The science that is being used here is; a few paint ball pellets get shot at the asteroid (the object is not to break off pieces that create different problems), the surface becomes covered which the paint-an estimated 5 micrometers worth. The cumulative effect of the solar radiation pressure should cause it to move to a different trajectory. Of course it could take 20 years. So that project I spoke of with the Sentinel would definitely have to be employed so we do not wait too long!
Of course while we are shooting paint at asteroids we might want to consider what else that might do. Anything in Space becomes a weapon. The best weapons or the things that cause the most damage aren’t necessarily lasers and nukes, but the simpler things pack more of a whallop and have a more destructive effect!
Think of the Enterprise chasing the Romulans in space. They fire their lasers, not bad, but now picture then firing some sort of projectile that causes results in hypervelocity and that means it would basically liquefy or vaporize its target. And it was cheaper to fire! And it doesn’t have to be a big size of a Volvo “bullet” it could be a bowling ball or a baseball or a pebble.
So, what are we to do?.....Well there is Deflection, or maybe fragmentation. The concern with deflection in this case is that many of the Asteroids are really just piles of rubble held together by gravity. A deflection attempt might result in just breaking it up without significantly altering its course. Fragmenting it isn’t much better if any of those fragments are more 35mm as they would not burn up in the atmosphere. Plus just try and track all 30 thousand individual pieces! Often the smaller impacts cause greater damage then the larger.
I don’t usually think a nuclear bomb is the answer but against some rubble piles it just may be. If it were delivered to it and penetrated to its center it would explode sending fragments in all directions, thus reducing the amount of material reaching the Earth. If we were really smart in how we placed it the surface area of the threat could be made such that enough of the pieces will burn up harmlessly high in the atmosphere. So there is no easy answer. Right now the best bet is to take it on a case by case basis as it is likely as time proceeds so will our abilities to alter it, heck maybe even utilize some of the loopholes from an FTL drive to make it skip various positions in space.