Yeah, there's a lot of weird details here that can complicate things; I was going for a very basic answer. Even in the kind of case you're talking about, it's unlikely that the object would stay in a stable equilibrium--if it's really that close, perturbations from other objects' gravity would almost certainly kick it out of that cycle. The solar system is chaotic, and orbital dynamics get messy. Thanks for the elaboration, though!
Of course! Moon fuckery alone messes up orbits enough that you quickly realize this is impossible even without bringing the gravity of the fucking sun or Jupiter into it. It was just meant as an example of how gravity works and what escape velocity is. So this is what orbital mechanics says would happen if there were only two bodies of matter in the entire universe.
Yeah, there's a lot of weird details here that can complicate things; I was going for a very basic answer. Even in the kind of case you're talking about, it's unlikely that the object would stay in a stable equilibrium--if it's really that close, perturbations from other objects' gravity would almost certainly kick it out of that cycle. The solar system is chaotic, and orbital dynamics get messy. Thanks for the elaboration, though!
Of course! Moon fuckery alone messes up orbits enough that you quickly realize this is impossible even without bringing the gravity of the fucking sun or Jupiter into it. It was just meant as an example of how gravity works and what escape velocity is. So this is what orbital mechanics says would happen if there were only two bodies of matter in the entire universe.