  Nonlocal gravity is the recent classical nonlocal generalization of
Einstein's theory of gravitation in which the past history of the gravitational
field is taken into account. In this theory, nonlocality appears to simulate
dark matter. The virial theorem for the Newtonian regime of nonlocal gravity
theory is derived and its consequences for "isolated" astronomical systems in
virial equilibrium at the present epoch are investigated. In particular, for a
sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's
baryonic diameter---namely, the diameter of the smallest sphere that completely
surrounds the baryonic system at the present time---is predicted to be larger
than the effective dark matter fraction times a universal length that is the
basic nonlocality length scale of about 3 kpc.
