# Long geodesics on the ellipsoid

@article{Rainsford1955LongGO, title={Long geodesics on the ellipsoid}, author={Hume F. Rainsford}, journal={Bulletin G{\'e}od{\'e}sique (1946-1975)}, year={1955}, volume={37}, pages={12-22} }

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 inverse problem, this is achieved by the method ofE. M. Sodano, Army Map Service, U.S.A. An adaptation of a method produced byG. T. McCaw is used for the direct problem.Results are given of five practical examples, including two which extend halfway round the world. Construction of further special…

## 24 Citations

Ministry of Overseas Development

- Mathematics
- 2002

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

An Algorithm for the Inverse Solution of Geodesic Sailing without Auxiliary Sphere

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An innovative algorithm to determine the inverse solution of a geodesic with the vertex or Clairaut constant located between two points on a spheroid is presented. This solution to the inverse…

Solving the Direct and Inverse Geodetic Problems on the Ellipsoid by Numerical Integration

- Mathematics
- 2012

Taking advantage of numerical integration, we solve the direct and inverse geodetic problems on the ellipsoid. In general, the solutions are composed of a strict solution for the sphere plus a…

Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula

- Mathematics
- 2005

Vincenty’s (1975) formulas for the direct and inverse geodetic problems (i.e., in relation to the geodesic) have been verified by comparing them with a new formula developed by adapting a…

A rigorous non-iterative procedure for rapid inverse solution of very long geodesics

- Geology
- 1958

The purpose of this paper is to unify, under a single cover, the many theoretical and practical aspects of a rigorous, yet rapid, non-iterative procedure for the inverse solution of very long…

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

- Mathematics
- 1970

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…

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

- Mathematics
- 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…

Numerical determination of the geodesic curves: the solution of a two-point boundary value problem

- Mathematics
- 2018

In this paper, we suggest a simple iterative method to find the geodesic path on a surface parameterized byorthogonal curvilinear system between two given points based on solving Boundary Value…

A Novel Approach to Loxodrome (Rhumb Line), Orthodrome (Great Circle) and Geodesic Line in ECDIS and Navigation in General

- Computer Science
- 2011

The navigation based on geodesic lines and connected software of the ship’s devices (electronic chart, positioning and steering systems) gives a strong argument to research and use geodesIC-based methods for calculations instead of the loxodromic trajectories in general.

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

- MathematicsArXiv
- 2016

It is concluded that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

## References

LONG LINES ON THE EARTH': VARIOUS FORMULAE

- Geology
- 1949

AbstractThe use of radar has already begun to revolutionise the science of surveying. It requires the computation of lines on the earth between a hundred and a thousand miles long for the fixation of…