When a nuclear bomb explodes it heats up the air surrounding it and a destructing shock wave is generated. Consider the same bomb exploding in space. This would be the case for example if we tried to blow up an incoming asteroid with nukes. How effective would they be in the vacuum of space?
[Physics] How effective are nuclear weapons in space
nuclear-physics
Best Answer
Not quite as effective.
We can separate the effects of a nuclear weapon into three main categories:
The first effect relies on there being some medium to conduct them - namely, air. Space is not a perfect vacuum, but obviously it is a pretty close approximation. Therefore, the blast and will be essentially nonexistent.
Thermal radiation is emitted In the ultraviolet, visible, and infrared portions of the electromagnetic spectrum. Some of it is absorbed and reradiated by the atmosphere, while other penetrates this and causes radiation burns. In space, this effect will still exist, and may be at an increased intensity.
Nuclear radiation, however, will behave differently. With no atmosphere to scatter or dilute it, its intensity will be greater at most distances than if there was an atmosphere. In some cases, this can be quite substantial.
Here is a graph of the intensity of the blast wave from a 20 kiloton explosion at sea level and in space (courtesy of NASA):
Source: Nuclear Weapon Effects in Space
Most of the energy of the explosion goes into the first two categories; this means that the explosion of a nuclear weapon in space will be less effective when compared with an explosion on Earth.
For an interesting theoretical treatment of the blast wave, you could try using the Sedov-Taylor solution, often used to model supernovae explosions. It can give the speed and temperature of the shock front at a given time and radius. The radius $R$ at some time $t$ in a medium of density $n$ is given by $$R\propto n^{-1/5}t^{2/5}$$