High-order resonances in the restricted three-body problem

Abstract

This paper consists in analyzing very simple resonance models for the j+i/j (i=2, 3, 4) resonance cases by averaging, truncating and scaling the restricted three body problem. The phase space, the equilibria, the critical areas and the probability of capture are analytically calculated for each case.

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References

  1. Abu-El-Ata, N. and Chapront, J.: 1975,Astron. Astrophys. 30, 57.

    Google Scholar 

  2. Henrard, J.: 1982, ‘Capture Into Resonance: On Extension of the Use of the Adiabatic Invariants’,Celest. Mech. 27, 3.

    Google Scholar 

  3. Henrard, J. and Lemaître, A.: 1983a, ‘A Second Fundamental Model for Resonance’, accepted for publication inCelest. Mech.

  4. Henrard, J. and Lemaître, A.: 1983b, ‘A Simple Mechanism of Formation for the Kirkwood's Gaps’, submitted for publication toIcarus.

  5. Message, P. J.: 1966, ‘On Nearly Commensurable Periods in the Restricted Problem of Three Bodies’,IAU Symp.,25, 197.

    Google Scholar 

  6. Poincaré, J.: 1902, ‘Sur les planètes du type d'Hécube’,Bull. Astron. XIX.

  7. Scholl, H. and Froeschlé, C.: 1976, ‘On the Dynamical Topology in the Kirkwood Gaps’,Astron. Astrophys. 48, 389.

    Google Scholar 

  8. Schubart, J.: 1964, SAO Special Report No. 149.

  9. Schubart, J.: 1966, ‘Special Cases of the Restricted Problem of Three Bodies’,IAU Symp. 25, 187.

    Google Scholar 

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Lemaître, A. High-order resonances in the restricted three-body problem. Celestial Mechanics 32, 109–126 (1984). https://doi.org/10.1007/BF01231119

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Keywords

  • Phase Space
  • Critical Area
  • Body Problem
  • Resonance Model
  • Resonance Case