  We present a new geometrical method for measuring the distance to the
Galactic center (R_0) by solving for the Keplerian orbit of individual stars
bound to the black hole associated with the Sgr A* from radial velocity and
proper motion measurements. We identify three stars to which the method may be
applied, and show that 1-5 % accuracy of R_0 can be expected after 15 years of
observing, and 0.5-2 % after 30 years of observing, depending on what the
orbital parameters of these three stars turn out to be. Combining the
measurements of the three stars with favorable orbital parameters leads to even
more precise values. In the example that we present, such combined solution
yields 4 % accuracy already by the year 2002. All these estimates assume that
annual position measurements will continue to be made with the 2 mas precision
recently reported by Ghez et al. The precision of the distance measurement is
relatively insensitive to the radial velocity errors, provided that the latter
are less than 50 km/s. Besides potentially giving an estimate of R_0 that is
better than any currently in use, the greatest advantage of this method is that
it is free from systematic errors.

Astrophysics