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Spherical Hyperbolae and Ellipses

Published online by Cambridge University Press:  23 November 2009

H. C. Freiesleben
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Abstract

Dr. Freiesleben, an Honorary Member of this Institute, discusses the geometry of ellipses and hyperbolae on the sphere. These are the curves which correspond to position lines based on the constant sum or difference of distances from two fixed points. Originally applied to astronomical position lines they now have a wider application to electronic fixing systems of global coverage like Omega.

Information

Type
Research Article
Information
The Journal of Navigation , Volume 29 , Issue 2 , April 1976 , pp. 194 - 199
Copyright
Copyright © The Royal Institute of Navigation 1976

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References

REFERENCES

1Freiesleben, H. C. (1948). Die standlinien in der navigation. Deutsche Hydrographische Zeitschrift I, 178—201.CrossRefGoogle Scholar
2Hydrographic Department of the Admiralty (1950). Professional Paper No. 9: An elementary account of hyperbolic lattice computations, London.Google Scholar
3Pierce, J. A. (1948). Loran, Radio Laboratory Series, Vol. 4, Mass. Institute of Technology, New York, Toronto, London.Google Scholar
4Ballarin, S. (1950). Geometric properties of position lines in hyperbolic navigation. Hydrographic Review, 27, II, 31—57.Google Scholar
5Wirtz, C. (1902). Uber eine neue 'kiummfreie' astronomische Standlinie. Archiv der Deutschcn Seewarte, 25, Nr. 2.Google Scholar