Is a fact that Earth is entering in a space where the asteroid activity is increasing, and some meteorites that were not detected at the time have passed very close to Earth (luckily), or in the worst case hit the planet causing more than 1000 deaths (Russia incident). For that reason I’m proposing the idea of building a Railgun on the International Space Station. It won’t be easy, cheap or safe but I think it's worth the effort.
First we have to consider how we are going to harvest the huge amount of energy. One option could be a nuclear reactor. Considering that in space there is a lot more gamma radiation, produced by the sun, than in any nuclear reactor made by mankind, it won’t be a problem. Also, if the reactor goes unstable, it won’t blow up by the absence of air, it only will radiate heat energy and gamma radiation. By the other hand we can set up a gas cycle (Rankine Cycle) To harvest the heat produced by the sun, concentrating this radiation to heat up pipelines which will contain a transfer fluid, that will be sent to a turbine to produce electric energy and the remanent heat can be used to keep crew warm or disposed to the space, returning it to the compressor. (See fig 1).
Second thing to consider is how to store the energy to be used when it is needed. In this case the best way is using what we know as supercapacitors, which works with low voltage and have capacitances 3000 Farads and higher, or we can use thin aluminium foils with very small gap between them, using the space vacuum as an electrical insulator. The difference between the super capacitors and aluminium foils are the sizes. The Supercapacitors store more energy per volume than common capacitors. For this case, the calculation must be done but the important thing is that technology exists. (See Fig. 2)
By last, we need to consider the railgun and projectile. To cause a change in direction on an asteroid in the space, mass and energy matter. So, the projectile must be made from heavy material (Lead or depleted uranium) plus I consider that inside it might carry two nuclear masses, in order when they hit the target and penetration begins, the masses fuse together achieving critical mass and, with the high pressures of impact, start the nuclear chain reaction inside the asteroid.
According to conservation of energy, the heat produced must be absorbed by the asteroid, causing a changing of state of the matter (solid - liquid - gas), causing an expansion that could cause a crack or a change of direction in the asteroid.
Fearing that when it is fired it could cause a recoil, it won’t. (See fig. 3) But it might interact with Earth's magnetic fields, causing a dangerous rotation. This interaction could be mitigated using common space maneuvering system.
For more information and critics see my blog http://mscienceworkshop.blogspot.com/