The 3:1 mean motion resonance between Miranda and the inner Uranian satellites, Cressida and Desdemona

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Abstract

We build a simple dissipative analytical model considering an averaged restricted 3-body problem taking into account the effect of the oblateness of a planet on a small satellite and on its perturber. We apply this model to the inner Uranian system and we follow the dynamical evolution of the satellites Cressida or Desdemona, these latter being close to a 3:1 commensurability with the large satellite Miranda. Our analysis shows that the positions of the two inner satellites, on both sides of the exact resonance, are temporary, Cressida having already crossed the resonance, and Desdemona approaching the commensurability to jump over later on.

Original languageEnglish
Pages (from-to)283-299
Number of pages17
JournalCelestial Mechanics and Dynamical Astronomy
Volume119
Issue number3-4
DOIs
Publication statusPublished - 2014

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Keywords

  • Inner Uranian system
  • Miranda-Cressida-Desdemona
  • Oblateness
  • Restricted 3-body problem

Cite this

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abstract = "We build a simple dissipative analytical model considering an averaged restricted 3-body problem taking into account the effect of the oblateness of a planet on a small satellite and on its perturber. We apply this model to the inner Uranian system and we follow the dynamical evolution of the satellites Cressida or Desdemona, these latter being close to a 3:1 commensurability with the large satellite Miranda. Our analysis shows that the positions of the two inner satellites, on both sides of the exact resonance, are temporary, Cressida having already crossed the resonance, and Desdemona approaching the commensurability to jump over later on.",
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T1 - The 3:1 mean motion resonance between Miranda and the inner Uranian satellites, Cressida and Desdemona

AU - Verheylewegen, Emilie

AU - Lemaitre, Anne

PY - 2014

Y1 - 2014

N2 - We build a simple dissipative analytical model considering an averaged restricted 3-body problem taking into account the effect of the oblateness of a planet on a small satellite and on its perturber. We apply this model to the inner Uranian system and we follow the dynamical evolution of the satellites Cressida or Desdemona, these latter being close to a 3:1 commensurability with the large satellite Miranda. Our analysis shows that the positions of the two inner satellites, on both sides of the exact resonance, are temporary, Cressida having already crossed the resonance, and Desdemona approaching the commensurability to jump over later on.

AB - We build a simple dissipative analytical model considering an averaged restricted 3-body problem taking into account the effect of the oblateness of a planet on a small satellite and on its perturber. We apply this model to the inner Uranian system and we follow the dynamical evolution of the satellites Cressida or Desdemona, these latter being close to a 3:1 commensurability with the large satellite Miranda. Our analysis shows that the positions of the two inner satellites, on both sides of the exact resonance, are temporary, Cressida having already crossed the resonance, and Desdemona approaching the commensurability to jump over later on.

KW - Inner Uranian system

KW - Miranda-Cressida-Desdemona

KW - Oblateness

KW - Restricted 3-body problem

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