Hi, No one has ever successfully made a dent in an icebreg, never mind an asteroid. And it has never been demonstrated that a nuclear explosion in a vaccuum would do much in the way of breaking up an asteroid.
Nuclear bombs , when detonated on earth, were detonated several miles above
ground zero for best effect, and that effect was both heat, and radiation in other spectrums. The intense heat is delivered in a shock wave front , the medium being air. If it was underwater, the medium would be water.
In space................what? the mass of a small suitcase? You might just make a lot of heat. Vaporize the mass in the bomb....80% of the force is radiated in other directions....just what actually tries to deflect or break up
the offending asteroid? ( I welcome opinions ).
Nuclear tests have been done underground, in a situation where the explosion can be moitored , and hopefully (but not always) contained. They drill a hole. Can't do that in space, unlike hollywood.
You might just do better taking some old Shuttle ME tanks and filling them with
water and accelerating them into the asteroid. It might do more good...but.
Perhaps they will one day practice on an asteroid that is no where near collision, and try to nudge it further away, and SEE what difference they make.
Cause and effect and observation. Something to do with scientific method.
Best regards, Dan