> Nuclear weapons will destroy a ship if they detonate exceedingly close to it. But if it is further away than about a kilometer, it won't do much more than singe the paint job and blind a few sensors. And in space a kilometer is pretty close range.
> Please understand: I am NOT saying that nuclear warheads are ineffective. I am saying that the amount of damage they inflict falls off very rapidly with increasing range. At least much more rapidly than with the same sized warhead detonated in an atmosphere.
> But if the nuke goes off one meter from your ship, your ship will probably be vaporized. Atmosphere or no.
Imagine a large combined bomb and asteroid at rest before it explodes, so combined momentum has to stay at zero after.
If explosion happens when not combined, particles from the bomb hit the asteroid and transfer their momentum to the rocket.
Nuclear weapons can do interesting things like fusion, but it isn't going to create persistent mass when detonated.
The actual proposed weapon was a W25, with a yield of 1.7 kilotons. That size of weapon is so small may non-nuclear explosions eclipse it.