The Collisional Evolution of Asteroids

Look at these pieces of evidence:

Asteroids are heavily cratered.
Asteroids must have a way of generating moons.

Hmm....

Add a few other pieces of evidence:

1. Asteroids have orbits which take them well out of the asteroid belt.

Something must have deflected them off their orbits.

These orbits give a heightened chance of collisions.

2. Some asteroids come in orbital families (Hirayama Families), where groups of asteroids all have similar orbital elements.
3. Asteroid densities are often significantly lower than the density of their compositional elements.

What does this suggest about their structure?

So where does that leave us?

Collisions of Asteroids

The velocity dispersion in the asteroid belt is a few km/s. This means typical collisional velocities will be a few km/s -- enough to fragment asteroids.
The fragments will have velocities (relative to the original asteroid) of 0.1 - 1 km/s.

If the fragment velocity exceeds the escape velocity of the asteroid, the asteroid won't reform. But these velocities are much less than the orbital velocity of the asteroid, so they will stay more or less on the same orbit, generating a new Hirayama Family.

If the fragment velocities are less than the escape velocity, the asteroid can reassemble as a "rubble pile."

In either case, fragments can settle into orbit around one another, forming a new asteroid/moon pair.