Motions of Galaxies in the Local Group and Beyond: an Astro2010 Science White Paper

Recent advances with the VLBA have resulted in ~10 micro-arcsec astrometry for compact sources in external galaxies, and measurement of the proper motion of Local Group galaxies has been demonstrated. With improved telescopes and equipment, we could greatly improve upon and expand these measurements, including a measurement of the proper motion of the Andromeda galaxy, which is key to understanding the history and fate of the Local Group. The combination of optical velocities and radio astrometric data would allow detailed modeling of the mass distributions of the disks, bulges, and dark matter halos of galaxies in clusters.