New comets in the inner Solar System might enter a new orbit or they might appear only once before getting kicked out of the Solar System or colliding with a planet, as Shoemaker-Levy famously and gloriously did when it crashed into Jupiter not so long ago—in 1994.
Why only new comets? Could Halley's Comet not run smack into Jupiter some day? Is the assumption here that any comet with a stable orbit has been around enough times that it would have hit Jupiter if their periodicity was inclines that way?
