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.
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