Title: A NEW APPROACH TO THE THEORY OF GEODESICS ON AN ELLIPSOID
Author(s): J. S. Holmstrom
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 23, Number 3
Pages: 237 - 244
Cite this article: Holmstrom, J. S., "A NEW APPROACH TO THE THEORY OF GEODESICS ON AN ELLIPSOID", NAVIGATION, Journal of The Institute of Navigation, Vol. 23, No. 3, Fall 1976, pp. 237-244.
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Abstract: The assumption underlying all ground-wave radio navigation work, e.g., LORAN, is that each signal travels from transmitter to receiver along a geodesic of the Earth’s surface. Therefore, accurate estimation of positions and azimuths along geodesics is an important component of radio navigation. Such computations are normally done under the simplifying assumption that the Earth is an oblate spheroid. In this paper, the theory of geodesics is developed for a general ellipsoid with three unequal axes, using cartesian coordinates instead of the customary latitude and longitude. A first-order solution is obtained for the case where the eccentricity of each of the principal cross-sections of the ellipsoid is small. Numerical results obtained for the special case of an ablate spheroid indicate that the first-order solution is sufficiently accurate for most applications involving groundwave radio navigation. The extension of the theory to second- and higher-order solutions, if greater accuracy is desired, is straight-forward.