Ergodic Considerations in the Gravitational Potential of the Milky Way

A method is proposed for constraining the Galactic gravitational potential from high precision observations of the phase space coordinates of a system of relaxed tracers. The method relies on an "ergodic" assumption that the observations are representative of the state of the system at any other time. The observed coordinates serve as initial conditions for moving the tracers forward in time in an assumed model for the gravitational field. The validity of the model is assessed by the statistical equivalence between the observations and the distribution of tracers at randomly selected times. The applicability of this ergodic method is not restricted by any assumption on the form or symmetry of the potential. However, it requires high recision observations as those that will be obtained from missions like SIM and GAIA.