The impact of Comet Shoemaker-Levy 9 (SL9) with Jupiter in 1994 was the ultimate confirmation of Eugene Shoemaker's theory that impacts are a common, fundamental process in the Solar System. On Earth, asteroid impacts have produced several near extinction level events. We tend to visualize these collisions as billiard balls hitting one another. But how, exactly, do they occur? The actual dynamics is much more complex and subtle because it is highly nonlinear and involves chaos in the Three-Body Problem. In this paper we investigate the effects of Lyapunov orbits, halo orbits, and their associated invariant manifolds, on the orbital motion of SL9. We demonstrate that periodic orbits act as gateways to Jupiter, and their invariant manifolds control the dynamics of SL9 during the Initial Capture Phase.