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Help with gravitational potential energy problem

  1. Nov 13, 2009 #1
    1. The problem statement, all variables and given/known data

    (a) Determine the energy, in kW·h, necessary to place a 1.0-kg object in low-Earth orbit. In low-Earth orbit, the height of the object above the surface of Earth is much smaller than Earth's radius. Take the orbital height to be 300 km.

    G = 6.67*10^-11
    Me = 5.97*10^24
    Re = 6.37*10^6
    m = 1
    Ro = 300000


    2. Relevant equations

    E = K + U

    U = (G*Me*m)/r

    K = .5U

    3. The attempt at a solution

    What I've done is plugged in all known variables into E = K + U where r = Re + Ro. I get a final answer of 29850000J. Converting to kWh using 1 kWh = 3600000J, I get 8.29kWh. According to the book, this is incorrect. My number should be 8.7kWh. I have plugged this number into my online homework site, and it is incorrect. Can someone tell me what I'm not doing correctly?
     
  2. jcsd
  3. Nov 13, 2009 #2

    rl.bhat

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    Homework Helper

    Initial PE = G*Me*m/R
    Final PE = G*Me*m/(R+h)
    KE = Final PE - Initial PE
     
  4. Nov 13, 2009 #3

    Delphi51

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    Homework Helper

    I'm getting 9.07 KWH. It would certainly be interesting to compare our solutions and perhaps correct them both!
    I used Fc = Fg
    mv²/R = GMm/R²
    v² = GM/R
    K = .5mGM/R = 2.985 E07 J.

    For the potential energy needed to lift from radius r to R I used
    U = GMm/r - GMm/R = GMm(1/r - 1/R) = 2.81 E06 J.
    Total of 3.27 E07 Joules.

    Oh, I forgot the initial kinetic energy! Thanks once again to rl.bhat.
     
  5. Nov 13, 2009 #4
    Thanks guys!
     
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