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The biggest misconceptions about the various approaches seems to be the understanding of how explosives work in space. Explosives get their power from pressure waves. Pressure waves are the compression of air/gas. There is no air in space thus there are no pressure waves and no 'explosions'. BUT there may be water/ice in the asteroid (lets face it rubble piles are glued together with ices) so some amount of expansion is expected due to heating. Now I admit that I am no expert but this is how it was explained to me by various scientists in the bis.....
What explosives will do is generate heat. Heat will evaporate material and the radiation/evaporation of material will have an impulse effect on the asteroid BUT it is slow and weak process (ie think YORP and Yarcovsky effects) - it is not an instantaneous effect. We then need to consider what effect such an approach will have on a rotating body. Equatorial placement then perhaps is of little value but placement on the poles are an option.
Of course the explosive does not need to be buried and to avoid any chance of shattering the asteroid (heating/expansion of gases on a monolithic asteroid - as opposed to rubble piles which can withstand almost any impact energy) a surface or above surface detonation is idea and real option. And, of course, it needs to be done long before the asteroid is going to hit us. This does NOT mean a long distance from us - ie it can be done on an earlier orbit when it is close to us.
The real problem cases are the objects we plot an impact trajectory on their first apparition. Probably not a lot we can do with these at the moment since, by the time we have calculated the orbit precisely enough to know it's an impactor, it will be too close to do anything about.
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