I was watching the movie Armageddon and it made me think of a few things. We would probably not need to send a crew to blow the asteroid in two, I think we could still send a warhead with enough power ...
If there are two asteroids $A$ and $B$ of equal mass (and density of 3000kg/m^3), with the same semi major axis of $a=$2.2 AU with asteroid $A$ having a circular orbit and no inclination, and ...
I think I remember a talk where a professor said that Vesta is a particularly important asteroid because its gravity is strong enough to perturb other asteroids. In spite of Vesta's size, this effect ...