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Satellite velocity and momentum

  1. Nov 5, 2009 #1
    1. The problem statement, all variables and given/known data
    A satellite moves around the Earth in a circular orbit of radius r.
    a) What is the speed vo of the satellite?
    Suddenly an explosion breaks the satellite into two pieces, with masses m and 4m. Immediately after the explosion the smaller piece of mass m is stationary with respect to the Earth and falls directly toward the Earth.
    b)What is the speed vi of the larger piece immediately after the explosion?
    c) Because of the increase in its speed this larger piece now moves in a new elliptical orbit. Find its distance away from the center of the Earth when it reaches the other end of the ellipse.


    2. Relevant equations
    K=.5mv^2
    E=-GMm/2r
    mv=mv
    E=-GMm/2a



    3. The attempt at a solution
    a) I think I got the answer to a:
    .5mv^2=GMm/2r
    v=sqrt(GM/r)
    Then substituting in the values of G and M (Mass of the Earth):
    v=1.99x10^7/sqrt(r)

    b) I am having trouble with this because I don't know if I can simply use linear momentum. If so then I can just assume that the smaller mass has no momentum in relation to the first.
    mv=mv
    5m(vo)=4m(vi)
    (5/4)vo=vi
    Is it really that simple?

    c) I'm kind of shooting in the dark with this one, but can I assume that the energy initially (GM(5m)/2r) is going to equal the second energy (GM(4m)/2a?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 5, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    OK, but I wouldn't bother plugging in numerical values. Leave your answer in terms of G, M, and r.

    Yes, that simple.

    Compare the energy of the masses before and after the explosion.
     
  4. Nov 5, 2009 #3
    what do you mean compare the energies?
    the energy before: .5m(vo)^2 - GM(5m)/2r
    the energy after: .5m(vi)^2 - GM(4m)/2a

    where do i go from there?
     
  5. Nov 6, 2009 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Express the total energy immediately after the explosion in terms of the energy before the collision. Then use that new energy to solve for length of the new orbit.
     
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