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jj975
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Homework Statement
A asteroid of mass m=5*10^20 kg , speed u=10km/s is on a direct course to hit earth. If nuclear weapons are used to split it into two equal pieces at a distance away of the moon's orbit, d, what is the minimum energy required for each half to miss Earth by s=600km.
Homework Equations
Conservation AM
Conservation of energy
The Attempt at a Solution
Let the asteroid have initial horizontal speed v0 (from the blast) and speed v normal to the radial direction at its closest point to the earth
Let the Earth have radius R, mass M
Conservation of angular momentum: m(v0)d=mv(R+d)
Conservation of energy: m/2 (u^2+(v0)^2) - GMm/d = m/2 v^2-GMm/(R+s)
Solving these yields m/2*u^2 = (m/2*u^2+GMm/(R+s)-GMm/d)/(d^2/(R+s)^2-1) = Eblast
After substituting numbers this gives a ridiculously high energy. Does this look like a correct method? Thanks in advance