No, when you carry through the calculations you will find that in equilibrium the density is monotonic with distance from the asteroid.
One easy way to see this: if there were increased density near the shell without any counterbalancing force attracting them to the shell, then there would be a net flow of particles away from the shell reducing the density. So this cannot be an equilibrium.
There may be transient microscopic density variations, but no macroscopic ones (absent some sort of Maxwell’s Demon).
It is also an incorrect assumption that the motion is nearly radial. At all heights the direction distribution is still uniformly random.
No, when you carry through the calculations you will find that in equilibrium the density is monotonic with distance from the asteroid.
One easy way to see this: if there were increased density near the shell without any counterbalancing force attracting them to the shell, then there would be a net flow of particles away from the shell reducing the density. So this cannot be an equilibrium.
There may be transient microscopic density variations, but no macroscopic ones (absent some sort of Maxwell’s Demon).
It is also an incorrect assumption that the motion is nearly radial. At all heights the direction distribution is still uniformly random.