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 ∼500 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- and low-velocity limits.

由星际彗星最近访问的推动下，随着持续的小天体的发现在太阳的轨道上沿，研究开始上轨道双曲线对象通过我们的太阳系捕获。使用的约500个亿数值实验合奏，这项工作通过计算俘获截面为渐近速度的功能概括以前的治疗。然后可以将所得的与速度相关的横截面与相对速度的任何分布进行卷积，以确定传入物体的捕获率。这个卷积用于通常麦克斯韦分布，以及预期的岩石碎片从行星系统喷出的速度分布进行。