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Realistically, I think our fate lies in early detection more than any other factor.
Also, the slow deflection method sounds most practical to me.
The idea of using thermonuclear detonation to destroy an inbound asteroid seems too risky. IMO, you run the risk of fracturing a 5km asteroid into two 2.5km asteroids, without substantially altering the course of either.
Why not fly a spacecraft out to the incoming rock, land on it and use solar sails and / or a series of solid-fuel booster to alter the course of the asteroid?
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