Jacobi's solution for geodesics on a triaxial ellipsoid
Geophysics
2026-02-18 v2 Differential Geometry
Computational Physics
Abstract
On Boxing Day, 1838, Jacobi found a solution to the problem of geodesics on a triaxial ellipsoid, with the course of the geodesic and the distance along it given in terms of one-dimensional integrals. Here, a numerical implementation of this solution is described. This entails accurately evaluating the integrals and solving the resulting coupled system of equations. The inverse problem, finding the shortest path between two points on the ellipsoid, can then be solved using a similar method as for biaxial ellipsoids.
Cite
@article{arxiv.2511.01621,
title = {Jacobi's solution for geodesics on a triaxial ellipsoid},
author = {Charles F. F. Karney},
journal= {arXiv preprint arXiv:2511.01621},
year = {2026}
}
Comments
20 pages, 9 figures. This version fixes typos in two equations and includes some updates to the text. Figures now appear in the HTML version