The gravitational energy of Earth is approximately 0.5(GM 2 E /RE ) where ME is the mass of Earth. This is approximately the energy needed to blow the planet into small fragments (the size of asteroids). How large would an antimatter meteorite the density of nickeliron (ρ = 5 × 103 kg/m3) have to be in order to blow up Earth when it strikes? Compute the energy involved in the particle-antiparticle annihilation and compare it with the total energy in all the nuclear arsenals of the world [~5000 megatons (MT), where 1 MT = 4.2 × 1015 J].
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