the direct and indirect geodetic problems on the ellipsoid

- Mathematics
- 2006

Summary Taking advantage of numerical integration solves the direct and indirect geodetic problems on the ellipsoid. In general the solutions are composed of a strict solution for the sphere plus a…

Long geodesics on the ellipsoid

- Mathematics
- 1955

SummaryThis article examines the practical application of formulae for computing long lines on the ellipsoid. The main aim is to eliminate the successive approximation generally required. For the…

Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermessungen

- Mathematics
- 1825

The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is a transcription of F. W. Bessel, Astronomische…

DIRECT AND INVERSE SOLUTIONS OF GEODESICS ON THE ELLIPSOID WITH APPLICATION OF NESTED EQUATIONS

- Mathematics
- 1975

AbstractThis paper gives compact formulae for the direct and inverse solutions of geodesics of any length. Existing formulae have been recast for efficient programming to conserve space and reduce…

2006b, Note on Lars E. Sjöberg: New solutions to the direct and indirect geodetic problems on the ellipsoid, ZfV

- ZfV,
- 2006