Mars and Jupiter seem to have moons that are asteroids that got captured by their gravity. Are they really captured asteroids? If so, how does that work? It seems to me that an asteroid that passes a planet would go off in a sort of hyperbolic orbit instead of being captured. What would cause it to go into an elliptical orbit?
Try this for a conceptual experiment: Take a normal bedsheet, and stretch it in a frame. Now throw a heavy object onto the sheet. The heavy object will create a depression. This is your ‘gravity well’. Now take a marble, and roll it quickly across the sheet, through the depression but not into the object in the center. If you roll it hard enough, the depression will bend its course in the direction of the object, but it’ll sail out of the other side and keep going. Roll it a little slower, and it’ll roll into the depresssion, lose energy on the way out, and come out the other side even slower. If you roll it slowly enough, it’ll never come out, but will simply stop and roll back into the center.
That is in effect what is happening. The main difference is that the marble on the sheet has a significant amount of friction acting on it, which is why it won’t orbit the heavy weight in the center. It’ll just keep losing energy until it rolls into the center against the other object and stops.
The bedsheet example only works because of friction, which is negligable in space. In Newtonian gravity, a lone body can’t capture anything. However, if you have two or more bodies (as, for instance, the planet and a pre-existing moon: Not all of them were gotten via a capture), then you can. The extra orbital energy of the incoming body, which would prevent a closed orbit, gets transfered to orbital energy of the pre-existing bodies.
An example: An asteroid approaches the vicinity of the Earth at a high speed, high enough that it would normally just hyperbolate back out. It happens to approach the Moon from behind, so its closing speed relative to the Moon is less than its closing speed relative to the Earth, swings around the Moon, reverses direction, and recedes at the same speed it approached, relative to the Moon. However, this is a much lower speed than before, realtive to the Earth, and it may even be a low enough speed that the asteroid can now orbit the Earth. We’ve just captured ourselves a second moon.
This process can also be used in reverse: A body in a closed orbit can use other orbiting bodies to slingshot it into an open orbit. It’s enough more difficult that this seldom happens accidentally, but spacecraft in planned orbits do it all the time.
So that’s how we know our moon was not captured. Thanks.
Thank you, Chronos.