I'm having some trouble with the opening salvo here: "Now imagine placing a marble somewhere on that slippery sheet -- it is guaranteed to fall into one of the funnels. " This holds for the case where there are two objects initially at rest, but I don't see it as obviously true if there are more than two objects in the universe.
I see two aspects to your question/comment: at-rest, and two-objects. The whole point of that comment was to apply only to at-rest things (he goes on to contrast it with objects with velocity), though I think maybe you got that. If you have a marble and two other objects, the other objects make two funnels, and there is a saddle (itself curved) where the two objects's funnels are equipotent. That's the three-body cas…
Re: Background on the Falcon 9 Launch
#141Right, the fact that all the bodies are acting on the other is what makes me feel the analogy is not kosher. The funnels are going to start moving around based on their mutual attraction, and I could see the marble being ejected to infinity, for example. It's less clear to me (but possible) that it could enter a stable orbit.