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A geometric property of Hill's curves

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Abstract

The following is proved in this note: If we construct a circle passing through a given primary in the planar circular restricted three-body problem, center of which is the remaining primary, then the minor arc of this circle with endpoints represented by the triangular libration points represents-when the given primary is excluded-locus of all the points on the Hill's curves that are the least distant points from the given primary.

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Reference

  • Moulton, F. R.: 1902,An Introduction to Celestial Mechanics, The Macmillan Company, New York, Macmillan & Co., Ltd., London.

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  1. Astronomical Institute, Czechoslovak Academy of Sciences, Budečská 6, Vinohrady, 120 23, Praha 2, Czechoslovakia

    Vladimír Matas

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  1. Vladimír Matas
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Matas, V. A geometric property of Hill's curves. Celestial Mechanics 17, 193–194 (1978). https://doi.org/10.1007/BF01371330

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  • DOI: https://doi.org/10.1007/BF01371330

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