The idea to nuke asteroids in an attempt to alter their trajectory is dumb. Scientists believe that a nuke in outer space creates a shockwave that pushes an asteroid into another direction.
Well, I have news for you, in the vacuum of outer space, shockwaves are not possible. You’d need a common carrier such as an atmosphere or a fluid of any kind to hold a shockwave. And in outer space, regardless of the presence of dark matter, no shockwave can be generated within the required parameters of pressure and direction.
Moreover, if a nuke missile cuts an asteroid into pieces, then you’d end up with many smaller asteroids. And they all keep moving into the original direction. That is way different from what you have seen in some movies. A nuclear blast in the vacuum of outer space will not work the way it does in an atmospheric environment. It simply radiates some heat and isotopes but it has certainly no push effect. And a few seconds heat up of an asteroid is pretty useless in space where the average temperature is near the absolute zero Kelvin.
Even scientists have been watching too many sci-fi movies, and so ending-up with irrealistic ideas about nuking asteroids.
Another very dumb idea of very dumb scientists is to move a spaceship nearby an asteroid as to use the asteroid’s gravity as a tractor beam connected to the spaceship. So where the spaceship goes, the asteroid goes. This is one of the dumbest ideas ever recorded in scientific history. Gravity is not the same as magnetism. And the mass of an asteroid is far greater than the mass of a spaceship, therefore – even if there is a tractor beam of some sort – the asteroid having the greater mass is leading. A bicycle riding next to a truck will not cause the truck go off-road, mind you! Check this with your physics professor.
If you really want to change the direction of an asteroid, then rather send an impactor to attach to the asteroid. That impactor contains a directional emanation source (read: rocket) that produces enough thrust to alter the asteroids trajectory. So basically you fix a vectoring engine onto the asteroid. Now the asteroid has become a steerable spaceship. A single nuclear blast is never enough, simply because of the enormous mass & speed of the asteroid and because no pressure wave is generated. A continuous directional force vector must be active, just like a steering rocket of a space vessel. The time lapse may span perhaps up to a year, but certainly not a few seconds burst. To change a trajectory takes a lot more than that. It is in space, where physics is quite different from that on Earth.
As an alternative, you’d have to install nukes inside of the asteroid at sweet locations and detonate all of them exactly the same moment. The asteroid will break-up but the trajectory will not change, because there is no shockwave that pushes away debris.
All in all, the idea of nuking an asteroid with missiles is a bit off. And please, “scientists”, go take some course in space physics. At a real school, in the Far East for example, NOT in the US or Europe, because there the schools appear too stigmatic in this discipline.