  I use the distances and motions of Local Group galaxies to test Modified
Newtonian Dynamics (MOND). The old Local Group timing argument of Kahn &
Woltjer, which assumed Newtonian gravity and a simple radial orbit, indicated
that the total mass of M31 and the Milky Way far exceeds their known baryonic
mass. Here I apply MOND to study the same problem. With the same radial orbit
assumption, I find that the total mass of M31 and the Milky Way predicted by
MOND is less than the known baryonic masses of these two galaxies. I find a
similar result holds for all the dwarf galaxies in the Local Group, if they are
assumed to move radially with respect to the center of mass of M31 and the
Milky Way. If the known baryonic mass of M31 and Milky Way is used, MOND
requires all galaxies in the Local Group to have non-radial motions with
respect to the center of mass of M31and the Milky Way in order to be consistent
with their observed motion and distance. The non-radial orbit requirement is
inconsistent with the requirement of high radial anisotropy in order to
reconcile MOND with the velocities of satellite galaxies around host galaxies
from the Sloan Digital Sky Survey.
