Non-perturbative investigation of low-eccentricity exterior mean motion resonances

Renu Malhotra, Zherui Chen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel properties in the low-eccentricity regime for interior mean motion resonances of Jupiter in the fundamental model of the circular planar restricted three-body model. Here, we extend the non-perturbative investigation to exterior mean motion resonances in the low-eccentricity regime (up to about 0.1) and for perturber mass in the range of ∼5 × 10−5 to 1 × 10−3 (in units of the central mass). Our results demonstrate that first-order exterior resonances have two branches at low eccentricity as well as low-eccentricity bridges connecting neighbouring first-order resonances. With increasing perturber mass, higher order resonances dissolve into chaos, whereas low-order resonances persist with larger widths in their radial extent but smaller azimuthal widths. For low-order resonances, we also detect secondary resonances arising from small-integer commensurabilities between resonant librations and the synodic frequency. These secondary resonances contribute significantly to generating the chaotic sea that typically occurs near mean motion resonances of higher mass perturbers.

Original languageEnglish (US)
Pages (from-to)1253-1263
Number of pages11
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
StatePublished - May 1 2023


  • celestial mechanics
  • chaos
  • methods:numerical
  • planetary systems

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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