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Work done by a force changing the distance of a satellite's orbit

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data

    A 5530-kg satellite is in a circular earth orbit that has a radius of 1.81 × 10^7 m. A net external force must act on the satellite to make it change to a circular orbit that has a radius of 8.01 × 10^6 m. What work must the net external force do?

    2. Relevant equations

    Orbital Speed:
    v = sqrt( G * M_e / r )
    where G is the gravitational constant and M_e is earth's mass

    Work-Kinetic Energy Theorem:
    W = K_f - K_i = .5*m*v_f^2 - .5*m*v_i^2

    3. The attempt at a solution

    v_i = sqrt( 6.674e-11 * 5.98e24kg / 1.81e7m )
    v_i = 4695.74m/s

    v_f = sqrt( 6.674e-11 * 5.98e24kg / 8.01e6m )
    v_f = 7058.74m/s

    W = .5*m*v_f^2 - .5*m*v_i^2
    W = .5*5530kg*7058.74m/s^2 - .5*5530kg*4695.74m/s^2
    W = 7.68002e10J
     
    Last edited: Nov 2, 2011
  2. jcsd
  3. Nov 2, 2011 #2

    Simon Bridge

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    Work = change in energy.
     
  4. Nov 2, 2011 #3
    I incorrectly found the work to be the difference between the initial and final kinetic energies above.
     
  5. Nov 3, 2011 #4

    Simon Bridge

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    Are there other forms of energy present?
     
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