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

Abstract

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.

30 pages, accepted to ApJ

References in corpus (4)

• Closest Star Seen Orbiting the Supermassive Black Hole at the Centre of the Milky Way
• The First Measurement of Spectral Lines in a Short-Period Star Bound to the Galaxy's Central Black Hole: A Paradox of Youth
• The Stellar Cusp Around the Supermassive Black Hole in the Galactic Center
• Stellar disk in the galactic center -- a remnant of a dense accretion disk?

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• Dynamical inference from a kinematic snapshot: The force law in the Solar System
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• Measuring the mass distribution in stellar systems