Comparing Extended System Interactions with Motions in Softened
  Potentials
  Using an $N$-body evolution code that does not rely on softened potentials, I
have created a suite of unbound interacting cluster pair simulations. The
motions of the centers of mass of the clusters have been tracked and compared
to the trajectories of point masses interacting via one of four different
softened potential prescriptions. I find that the relationship between the
impact parameter of the cluster interaction and the point-mass softening length
that best approximates each cluster's center-of-mass motion depends on the
adopted prescription. In general, the range of allowed softening lengths grows
roughly linearly with the impact parameter, but zero softening is acceptable in
the majority of situations. In an $N$-body simulation that adopts a fixed
softening length, such relationships lead to the possibility of two-body
effects, like dynamical friction, being either larger or smaller than the
corresponding cluster situation. Further consideration of more specific
$N$-body situations leads estimating that a very small fraction of point-mass
encounters experience two-body effects significantly different than those of
equivalent clusters.
