Celestial mechanics

, Volume 32, Issue 2, pp 109–126 | Cite as

High-order resonances in the restricted three-body problem

  • A. Lemaître


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.


Phase Space Critical Area Body Problem Resonance Model Resonance Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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. Google Scholar
  4. Henrard, J. and Lemaître, A.: 1983b, ‘A Simple Mechanism of Formation for the Kirkwood's Gaps’, submitted for publication toIcarus.Google Scholar
  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.Google Scholar
  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.Google Scholar
  9. Schubart, J.: 1966, ‘Special Cases of the Restricted Problem of Three Bodies’,IAU Symp. 25, 187.Google Scholar

Copyright information

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • A. Lemaître
    • 1
  1. 1.Department of MathematicsFNDPNamurBelgium

Personalised recommendations