An integral for geodesic length

Craig M. Rollins

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Historical Geography and Cartography Mathematics and Applications Geodetic Measurements and Engineering Structures

Abstract

Using a change of variable suggested by P. D. Thomas (1952), the arclength of a segment of a geodesic curve on an ellipsoid becomes an integral having the same form as arclength on an ellipse, a simpler problem. This leads to a succinct theoretical solution to the Direct and Indirect Problems of geodesics. With modern mathematical software, it is also a practical solution.

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References

1991Geometric Geodesy Part I 2007Precise Determination of the Clairaut Constant in Ellipsoidal Geodesy

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2017Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid 2011The Direct and Indirect Problem for Loxodromes 2010A fourth order solution for geodesics on ellipsoids of revolution

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