Orbital Roulette: A New Method of Gravity Estimation from Observed Motions

The traditional way of estimating the gravitational field from observedmotions of test objects is based on the virial relation between their kineticand potential energy. We find a more efficient method. It is based on thenatural presumption that the objects are observed at a random moment of timeand therefore have random orbital time phases. The proposed estimator, which wecall "orbital roulette", checks the randomness of the phases. The method hasthe following advantages: (1) It estimates accurately Keplerian (point-mass)potentials as well as non-Keplerian potentials where the unknown gravitatingmass is distributed in space. (2) It is a complete statistical estimator: itchecks a trial potential and accepts it or rules it out with a certainsignificance level; the best-fit measurement is thus supplemented with errorbars at any confidence level. (3) It needs no a priori assumptions about thedistribution of orbital parameters of the test bodies. We test our estimatorwith Monte-Carlo-generated motions and demonstrate its efficiency. Usefulapplications include the Galactic Center, dark-matter halo of the Galaxy, andclusters of stars or galaxies.Comment: 30 pages, accepted to Ap