Net result is that if we know long enough in advance, a couple well placed nukes could nudge the orbit.
But we can't be blindsided by something and only have a weeks time to work on it.
te problem is that in the '70's we didn'y know much about the structure of asteroids. A nuke may nudge it, or it may shatter it so we get carpet bombed by dozens of smaller asteroids. The current thinking is that some, possibly many, asteroids may be more like giant gravel piles losely held together by gravity than solid, hard objects. You blow them up and gravity just re-condenses them. It's better to find a gentle way of steering them than hitting them with a hammer. Sending astronauts there is a good first step in learning more about these objects and how we can manipulate their course.
If they are just packed rubble...nuking them won't require a landing, and will have a good vaporization profile.
Its a choice between a slug or buckshot.
If that was the case, it would make sense that the asteroid might fragment upon entry to the atmosphere, then the smaller pieces with greater surface exposure could burn up, or at least dissipate some energy.
You blow them up and gravity just re-condenses them.
In time, yes. But wouldn't inertial forces from an explosion cause the pieces to move away from each other until acceleration (or deceleration) of gravity cause the imparted motion to reverse, then reassemble? Seems that would take a long time, perhaps enough to reach the earth's orbital plane. Insert obligatory Holiday Inn Express reference here.
It appears that once asteroids are blown up they stay blown up and eventually form a meteor swarm. No such asteroids have been observed to reassemble themselves.