Stability of Minor-Body Orbits in Systems with Two Giant Planets
Bibliographic record
Abstract
We have performed a large ensemble of long-term numerical integrations to study the stability of the orbits of minor bodies in systems containing a solar-mass star and two giant planets. Given the large parameter space involved, we have focused on systems in which the inner planet has the mass of Jupiter ( M J ) and the outer planet has a mass equal to either M J or M J , and where we use an initially dynamically cold ( e = 0) minor-body population. We investigated the effects of the planetary semimajor-axis ratio, eccentricity, and inclination on the stability of orbits distributed throughout the system. We show that the behavior of the particles varies from region to region as the result of a complex interplay of the two major types of resonances: "mean motion" resonances associated with commensurabilities of orbital frequencies, and "secular" resonances associated with commensurabilities of orbital precession frequencies. In the region inward of the inner planet, mean motion resonances produce instabilities and secular resonances induce high eccentricities in the particles. Between the planets, the mean motion resonances are dominant and generally induce instability. Beyond the outer planet, secular and mean motion resonances overlap and produce wide-scale instability. In this last region, many stable particles are associated with mean motion resonances in various kinds of protective mechanisms. We also show that increased planetary eccentricity generally results in increased instability and that high initial inclination of both planet and test particles greatly changes the final structure of the system. Overall, our results show trends that make it possible to predict the general features of the minor-body distribution for a given set of orbital elements of the planets. We demonstrate this with two examples drawn from the set of observed extrasolar planetary systems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".