It seems to this clueless-layman that if we resorted to a nuclear explosion in an attempt to divert an asteroid, the detonation would need to be as far away from earth as possible. Even then, we we might still have a potentially destructive meteor shower raining down on us from the fragments — fragments of all sizes — with the added bonus that it would now be highly radioactive.
Maybe I’m wrong and they have it all figured out. I mean, with the 0bama administration meddling in the effort for political reasons, what could we possibly have to worry about?
Spend a few minutes with Google and Wikipedia and a spreadsheet... Lets pick asteroid 48 Doris. Good sized beast at 222 km dia and 12x10^18 kg mass. Ok, she's a little big. Lets say we go with one 1/10th as massive, at around 103 km dia (64 miles) and only 1.2x10^18 kg mass.
Typical impact velocities for asteroids are supposed to be 17 km/sec. So lets say we plan to intercept our Earth-killer out there at oh, twice as far away as the moon. That'll give us plenty of time to divert it, right? After all, we don't want to simply blow it apart - then we'll just get hit by roughly the same mass just spread out more. (shotgun pellets vs .45 slug - still going to hurt!)
Twice as far away as the moon is roughly 768,000 km. So if our girl is booking along at 17 km/s we've got over 45,000 seconds to push on her to divert her. Hmm, that's only 12.5 hrs.
The diameter of the Earth is a little over 12,000 km. So lets say she's going to hit dead center. So we need to move her say 7000 km to the side in 12 hrs or so. Distance being one half acceleration times time squared... Hey great, we only need to accelerate this beast to the side at 0.0069 meters per second squared. That's nothing, heck gravity is a whopping 9.8 m/s/s in comparison...
But wait, this beast is fairly massive. Force equals mass times acceleration... Turns out we need to push on her with a force of 8.3x10^15 kg/m/s/s (newtons) or 1.85x10^15 lbs (force). That's 1.85 million, trillion lbs. (930 trillion tons) That's a ridiculous amount of force.
Now, you get no real push in space from a nuclear detonation. You get energy release. So maybe a few mega ton blast can vaporize a few square miles of material down to a few feet. This energetic material flies off into space, pushing against the asteroid. (action/reaction) But that's at best going to be in the neighborhood of a few thousand tons of force. (don't have time this AM to work that out, so I'm guest-i-mating here) Looks like you'd need thousands of multi-megaton bombs going off beside it continuously for 12 hrs to move it...
You can gain some numerical advantages by going out - way out. The further out you intercept, the more time you have, the less acceleration (ie. force) you need to divert its path. But still, looks like a problem we may not have the technology to solve just yet.