# Asteroid on course with planet problem

**1. The problem statement, all variables and given/known data**

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.

**2. Relevant equations**

Conservation AM

Conservation of energy

**3. 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

http://ift.tt/1jqwrRq

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