Bulletin Géodésique (1946-1975)

, Volume 98, Issue 1, pp 341–373

The computation of long geodesics on the ellipsoid by non-series expanding procedure

  • Tsutomu Saito

DOI: 10.1007/BF02522166

Cite this article as:
Saito, T. Bull. Geodesique (1970) 98: 341. doi:10.1007/BF02522166


In this paper the author shows a procedure to settle the computation of very long geodesic lines on the ellipsoid without using the series expansion. The integration of elliptic integrals appearing in the procedure is numerically carried out by means of a mechanical quadrature-the method of Repeated Interval Halving.

The author also devises formulae for the numerical solution of the problem, in order to make the amount of significance error least and determine the kind of quadrant for the computation of inverse trigonometric function.

The anti-podal problem for the direct and inverse solution is rigorously solved by this method.

Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1970

Authors and Affiliations

  • Tsutomu Saito
    • 1
  1. 1.Geographical Survey InstituteTokyo

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