Do space objects stay in orbit once they get sucked in? Can they escape?

Question

Think of my question with respect to 2020 CD$_3$ minimoon that's been recently discovered.

If an object gets caught into a planet's orbit, can it ever escape it? Obviously it may escape on the first pass without making any full revolution. But if one or two revolutions took place, can it ever escape the planet's orbit on its own momentum it came in with?

Answer 1

If it can get captured, it can escape: we know this because the law of gravity is time-symmetric. If there is a trajectory that leads to a capture, then by running time backwards, there is a trajectory that leads to escape.

What happens with small objects like 2020CD3, is that they pass into the space between the Earth and moon, and it is the interaction between the Earth and Moon (and sun) that slows them down and allows them to enter into a long looping orbit.

But this orbit is too close to the moon to be really stable. Usually they go around in a complex orbit that changes each time, as they are affected by the gravity of the Earth, moon, (and sun). Usually after a few orbits they will have another interaction with the moon, but this time it will speed the object up, and eject it from the Earth's gravity well. Interactions that lead to a permanent capture are rare.

There are no objects in Earth orbit that have been captured. Asteroids are rather rare in the inner solar system, and the moon probably does a good job of ejecting any that do get into an orbit around the Earth. There are two captured asteroids around Mars, and many of Jupiter and Saturn's moons may have started out as asteroids. Triton is also probably a captured body. So it is possible for a body to get into a stable orbit from capture, but it is rare.

There is no sucking effect. Instead the orbit of the asteroid around the sun gets tangled up in the gravity field of the Earth and moon for a while, but eventually it will almost always escape.