Pfhorrest wrote:Ok so does this same principle apply to all other objects? If you were to blow up Titan (pump enough more energy than its gravitational binding energy into it), would Titan-dust scatter far and wide (getting sucked in by other nearby massive objects of course), or would Saturn just get another ring?
In the Jupiter case, it was open and shut because the angular momentum simply disappeared. This means that Jupiter can be described as an expanding sphere with nothing else affecting it (regardless of other planets that might impart some momentum, but do so by capturing the gasses and dust). When it comes to the general case I am not so sure. When Titan is blown up (or Jupiter if it was not done in so specific a manner) I could imagine it in one of two ways. If we continue with the expanding sphere analogy, this would be an expanding sphere on a rotating plane. I would expect no difference in this circumstance (since the expanding sphere would still be subject to the same forces in the rotating frame as in the stationary frame). That is an oversimplification though.
When you look at the exploding rotating body, each particle, by virtue of being in the larger body as a whole, has a velocity vector. When the planet explodes, this vector will change, but its final value will depend upon the speed of each particle before the planet blew up and its relative position on the planet (use vector addition). If we use exactly the gravitational binding energy to blow up the offending planet, then it stands to reason that at the surface of the planet (moon, asteroid, whatever) each particle would be moving at exactly escape velocity. Note that the vector that results from this will vary wildly based upon where they were when the planet blew up. So you can think of each particle having a completely new orbit from every other particle. In order for matter to collect in the fashion you would expect to reform the planet you blew up, they would need to be on similar orbital paths (or redirected into similar orbital paths). This isn't like the beginning of the solar system. We don't have a large collector of matter to suck in mass that is on a very different orbit. So until a large portion of this matter forms, the planet will not become a planet (or moon, or whatever).
Is there something that would reform? I doubt it, but my bet is go smaller. Like rock or astronomical dust bunny small. Ignoring everything else, the gravitational binding energy of such a small object is so low and the escape velocity is so small, that I imagine that the particulate would still be in a similar orbital path. Gravity is weaker of course so going smaller might not be useful, but at least it solves the proximity problem (and gravity's strength is proportional to the mass and the square of the inverse distance). If this does work, I don't know how small something needs to be to use this.