Exoplanets, -moons, -comets

Orbital Stability Of Compact Three-planet Systems III. The Role Of Three-body Resonances

By Keith Cowing
Status Report
astro-ph.EP
January 29, 2026
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Orbital Stability Of Compact Three-planet Systems III. The Role Of Three-body Resonances
Period-ratio plane with triplets of adjacent planets in Kepler systems in the region 0.58 < Pj/Pj+1 < 0.90 (Lissauer et al. 2024). The black markers show the position of triplets of planets inside three-planet systems. The blue markers show triplets inside four-planet systems (up to two markers per system) where the empty circles, and squares represent the triplets in Kepler-60 and Kepler-223, respectively. The yellow markers show triplets in five-planet systems (up to three markers per system) where the empty circles, squares, and crosses represent the triplets in Kepler-1371 and Kepler-1542, and Kepler-444, respectively, and the purple markers show the triplets in six-planet systems (up to four markers per system) where the empty circles, squares, and crosses represent the triplets in Kepler-80, Kepler-11, and Kepler-102, respectively. The triplets in the eight-planet system Kepler-90 are shown by the light green stars. For comparison, the red stars show the successive triplets in the TRAPPIST-1 system. The solid, dashed, and dotted black lines are the firstorder, second-order, and third-order two-body mean motion resonances, respectively. The oblique green lines are the zerothorder three-body mean motion resonances, where the bold green ones represent resonances with α = 1, α = 2, and α = 3/2, which are the three most isolated three-body resonances in the vicinity of the main diagonal. -- astro-ph.EP

Observational surveys show that at least ~ 30% of short-period multiplanetary systems host tightly packed planets, some of which are locked in stable chains of mean-motion resonances.

Despite recent progress, the dynamical stability of these systems remains only partially understood. Numerical simulations have established a general exponential increase in system lifetime with orbital separation, with mean-motion resonances playing a key role in regulating stability.

Tightly packed three-planet systems exhibit a distinctive behavior not seen in higher-multiplicity systems: a small yet significant region of phase space is anomalously stable. This study investigates the dynamics of extremely compact three-planet systems, focusing on anomalously long-lived configurations and their connection to resonant chains observed in exoplanetary systems.

We perform numerical integrations of coplanar, initially circular, equal-mass three-planet systems over stellar-lifetime timescales and at high resolution in orbital separation, and interpret the results in the context of recent analytical work. We identify regions of phase space hosting anomalously stable orbits, including systems surviving multiple orders of magnitude longer than predicted by the exponential trend.

We demonstrate a clear link between stability and isolated three-body mean-motion resonances, showing that extremely compact systems can remain stable when captured into a small subset of isolated zeroth-order resonances. Stability further depends on the initial orbital longitudes and on the interplay between the three-body and two-body resonance networks.

Sacha Gavino, Jack J. Lissauer

Comments: 19 pages, 24 figures, A&A
Subjects: Earth and Planetary Astrophysics (astro-ph.EP)
Cite as: arXiv:2601.20220 [astro-ph.EP] (or arXiv:2601.20220v1 [astro-ph.EP] for this version)
https://doi.org/10.48550/arXiv.2601.20220
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Submission history
From: Sacha Gavino
[v1] Wed, 28 Jan 2026 03:42:42 UTC (15,404 KB)
https://arxiv.org/abs/2601.20220
Astrobiology

Keith Cowing

Explorers Club Fellow, ex-NASA Space Station Payload manager/space biologist, Away Teams, Journalist, Lapsed climber, Synaesthete, Na’Vi-Jedi-Freman-Buddhist-mix, ASL, Devon Island and Everest Base Camp veteran, (he/him) 🖖🏻

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