## The Distance to the Center of the Milky Way

For nearly a century astronomers have expended considerable effort to determine the size of the Milky Way. This effort is worthwhile because any change in the value of the distance from the Sun to the center of the Galaxy, Ro, has widespread impact on astronomy and astrophysics. All distances determined from observed radial velocities and a rotation model of the Galaxy are directly proportional to Ro. Most estimates of the gravitational and luminous mass of the Galaxy scale with Ro. Similarly, the mass and luminosity of objects within the Galaxy, such as giant molecular clouds and the non-thermal source at the Galactic center depend on Ro. On a larger scale, since extra-galactic distances are based on Galactic calibrations, the Hubble constant and Ro are interrelated. Indeed, it may be possible to use the size of the Milky Way as an extra-galactic "meter stick" and determine distances to similar spiral galaxies.

More than eighty years after Shapley published his estimate of Ro, there is a reasonable consensus as to its value. Nearly all methods of determining Ro now yield values between 7 and 9 kpc. An analysis of all methods and measurements prior to 1993 yields a best estimate for Ro of 8.0 kpc, with a standard error of about 0.5 kpc (References: Reid 1993, Ann. Rev. Astron. Astrophys., 31, 345). Still, there is a lot to be gained by making simpler and more accurate methods.

 The most fundamental and straight-forward method of measuring distances is a trigonometric parallax. A trigonometric parallax uses the simple surveying technique of triangulation. For astronomical applications, one leg of the triangle is formed by the extremes of the Earth's orbit about the Sun. By measuring the difference in position of a source in the Galactic Center when observed 6 months apart in time (allowing the Earth to move halfway around in its orbit), one can directly calculate the distance. See the schematic figure on the left, which is not drawn to scale, for details. Reid & Brunthaler (2004, ApJ, 616, 872) have measured the proper motion (caused by the Sun's 200 million year orbit about the Galaxy) to high accuracy, but not the parallax.
The apparent shift in position caused by the Earth's orbit is measured against very distant Quasars and, of course, is a very tiny shift of about 0.1 milli-arcseconds. Such a small shift can, be measured by Very Long Baseline Interferometry. The results of 1 year of observation of water masers in Sgr B2, a star forming region that is very close to the Galactic Center, has yielded very encourang results. The plot below (from Reid et al 2009, ApJ, 705, 1548) shows the motion on the sky (left panel) and the change in position vs time (center and right panel), with the Eastward component in blue and the Northward component in green. The center panel shows the measured positions and the right panel has the proper motion removed to better show the parallax effect. This data gives a distance to the Galactic Center of 7.9 +/- 0.8 kpc.

Hopefully in few years the distance to the center of the Milky Way can be measured to very high accuracy with this simple and elegant technique.