  Motivated by recent visits from interstellar comets, along with continuing
discoveries of minor bodies in orbit of the Sun, this paper studies the capture
of objects on initially hyperbolic orbits by our solar system. Using an
ensemble of $\sim500$ million numerical experiments, this work generalizes
previous treatments by calculating the capture cross section as a function of
asymptotic speed. The resulting velocity-dependent cross section can then be
convolved with any distribution of relative speeds to determine the capture
rate for incoming bodies. This convolution is carried out for the usual
Maxwellian distribution, as well as the velocity distribution expected for
rocky debris ejected from planetary systems. We also construct an analytic
description of the capture process that provides an explanation for the
functional form of the capture cross section in both the high velocity and low
velocity limits.
