Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems
Bibliographic record
Abstract
Abstract N -body simulations of nonresonant, tightly packed planetary systems have found that their survival time (i.e., time to first close encounter) grows exponentially with their interplanetary spacing and planetary masses. Although this result has important consequences for the assembly of planetary systems by giant collisions and their long-term evolution, this underlying exponential dependence is not understood from first principles, and previous attempts based on orbital diffusion have only yielded power-law scalings. We propose a different picture, where large deviations of the system from its initial conditions is due to a few slowly developing high-order resonances. Thus, we show that the survival time of the system T can be estimated using a heuristic motivated by Nekhoroshev’s theorem, and obtain a formula for systems away from overlapping two-body mean-motion resonances as , where P is the average Keplerian period, a is the average semimajor axis, Δ a ≪ a is the difference between the semimajor axes of neighboring planets, μ is the planet-to-star mass ratio, and c 1 and c 2 are dimensionless constants. We show that this formula is in good agreement with numerical N -body experiments for c 1 = 5 × 10 −4 and c 2 = 8.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".