# Sgr A* ``Visual Binaries'': A Direct Measurement of the Galactocentric Distance

## Samir Salim, Andrew Gould

Ohio State University, Department of Astronomy, 174 West 18th Ave., Columbus, OH 43210

E-mail: samir@astronomy.ohio-state.edu,ould@astronomy.ohio-state.edu

### Paper: Submitted to ApJ

**Abstract:**
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 fter 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 sigma_{rho} = 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/sec . 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.

Preprints available from the authors at samir@astronomy.ohio-state.edu
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