Minimum mass of asteroid that could knock moon away What is theoretically the minimum mass of asteroid, coming from deep space, that could knock the Moon away from Earth? The asteroid is not hitting the Moon, just interacting with it by gravity.
I was simulating the scenarios with asteroid of mass $10^{20} \;\text{kg}$ and it seems that this is absolutely not heavy enough. I wasted couple of hours and tried to make asteroid go very very close to the moon, but it still hasn't worked. So I came to the question: What should the minimum mass of asteroid be that moon could get knocked away?
By knocking the Moon away, I mean give it enough energy to leave the gravitational field of Earth?
Thanks for your help.
 A: A very approximate back of the envelope calculation.
The escape velocity for an orbiting body is Sqrt(2) x orbital-velocity.
The moon is at radius ~3.84E8 metres so circumference of orbit is ~2.2E9 metres.
One orbit takes ~28 days or 2.0E6 seconds, so orbital velocity is ~1E3 m/s.
We need to increase that by ~4E2 m/s in order for it to achieve escape velocity.
Assuming a body from outer space flies past, we might expect it to be travelling at a minimum of ~10 Km/s relative to the earth/moon (likely much faster in practice), so it will cover tehe earth/moon radial distance in around 38,000 seconds.
Approximating the attraction of the body to the moon to be constant over that time means that the object would have to be continuously accelerating the moon at ~1E-2 m/s^2 over that time in order to accelerate moon by 400 m/s.
From moon's mass (~7E22 kg) and using F=mA, this means that the average force on the moon would need to be ~7E20 N.
Using F=(G x M1 x M2)/r^2 , and an average radial separation of half the earth-moon separation results in a required mass of ~6E24 kg for the body to knock the moon out of orbit.
This is surprisingly close to the earth's mass (5.97E24 kg). It is only a rough approximation - for example, if the body is much closer to the moon then the required mass would fall a bit, but if it was mooving faster then its mass might need to be greater. But it also assumes that the moon/body gravitatiopnal interaction is in a direction to accelerate the moon's velocity throughoutthe entire passage. I believe that my estimated body mass is better than 'order-of-magnitude' accuracy.
