We know that Jupiter has 60+ moons, and the other giant planets have many as well. The largest are usually believed to be formed when the planet formed, and the smaller, non-spherical moons on more eccentric and inclined orbits are likely captured asteroids. But how do they get captured? A single asteroid flying by a planet cannot become bound to the planet unless it loses energy.
One possible energy loss mechanism is the gas disk that existed around the giant planets when they formed. An asteroid could get caught in this disk and lose enough energy to remain bound as a new moon of the planet. A problem with this, however, is that the newly captured moon would continue to lose more and more energy in the gas disk and crash into the planet unless the gas went away quickly.
Another possible mechanism for capturing these small 'irregular' satellites is to have binary asteroids (two asteroids orbiting each other) flying by the planet. If this happens, then when they encounter the planet, one of the pair can be captured as a satellite while the other is flung away with the excess energy. This is the process I am examining in my research.
One source for asteroids which would cross a planet's orbit is the Trojan population near Jupiter. These asteroids orbit the Sun at the same distance as Jupiter but always either ahead of or behind the planet. Also, their orbit speed becomes a little slower and a little faster over time, so that if you rotated a coordinate frame so that Jupiter stayed in the same spot, the Trojans trace out tadpole-like shapes.
The star at the center is the Sun, Jupiter is the circle at (5.2, 0), and the Trojans orbits are the green tadpole shapes.
This coordinate frame is rotated at Jupiter's orbital speed so that Jupiter is always in the same place.
It is also known that the Trojans are slowly leaking out of their tadpoles over time. When they become unstable, their tadpole shapes grow into larger and eventually look like horseshoes, which bring the asteroid close to Jupiter. Eventually the asteroid will suffer the effects of a close approach with Jupiter and it will get kicked out of the region altogether.
Again, the Sun is the star at the center, and Jupiter is at (5.2, 0). This shows the orbital growth and
escape of a Trojan which began in the upper tadpole swarm. A close approach with Jupiter causes escape.
An important thing to know before we can determine whether binary Trojan asteroids could be captured as moons is what their escape paths look like when close to Jupiter. We can numerically simulate escaping Trojans and look at things such as how close they get to Jupiter and what their speeds are during the encounter. These factors will be important in determining whether binary asteroids on the same paths will get split apart and facilitate a capture. Here is an example of a simulation where we recorded all close approaches within .36 AU, the "Hill radius" of Jupiter, inside which its gravity dominates over the Sun. Here Jupiter is at the center, and each arrow represents a close approach of a Trojan. The arrows point in the direction of the asteroid's velocity at the time of closest encounter, and the length of the arrow corresponds to how fast the Trojan was moving. The colors indicate how early in time the approach occurred - red is earliest, followed by yellow, and then green. Note that the green arrows are in general longer than the red ones, suggesting that later in time, the asteroids have come close to Jupiter a number of times already, and have been kicked to higher speeds.
