Is it possible that you could use the force from a nuclear missile to divert an asteroids trajectory? Why does it have to be blown up?
Definitely. It's one of the plans that NASA has, and one of only two considered viable (gravity tractor being the other). The problem, though, is it's something that has to be timed out very well and you need to know about the strength of the target --- which, once again, this test gave us information about --- otherwise you run the risk of fracturing it. Even if you succeed in diverting it, don't break it, but do fracture it, the tidal forces when it comes close to the Earth, or possible the moon depending on it's trajectory, could cause the fracture to break and then the orbit would change. If we were to change an orbit of an NEO, we'd want to change it in a way that is very predictable for a long time.
Still, given the alternative, in the event it is too late for a gravity tractor, it'd most definitely be used, but we'd still need months of warning to make it effective (the closer an NEO is, the harder to change the orbit. A small 1
o change far enough out out would cause the object to easily miss us.)