Mean-motion resonances in the Solar system
A curated collection of essential papers on mean-motion resonances in the asteroid belt, TNO, and beyond.
Smirnov, Evgeny (2025)
Through two large-scale numerical searches and automated classification, the paper demonstrates that mean-motion resonances—especially two-body resonances with Neptune—affect nearly half to two-thirds of objects in the Neptune region, implying resonances dominate trans-Neptunian dynamics far more than in the main belt.
The paper reports a systematic, automated search for two-body and three-body mean-motion resonances in the Neptune region using two large numerical simulations that scan resonances up to higher orders and coefficient ranges. It finds a very high resonant fraction (49.3% confirmed, 65.1% including controversial cases) dominated by Neptune two-body resonances, with many new resonances discovered and some objects trapped in multiple resonances simultaneously, implying MMRs strongly shape the trans-Neptunian region.
numerical integration
mean-motion resonances
This study presents a large-scale numerical investigation of resonant objects in the Neptune region, focusing on both two-body and three-body mean-motion resonances (MMRs). Two simulations were conducted: Simulation 1 examined two-body MMRs with Uranus and Neptune up to resonant order q ≤ 10 and three-body MMRs involving both planets up to order q ≤ 6, while Simulation 2 extended the search to higher-order two-body resonances with Neptune up to q ≤ 20 and high integer coefficients up to m_i ≤ 50. Automated resonance classification found that 42.1% of objects are confirmed resonant in Simulation 1 (58.2% including controversial cases), with two-body Neptune resonances dominating and notable contributions from three-body resonances and Uranus resonances. Simulation 2 added 108 resonances and 104 newly confirmed resonant objects, increasing the resonant fraction to 49.3% confirmed and 65.1% including controversial cases, and revealed many additional two-body Neptune MMRs and cases of simultaneous multiple-resonance trapping. The results indicate MMRs are much more prevalent in the trans-Neptunian region than in the main asteroid belt, suggesting that the majority of objects in this region may be resonant.
It seems that almost all TNOs are in two-body resonances with Neptune...
— ES