I’d like to point to a frequent mistake made by many celebrity physics professors, who keep telling us this on the Discovery Channel, National Geographic Channel, and other broadcast channels. It’s more ignorance than a mistake. Doesn’t really matter that many movie directors in Hollywood agree with them.
They say God forbid smashing an incoming asteroid with a big nuclear bomb! That the parts of a broken asteroid are even more dangerous. That many more pieces will be hitting us, better to leave it in one big chunk.
Well, this is baloney. Maybe if we decided to detonate very near our planet. In which case no method would work anyway. But if we destroy the asteroid far away from us, many years and many billion kilometers before the scheduled impact, then it poses no danger whatsoever.
The gravity center of the asteroid could still meet us here. But it will be an empty center made of cold interplanetary vacuum from which all the pieces will have already escaped. This is called the Conservation of Momentum. It would be incredibly hard to keep a smaller piece of the exploded asteroid in the old orbit. Of the original rock merely a bunch of spin off trajectories, less dangerous than the average asteroid would remain.
You can imagine the Halley comet splitting into only two smaller parts because of an internal explosion. Let’s say that before the explosion, Haley is 10 years from smashing into Mars. The two orbits after dividing will both be very different from the old one. Neither one will hit Mars. The same holds for any number of parts an explosion could make.
Next time, just send a big H bomb toward the incoming comet! Don’t worry about small pieces, they will be million of miles away.