Orbital Roulette: A New Method of Gravity Estimation from Observed Motions
Bibliographic record
Abstract
The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural presumption that the objects are observed at a random moment of time and therefore have random orbital time phases. The proposed estimator, which we call "orbital roulette," checks the randomness of the phases. The method has the following advantages: (1) It accurately estimates Keplerian (point-mass) potentials as well as non-Keplerian potentials, where the unknown gravitating mass is distributed in space. (2) It is a complete statistical estimator: it checks a trial potential and accepts it or rules it out with a certain significance level; the best-fit measurement is thus supplemented with error bars at any confidence level. (3) It needs no a priori assumptions about the distribution of orbital parameters of the test bodies. We test our estimator with Monte Carlo-generated motions and demonstrate its efficiency. Useful applications include the Galactic Center, dark-matter halo of the Galaxy, and clusters of stars or galaxies.
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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 | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".