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Planetary collision problem

  1. Sep 24, 2008 #1

    lzh

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

    Given: G = 6.67259 × 10^−11 Nm2/kg2
    Two hypothetical planets of masses 2.5 × 10^23 kg and 7.8×10^23 kg and radii 3.2×10^6 m
    and 7.1×10^6 m, respectively, are at rest when
    they are an infinite distance apart. Because
    of their gravitational attraction, they head
    toward each other on a collision course.

    When their center-to-center separation is
    4.5 × 10^8 m, find their relative velocity. An-
    swer in units of m/s.

    2. Relevant equations
    3. The attempt at a solution

    F=GMm/r^2
    M=7.8e23 kg
    m=2.5e23 kg
    Ki+Ui=Kf+Uf
    r=4.5e8+3.2e6 +7.1e6=460300000m
    0+0=.5mv^2+(-GMm/r)
    .5v^2=GM/r
    v=475.54 m/s


    Is this answer correct?
     
  2. jcsd
  3. Sep 24, 2008 #2

    lzh

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    I just tried to take the velocity from above and added the following:
    v=at
    475.54=at
    F=ma
    F=GMm/r^2
    a=F/m
    475.54/a=t

    then I took the t value and tried to solve the velocity for the M mass. Then I found the difference between the two velocities. However, this is not right....any help is greatly appreciated!
     
  4. Sep 24, 2008 #3

    Dick

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    Science Advisor
    Homework Helper

    In the frame where the origin is the center of mass of the two planets (which is where you should be working), the two planets don't move with equal velocity. They have to have 0 net momentum as well. m*v=M*V.
     
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