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Satellites, Orbits and Gravitational Energy

  1. Apr 9, 2009 #1

    Two satellites, A and B, both of mass m = 110 kg, move in the same circular orbit of radius r = 7.45 x 10^6 m around Earth but in opposite senses of rotation and therefore on a collision course.

    (a) What is the total mechanical energy EA + EB of the two satellites + Earth system before the collision?

    (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass=2m), what is the total mechanical energy immediately after the collision?




    U = -GMm/r
    K = -GMm/2r



    Total E = U + K

    U is the Earth system's energy, K is the satellites' energy
    There are 2 satellites for (a), so I figure m = 2m
    r is radius of earth + radius of orbit

    E = -GMm/2r
    E = -GM(2)m
    E = -6.67e-11 * 5.98e24 * 2(110) / (6.38e6 + 7.54e6)
    E = -6344939986 J

    For part (b), since m also equals 2m, I also get
    -6344939986 J


    Is there anything wrong? Because my online thing isn't accepting my answer...
     
  2. jcsd
  3. Apr 10, 2009 #2

    D H

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    Staff Emeritus
    Science Advisor

    You have several things wrong here.
    1. K = -GMm/2r
      Kinetic energy, 1/2mv2, is always positive.

    2. 6.38e6 + 7.54e6
      Your problem statement indicates r=7.54e6 meters is the orbital radius, not the orbital altitude. Which is correct?

    3. For part (b), since m also equals 2m, I also get -6344939986 J
      What is the kinetic energy after the collision?
     
  4. Apr 10, 2009 #3
    Thanks---Your hints worked!
     
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