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- Exorcet
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An atomic explosion in vacuum creates a relatively small extremely hot bubble with a lot of radiation. A little sun for the fraction of a second. And thats it.
Which heats the surface of nearby bodies, possibly to the point of surface vaporization, turning the target body into a kind of rocket.
You can combine this with surface impacts to increase the efficiency of nuclear steering by directing the blast with the shape of the object itself.
You can do more than that, including destroying the asteroid outright (although I don't know the range on size that makes this applicable). If you plant the bomb under the surface, all the energy is transferred to the asteroid.There is no blast wave that tears apart stuff like here on earth. The best you can do is cook the asteroid a little.
NASA doesn't use anything, no one has tried steering asteroids as of yet.Thats why NASA uses impactors and not bombs, projectiles with a lot of mass and speed, and you can only destroy little asteroids with that. Big ones need to be deflected with such device.