Orbital roulette: A new method of gravity estimation from observed motions

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.