  Previously, in Penner (2016a, 2016b), a theory of gravitational
anti-screening was shown to lead naturally to the Baryonic Tully-Fisher
Relationship. In addition, it was shown to agree with the observed rotational
curve of the Galaxy, the observed features in the rotational curves of other
spiral galaxies, with observations of the Coma cluster, and with a
geometrically flat universe. In this paper the theory will now be applied to
binary galaxies. It is shown that there is a relationship between the
line-of-sight velocity difference of the pair and the individual rotational
velocities of the galaxies. The resulting probability function for beta,
defined as the ratio of the line-of-sight velocity difference to the rotational
velocity of the larger galaxy of the pair, is in excellent agreement with the
observations taken by multiple researchers for the case of the binaries being
on radial orbits.
