Early signals of ejection in the three-body problem: the role of mass ratios

We ask whether the binary that survives the disruption of a three-body system can be recognized before the third body is ejected. In 7,000 regularized planar integrations, starting from rest and with virial ratio 0.5, we compare equal masses, two small and one large, and two large and one small. With equal masses there is no early signal: the final pair only becomes definitively the most bound at the last close encounter, and the predictor based on pair energies is correct 35% to 45% of the time, close to chance. With unequal masses, the lightest body is ejected in 92% to 99.8% of the cases, in agreement with the approximate m⁻³ law, and the signal grows with the disparity: with masses 10, 10, and 1, the final pair is determined at half the time preceding the ejection. Even so, the rule that the two heaviest bodies remain predicts the outcome as well as or better than any dynamical signal. Two large masses eject the small one earlier and with fewer escape attempts.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23963354
Primary Topic
Stellar, planetary, and galactic studies
Type
article
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article

Early signals of ejection in the three-body problem: the role of mass ratios

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

Early signals of ejection in the three-body problem: the role of mass ratios

Willian Wistuba Melo da Cunha
article en

Abstract

We ask whether the binary that survives the disruption of a three-body system can be recognized before the third body is ejected. In 7,000 regularized planar integrations, starting from rest and with virial ratio 0.5, we compare equal masses, two small and one large, and two large and one small. With equal masses there is no early signal: the final pair only becomes definitively the most bound at the last close encounter, and the predictor based on pair energies is correct 35% to 45% of the time, close to chance. With unequal masses, the lightest body is ejected in 92% to 99.8% of the cases, in agreement with the approximate m⁻³ law, and the signal grows with the disparity: with masses 10, 10, and 1, the final pair is determined at half the time preceding the ejection. Even so, the rule that the two heaviest bodies remain predicts the outcome as well as or better than any dynamical signal. Two large masses eject the small one earlier and with fewer escape attempts.

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