[Paradox]

As for the energy transfer, the energetic particles of the bomb itself would transfer their energy to the matter of the asteroid, and since it's vacuum on one side, and rock on the other, the explosive vaporization would be on the side of the bomb blast, producing a massive short-term thrust along the rough line of the original blast. It's all Newtonian physics from there (g)

Actually, much of the energy transfer would be in the vaporization of the surface of the asteroid that is exposed to the blast (via radiation). This vaporization would lead to a "jet" of sorts, nudging the asteroid. 'least dats what I reads...

[Salgak]

That's what I said. The energetic photons from the bomb would be absorbed by the matter of the asteroid, thus imparting energy to it. The net effect of the energy input is conversion from gamma energetic photons to heat, resulting in explosive vaporization, and thus, thrust. I was just getting down to detail on the energy transfer mechanism. . .