I only knew what the hell Mitchell was talking about with the slingshot thing because I just happened to remember it being properly explained in the movie Armageddon.

Yes, the exposition sucks; in this case, though, I think the whole slingshot thing was a deliberate Farscape reference. I only ever really watched the pilot of that show, but Ben Browder's character there had this whole thing going on with his theory about using Earth's gravity to slingshot off at high speed.