I read one of the related questions here, but what i'm curious to know is how do we deflect imminent collision courses of comets, if we detect them at a later stage? I read somewhere else that there are systems which use powerful lasers (radiation pressure) to deflect them, but honestly, i don't understand why something like radiation pressure will work on something travelling at about 40km/s through space, and still manage to cause a large enough deflection. Are there other methods ?
Fortunately it is not something that we have yet had to face.
Diverting the impact of a comet would not be easy, especially if it was a newly discovered comet on a nearly parabolic orbit. We would probably have less than 2 years to prepare.
Remember that the Earth is orbiting the sun at 30 km/s. So if we can delay the comet by three or four minutes, that turns a direct hit into a miss. But most of the plans to divert objects apply to asteroids whose orbit is well known and for which we could have tens of years in which to act. For a new comet there may not be time.
Difficulty is hard to say, but the reason a laser might work is because the laser is supposed to melt one side of the comet, which, as it melts, gas particles fly off at relatively high velocity, which redirects the momentum of the comet somewhat. It's not the pressure from the laser, it's the heat from the laser and the fact that comets are made largely from ice, which can be melted or "zapped" into fast moving jets of gas.
The approach wouldn't be a laser on or orbiting Earth shooting comets from a great distance but spacecrafts flying up close to the comet and using lasers to target one side. It would be difficult to fire a laser so pinpoint as to target one side of the comet from earth and create localized heat that would create the necessary directional out-gassing. This article proposes spacecraft, perhaps several, flying adjacent to the comet.
A nuclear weapon would be way more effective, however, depending on how fast we'd needed to push it. This article mentions a pulse laser landing on the comet or asteroid as well as other methods that might work.
Space is really very empty and large. The Earth moves one radius in orbit every 3½ minutes. There are half a million minutes per year. So a pretty tiny push is enough to make the difference between a hit and a miss, given that there are a few years' warning and prompt action.