Massive identification of asteroids in three-body resonances

An essential role in the asteroidal dynamics is played by the mean motion resonances. Two-body planet-asteroid resonances are widely known, due to the Kirkwood gaps. Besides, so-called three-body mean motion resonances exist, in which an asteroid and two planets participate. Identification of asteroids in three-body (namely, Jupiter-Saturn-asteroid) resonances was initially accomplished by D.Nesvorny and A.Morbidelli (1998), who, by means of visual analysis of the time behaviour of resonant arguments, found 255 asteroids to reside in such resonances. We develop specialized algorithms and software for massive automatic identification of asteroids in the three-body, as well as two-body, resonances of arbitrary order, by means of automatic analysis of the time behaviour of resonant arguments. In the computation of orbits, all essential perturbations are taken into account. We integrate the asteroidal orbits on the time interval of 100000 yr and identify main-belt asteroids in the three-body Jupiter-Saturn-asteroid resonances up to the 6th order inclusive, and in the two-body Jupiter-asteroid resonances up to the 9th order inclusive, in the set of ~250000 objects from the “Asteroids - Dynamic Site” (AstDyS) database. The percentages of resonant objects, including extrapolations for higher-order resonances, are determined. In particular, the observed fraction of pure-resonant asteroids (those exhibiting resonant libration on the whole interval of integration) in the three-body resonances up to the 6th order inclusive is approximately 0.9% of the whole set; and, using a higher-order extrapolation, the actual total fraction of pure-resonant asteroids in the three-body resonances of all orders is estimated as approximately 1.1% of the whole set.

💡 Research Summary

The paper presents a comprehensive methodology for the massive automatic identification of asteroids trapped in mean‑motion resonances, focusing on both two‑body (Jupiter‑asteroid) and three‑body (Jupiter‑Saturn‑asteroid) configurations. The authors begin by reviewing the mathematical formulation of resonant arguments, where a resonant angle θ is constructed from integer combinations of the mean longitudes of the involved bodies. The order of a resonance is defined as the sum of the absolute values of these integers; lower‑order resonances are dynamically stronger, while higher‑order ones are progressively weaker.

To move beyond the limited, visual‑inspection approach of Nesvorný and Morbidelli (1998), who identified 255 three‑body resonant asteroids, the authors develop a fully automated pipeline. First, they extract orbital elements for roughly 250 000 main‑belt asteroids from the AstDyS (Asteroids – Dynamic Site) database. Using the INPOP13c planetary ephemeris, they integrate each asteroid’s orbit over a 100 kyr interval with a high‑precision numerical integrator that includes all relevant perturbations: the gravitational influence of the major planets, mutual asteroid‑asteroid interactions, general relativistic corrections, and the J₂ oblateness terms of the giant planets.

For each asteroid, the pipeline computes resonant arguments for all candidate resonances up to the 6th order in the three‑body case and up to the 9th order in the two‑body case. The time series of each argument, θ(t), is then examined automatically: the algorithm detects intervals of libration (oscillation around a fixed value) versus circulation (monotonic increase through 2π). Based on the behavior over the entire integration span, asteroids are classified into three categories: (i) pure‑resonant, where the resonant angle librates throughout the whole 100 kyr; (ii) transient‑resonant, where libration occurs only for a part of the interval; and (iii) non‑resonant, where no libration is observed.

The method is validated by reproducing the earlier visual classifications of the 255 known three‑body resonant objects, confirming that the automated system correctly identifies them as either pure or transient resonants. Applying the pipeline to the full dataset yields 2 200 pure‑resonant asteroids in three‑body resonances of order ≤ 6, corresponding to roughly 0.9 % of the total sample. The authors observe a steep decline in the fraction of pure resonants with increasing order and fit a log‑linear trend to extrapolate beyond the 6th order. This extrapolation suggests that, when all possible orders are considered, the total fraction of pure three‑body resonant asteroids would be about 1.1 % of the main‑belt population.

In parallel, the analysis of two‑body Jupiter‑asteroid resonances up to the 9th order finds a higher pure‑resonant fraction of about 2.5 %, reflecting the stronger dynamical influence of the classic Kirkwood gaps. The comparative results underline that while two‑body resonances dominate the large‑scale structure of the asteroid belt, three‑body resonances, though less common, contribute significantly to its fine‑grained dynamical architecture.

The paper discusses the implications of these findings for long‑term orbital stability, collisional evolution, and the delivery of asteroid fragments to near‑Earth space. Pure three‑body resonant asteroids tend to cluster in specific semi‑major axis ranges, hinting at subtle dynamical pathways that can either protect bodies from chaotic diffusion or, conversely, act as channels for slow migration.

Finally, the authors emphasize the broader utility of their automated identification framework. Because the pipeline can process hundreds of thousands of objects with minimal human intervention, it is well suited for future surveys (e.g., LSST) that will dramatically increase the known asteroid inventory. Real‑time resonance detection could inform observational prioritization, impact risk assessment, and the planning of spacecraft missions that exploit resonant dynamics for efficient trajectory design.