  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 estimates accurately 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.
