Advertisement

Temporary Capture into Resonance

  • Jacques Henrard
Part of the NATO ASI Series book series (NSSB, volume 272)

Abstract

It seems likely that some pairs of satellites of Uranus have been temporarily captured into resonance in the past. In order to analyze these temporary captures, one must modify the model constructed for the capture into resonance of the satellites of Jupiter and Saturn. The key factor is the value of the oblateness of Uranus which is smaller than the corresponding value for Jupiter or Saturn. The smaller value allows some overlap of nearby resonances producing chaos and secondary resonances. The secondary resonances are instrumental in dragging the captured orbit back to the chaotic layer surrounding the primary resonance from which it can escape in the regular region outside the resonance.

Keywords

Primary Resonance Tidal Effect Secondary Resonance Regular Region Orbital Resonance 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dermott, S.F.: 1984,”Origin and evolution of the Uranian and Neptunian satellites: some dynamical considerations”, in Uranus and Neptune (J Bergstrahl Ed.), Nasa Conf. Pub. 2330, pp 377–404.Google Scholar
  2. Dermott, S.F., Malhotra, R. and Murray C.D.: 1988, “Dynamics of the Uranian and Saturnian satellite systems: A chaotic route to melting Miranda?” Icarus, 76, 295–334.ADSCrossRefGoogle Scholar
  3. Goldreich, P.: 1965, “An explanation of the frequent occurence of commensurable mean motions in the Solar system”, M.N.R.A.S., 130, 159–181.ADSGoogle Scholar
  4. Henrard, J.: 1982, “Capture into resonance: An extension of the use of the adiabatic invariants”, Celest. Mech, 27, 3–22.MathSciNetADSMATHCrossRefGoogle Scholar
  5. Henrard, J. and Lemaître, A.: 1983, “A second fundamental model for resonance”,Celest Mech., 30, 197–218.ADSMATHCrossRefGoogle Scholar
  6. Henrard, J., and Sato, M.: 1990, “The origin of chaotic behaviour in the Miranda-Umbriel 3/1 resonance”. Celest Mech., submitted.Google Scholar
  7. Lemaître, A.: 1984, “High order resonance in the restricted three body problem”, Celest Mech., 32, 109–126.ADSMATHCrossRefGoogle Scholar
  8. Malhotra, R.: 1990, “Capture probabilities for secondary resonances”. Icarus, in print.Google Scholar
  9. Malhotra, R. and Dermott, S.F.: 1989, “The role of secondary resonances in the orbital history of Miranda”, Icarus, 85, 444–480.ADSCrossRefGoogle Scholar
  10. Peale, S.J.: 1986, “Orbital resonance, unusual configurations and exotic rotation states”, in Satellites (J. Burns and M. Matthews eds.), Univ. of Arizona Press, 159–223.Google Scholar
  11. Tittermore, W.C. and Wisdom, J.: 1988, “Tidal evolution of the Uranian satellites. I. Passage of Ariel and Umbriel through the 5:3 mean-motion commensurability”,Icarus, 74, 172–230.ADSCrossRefGoogle Scholar
  12. Tittermore, W.C. and Wisdom, J.: 1989, “Tidal evolution of the Uranian satellites. II. An explanation of the anomalously high orbital inclination of Miranda”, Icarus, 78, 63–89.ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Jacques Henrard
    • 1
  1. 1.Département de MathématiqueFUNDPNamurBelgique

Personalised recommendations