Is there a universal coupling threshold for few-body stability?

We test the hypothesis that a single value of tidal coupling between Keplerian subsystems determines the stability threshold of few-body configurations. We define a standardized measure, the ratio of the tidal acceleration due to the external bodies to the internal acceleration of each subsystem, and compute it at nine simulated thresholds from three families: Lagrange triangles with unequal masses, Maxwell rings, and hierarchical systems. The values range from 0.66% to 5.1%, a spread of about a factor of eight, which refutes the universal constant and preserves an order-of-magnitude rule. Rings with n ≤ 6 are unstable even with coupling well below 1%. We propose that resonance overlap, in the sense of Chirikov, better explains both the common scale and the systematic differences between families.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23962928
Primary Topic
Stellar, planetary, and galactic studies
Type
article
Field-Weighted Citation Impact
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article

Is there a universal coupling threshold for few-body stability?

Willian Wistuba Melo da Cunha
Zenodo (CERN European Organization for Nuclear Research)
Stellar, planetary, and galactic studies
article

Is there a universal coupling threshold for few-body stability?

Willian Wistuba Melo da Cunha
article en

Abstract

We test the hypothesis that a single value of tidal coupling between Keplerian subsystems determines the stability threshold of few-body configurations. We define a standardized measure, the ratio of the tidal acceleration due to the external bodies to the internal acceleration of each subsystem, and compute it at nine simulated thresholds from three families: Lagrange triangles with unequal masses, Maxwell rings, and hierarchical systems. The values range from 0.66% to 5.1%, a spread of about a factor of eight, which refutes the universal constant and preserves an order-of-magnitude rule. Rings with n ≤ 6 are unstable even with coupling well below 1%. We propose that resonance overlap, in the sense of Chirikov, better explains both the common scale and the systematic differences between families.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 16%
Stellar, planetary, and galactic studies
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