I can’t do the maths but I can explain it quite simply I think.
Unlike most other forces (like magnetism), gravity doesn’t have a “finite range”. Gravity works across as long a distance as you’d like. The only thing is that gravity drops off as you get further away.
However, for something to be in orbit, it just needs to fly around an object as fast as it is pulled towards it by gravity. So the weaker gravity is, the slower the orbiting body must move. That’s why a Mars year is longer than an Earth year - the Sun’s gravity pulls less on Mars as it’s further away, and thus Mars moves slower around the sun (it’s also a larger orbit so there’s more distance to travel).
So the asteroid need not weigh a lot to have a moon that is far away. The moon just needs to go sufficiently slow around the asteroid.
Also, it’s likely that the orbit is not circular but rather an eccentric ellipse. So sometimes the moon would be closer, sometimes further away.
I can’t do the maths but I can explain it quite simply I think.
Unlike most other forces (like magnetism), gravity doesn’t have a “finite range”. Gravity works across as long a distance as you’d like. The only thing is that gravity drops off as you get further away.
However, for something to be in orbit, it just needs to fly around an object as fast as it is pulled towards it by gravity. So the weaker gravity is, the slower the orbiting body must move. That’s why a Mars year is longer than an Earth year - the Sun’s gravity pulls less on Mars as it’s further away, and thus Mars moves slower around the sun (it’s also a larger orbit so there’s more distance to travel).
So the asteroid need not weigh a lot to have a moon that is far away. The moon just needs to go sufficiently slow around the asteroid.
Also, it’s likely that the orbit is not circular but rather an eccentric ellipse. So sometimes the moon would be closer, sometimes further away.