The Proper Motion and Parallax of Barnard's Star: Errors and Precision in Small-Telescope Astrometry

This paper examines a series of measurements made to determine the proper motion and parallax of Barnard's Star using differential astrometry. In differential astrometry, the same reference stars are used for every coordinate determination. Although the absolute coordinate solution is offset by a constant due to the imprecisely known positions of the reference stars, relative coordinate solutions can be precise. For this study, observations of the field of Barnard's Star were made in 2009 and 2010 using an 8-inch f/4 Newtonian telescope. The singlenight standard error in each coordinate can be as low as 10 mas. We discuss the errors, error distribution, and error sources in the astrometric solution, as well as the derived proper and parallax motions of the star.