On the divergence of first-order resonance widths at low eccentricities

Renu Malhotra, Nan Zhang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first-order mean motion resonances diverge for nearly circular orbits. Here, we examine the nature of this divergence with a non-perturbative analysis of a few first-order resonances interior to a Jupiter-mass planet. We show that a first-order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centres of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of ‘bridges’ between adjacent first-order resonances: at low eccentricities, the apocentric libration zone of a first-order resonance smoothly connects with the pericentric libration zone of the neighbouring first-order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low-eccentricity regime.

Original languageEnglish (US)
Pages (from-to)3152-3160
Number of pages9
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
StatePublished - 2020


  • Celestial mechanics
  • Planetary systems
  • Planets and satellites: dynamical evolution and stability

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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