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Asteroid on course with planet problem

  1. Apr 8, 2014 #1
    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
     
  2. jcsd
  3. Apr 8, 2014 #2
    I assume you mean by "horizontal speed" you are talking about a speed in a direction perpendicular to u. Your last equation equates the blast energy to the total kinetic energy of the asteroid which doesn't sound right.

    And I am not sure why you think angular momentum would apply here. The angular momentum of the earth-asteroid system before the nuclear explosion is zero since it is on a direct course. The explosion does give it an angular momentum but the question is what energy amount is required to cause this?

    My guess is you simply have to find the time to impact and this will give you the required "horizontal" velocity and plug this into the conservation of energy equation:

    total energy of asteroid before explosion = total energy of asteroid at point where s=600km
     
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