I think the proof shows that these kinds of systems can be stable without any rebalancing for very long periods of time but then suddenly they are not.
no way. Earth orbital speed is 20,000 m/s. Meteroites are about the same speed. Earth mass is 10^25, total meteorite mass / day is 44t, or about 4x10^4.
Generously assuming all meteorites hit from the same direction, given the mass of the meteorite swarm is 1e-21 smaller, the total delta v is 10 to the minus 16. Double integrate that, and you get x^2/20000000000000000
Set equal to your desired difference, say one meter. You get over 100,000,000 days. That's 273,973 years to affect a 1 meter difference in position in the worst case.
