Corrected entry: This movie makes the same mistake several others do about the effects of nuclear explosions. Without an atmosphere, you get a very hot fireball and some radiation. there is no air to create a pressure wave which would blow the asteroid apart. At the most, you have a melted center and maybe the asteroid would collapse on itself if it had enough gravity.
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Correction: The explosion of a nuclear bomb is done by the bomb itself, atmosphere can cause additional damage but isn't necessary for a nuclear bomb to work. The energy released by the chain reaction needs to escape and if its stuck in a tiny space it will break free, thus breaking apart the asteroid down its fault. That's why they drilled the hole in the first place.
lionhead