The Last-Ditch Nuke

I think the analysis in the video below is fundamentally flawed. It may be a case of simplifying things beyond their breaking point.

I checked his numbers, and his estimates for the size, mass and energy of the asteroid all seem sound. I'm not so sure about the size of the nuke you'd need to blast the asteroid to bits though. In principle you just want to accelerate the entire mass up to its escape velocity, in this case 5 m/s. That's only 3 megatons of TNT, not 100, though he does specify you want it to expand at 100 km/h, which is indeed about 100 megatons.

The first problem is that you're probably going to need a lot more energy to break the asteroid apart than this. For starters 100 megatons is only equivalent to raising the asteroid's temperature by about 0.5 degrees, assuming a specific heat capacity equivalent to basalt (this isn't going to affect things by more than a factor of a few). But you also need to break up the rock into pieces, and I can't remember how to calculate the energy needed to do that. I'm willing to bet it's quite a lot.

But let's assume that the nuke does have the power to do this. At 100 km/h, in 24 hours the debris cloud will only be 2400 km in radius, considerably smaller than the 6371 km radius of the Earth. Never mind, that's not a huge difference so let's assume the Earth really does receive a rain of gravel-sized debris over 24 hours (though we might wonder why this should be - if the nuke had gone off just a few days earlier the cloud could be, say, five times the Earth's radius and we'd only absorb 4% percent of the debris !).

I don't think it makes sense to say that since the net KE of the debris cloud is still 2E23 J, the heat received by the Earth will be 2E23 J. Even if that were true, given the mass and heat capacity of the atmosphere it would only raise the temperature by around 40 C, not 1000 C as in the original video or even 100 C as a commenter on YouTube pointed out. 

I think he also calculates the power received by the Earth incorrectly - he's using the area of the surface of the Earth, but I would have thought the cross-section of the Earth to the debris would have been what you'd want. If so, he's underestimating the flux by a factor of two.

But more importantly, this is waaaay too simplistic a way to estimate the change in temperature. First, gravel-sized pellets are going to burn up at >10 km altitude, so it's going to take a while for that heat to penetrate downwards by conduction. Secondly the glowing meteors are going to radiate isotropically, so ~half their energy is going to escape into space. Then, only a fraction of that energy is actually going to be absorbed by the atmosphere and raise its temperature. According to :
http://earthobservatory.nasa.gov/Features/EnergyBalance/page4.php
About 30% is going to be reflected back into space, 23% absorbed and 48% absorbed by the Earth itself.

So given the isotropically radiating meteor, that means only about 0.5x0.2 = 10% of the energy emitted is going to raise the temperature of the atmosphere. Which means we're looking at more like a 4 C rise in temperature. That's certainly going to cause weather chaos, but it's hardly as bad as if the asteroid actually impacted.

Anyway my calculations are also likely similarly naive and simplistic. I really just want to point out that you can't always get away with approximations - the "details" can change the results dramatically. To say nothing as to at what point you could use the nuke to deflect the asteroid instead of blowing it to bits...

For comparison, the Pinatubo volcanic eruption injected about 5 cubic km of material into the atmosphere and it caused a global cooling :
https://en.wikipedia.org/wiki/Mount_Pinatubo#Global_environmental_effects
This asteroid would inject about 100x more material.

So I agree, a last-minute nuke is not what you want to do to avoid an asteroid - but not necessarily because it the asteroid would still heat up the planet. But we are talking about orders of magnitude difference here depending on if you blow up the asteroid a day in advance, a week or  a month. So don't throw out the nukes juuuust yet. 
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