I don’t get it. How can a body be captured by gravity make a few orbits then spin off again? Seems like once you are in gravity’s grip there would be no letting go......? Either orbit forever (moon), crash into the planet, or a near miss anf off you go again.
Think of it like playing pool in 3D
If it were a simple two body problem, you would be correct, except that the two body problem doesn't allow any mechanism for capture in the first place.
The comet was originally in orbit around the sun. Depending on how it approached Jupiter, he may have imparted more velocity and flung it out of the solar system or in this case, the gravitional drag of Jupiter slowed it down just enough that it no longer had escape velocity from Jupiter and was "captured".
If the comet was moving away from Jupiter as it approached his orbit, Jupiter would have slowed him down. The angular momentum of the Jupiter-Comet system is in variant in a coordinate system centered on the sun. Jupiter just took a little of the comets angular momentum and sped up very slightly, while the comet was slowed down.
The resulting orbit will be perturbed by the influence of the sun, Jupiter's moons and other gas giants and may eventually acquire enough velocity, relative to Jupiter, to escape Jupiter (for now) and continue on his way, either out to the Oort Cloud or back towards the sun.
Since the comet's resulting orbit crosses Jupiter's, it will have other encounters with Jupiter until it eventually is flung from the solar system or collides with him or an encounter with another body deflects his orbit away from Jupiter's.
If you want to see really weird orbital mechanics, read up on horseshoe orbits.
Some say gravity isn’t the only force in effect on celestial bodies. Electromagnetic factors may be in play. This is based on plasma cosmology.
If you’re interested, here is a movie on the subject:
http://video.google.com/videoplay?docid=4773590301316220374&ei=-jEwSpveL4nKqgK5osCtDw&q=thunderbolts+of+the+gods&hl=en
Picture of the orbit.More Moons Around Earth? It’s Not So LoonyEarth has a second moon, of sorts, and could have many others. Cruithne, the 3-mile-wide (5-km) satellite, takes 770 years to complete a horseshoe-shaped orbit around Earth, and will remain in a suspended state around Earth for at least 5,000 years. Every 385 years, it comes to its closest point to Earth, some 9.3 million miles (15 million kilometers) away. Its next close approach to Earth comes in 2285. "We found new dynamical channels through which free asteroids become temporarily moons of Earth and stay there from a few thousand years to several tens of thousands of years," said Fathi Namouni, one of the researchers, now at Princeton University. Namouni’s colleague Apostolos Christou said, "At specific points in its orbit, it reverses its rate of motion with respect to Earth so it will appear to go back and forth." In his view, there are three classes of moons – large moons in near-circular orbits around a planet, having formed soon after the planet; smaller fragments that are the products of collisions; and outer, irregular moons in odd orbits, or captured asteroids like Cruithne. In the past year, astronomers have reported finding such objects around Uranus.
by Robin Lloyd
October 29 1999
It can happen. You should not look at the planet and the comet in isolation- there are other gravitational forces at play, too- for example, that of nearby moons, planets and the entire solar system.
Occasionally, the orbital positions may create a situation where the forces from those external fields, or from orbital eccentricity, may allow for the captured body to escape.