SIMBAD references

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.