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On The Concept Of Periapsis In Hill’s Problem

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Abstract

The concept of closest approach is analyzed in Hill’s problem, resulting in a partitioning of the position space. The different behavior between the direct and retrograde motion is explained analytically, resulting in a simple estimate of the variation of Hill’s periodic and quasi-circular orbits as a function of the Jacobi constant. The local behavior of the orbits on the zero velocity surfaces and an analytical definition of local escape and capture in Hill’s problem are also given.

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References

  • N.B. Conkwright (1957) Introduction to the Theory of Equations Ginn Boston

    Google Scholar 

  • Gómez, G., Koon, W.S., Lo, M.W., Marsden, I.E., Masdemont, J., and Ross, S.D.: 2001, ‘Invariant manifolds, the spatial three-body problem and space mission design’, the Proceedings of AIAA/AAS Astrodynamics Specialist Meeting, Quebec City, Quebec, Canada, August 2001.

  • M. Hénon (1969) ArticleTitle‘Numerical exploration of the Restricted Problem. V. Hill’s case: Periodic Orbits and Their Stability’ Astr. Astrophys 1 223–238

    Google Scholar 

  • M. Hénon J.M. Petit (1986) ArticleTitleSeries expansions for encounter-type solutions of Hill’s problem Celest. Mech. Dyn. Astr. 38 IssueID1 67–100 Occurrence Handle10.1007/BF01234287

    Article  Google Scholar 

  • G.W. Hill (1878) ArticleTitle‘Researches in the Lunar theory’ Amer. J. Math 1 5–26 Occurrence HandleMR1505148

    MathSciNet  Google Scholar 

  • V. Szebehely (1967) Theory of Orbits the Restricted Problem of Three Bodies Academic Press, New York

    Google Scholar 

  • Villac, B.F.: 2003, Dynamics in the Hill problem with applications to spacecraft maneuvers, Ph.D thesis, The University of Michigan.

  • B.F. Villac D.J. Scheeres (2003) ArticleTitleEscaping trajectories in the Hill three-body problem and applications J. Guidance Control Dyn. 26 IssueID2 224–232

    Google Scholar 

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Authors and Affiliations

  1. Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI, USA

    B.F. Villac & D.J. Scheeres

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  1. B.F. Villac
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  2. D.J. Scheeres
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Correspondence to B.F. Villac.

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Villac, B., Scheeres, D. On The Concept Of Periapsis In Hill’s Problem. Celestial Mech Dyn Astr 90, 165–178 (2004). https://doi.org/10.1007/s10569-004-0405-9

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  • DOI: https://doi.org/10.1007/s10569-004-0405-9

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