2004/05/27 by Andrei M. Beloborodov, Yuri Levin, Yuri levin · 23 citations
Physics and Astronomy · #A priori and a posteriori #Celestial mechanics #Estimator #Gravitational potential #Moment (physics) #Orbital elements #Pulsars and Gravitational Waves Research #Randomness #Statistical Mechanics and Entropy #Stellar, planetary, and galactic studies #Test particle #Virial theorem #astro-ph
paper · pdf · doi:10.1086/422908
published in The Astrophysical Journal 613(1), 224-237 (IOP Publishing) · 30 pages, accepted to ApJ
arxiv created 2004/05/27 · openalex publication_date 2004/09/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.