# Can the collision of asteroids form another moon?

In the lifetime of the earth, is it possible for sufficient collisions to occur in the asteroid belt to form a prototype moon?

The total mass of the asteroid belt is somewhere between $2.8\times 10^{21}$ to $3.2\times 10^{21}$ kg, about 4% of the mass of the Moon which is $7.3 × 10^{22}$ kg.
Now, we might accept a tiny moon as a moon: consider Phobos (mass $1.07 × 10^{16}$ kg) or the outer moons of Saturn (even less massive). But the asteroid belt is also unlikely to coalesce into a moon. Obviously it has not done so over the past 4.5 billion years of the solar system, and is hence relatively unlikely to do so in the future unless conditions change. The total mass is so small compared to the planets that self-gravity is unlikely to overcome their influence (many of the asteroid families are locked in orbital resonances with Jupiter).