  Near-future surveys promise a dramatic improvement in the number and
precision of astrometric, photometric and spectroscopic measurements of stars
in the Milky Way's disk. We examine the impact of such surveys on our
understanding of the Galaxy by "observing" particle realizations of
non-axisymmetric disk distributions orbiting in an axisymmetric halo with
appropriate errors and then attempting to recover the underlying potential
using a Markov Chain Monte Carlo (MCMC) approach. We demonstrate that the
azimuthally averaged gravitational force field in the Galactic plane--and
hence, to a lesser extent, the Galactic mass distribution--can be tightly
constrained over a large range of radii using a variety of types of surveys so
long as the error distribution of the measurements of the parallax, proper
motion and radial velocity are well-understood and the disk is surveyed
globally. One advantage of our method is that the target stars can be selected
non-randomly in real or apparent-magnitude space to ensure just such a global
sample without biasing the results. Assuming we can always measure the
line-of-sight velocity of a star with at least 1 km/s precision, we demonstrate
that the force field can be determined to better than ~1% for Galactocentric
radii in the range R=4-20 kpc We conclude that near-future surveys, like SIM
Lite, Gaia, and VERA, will provide the first precise mapping of the
gravitational force field in the region of the Galactic disk.
