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Satellite Energy Problem HELP!

  1. Nov 15, 2005 #1
    Hey everyone,

    The following question is giving my friend and I a really hard time. My work is shown below.

    'what is the total amount of energy needed to place a 2.0 x 10^3 kg satellite in circular Earth orbit, at an altitude of 5.0 x 10^2km above the surface of the earth?

    Here are all the numbers needed to carry out the problem:

    M = 5.8 x 10^24 kg (mass of earth)
    m = 5.0 x 10 3 kg (mass of satellite)
    r1 = 6.38 x 10^6 m (radius of earth)
    r2 = 5.0 x 10^5 m + 6.38 x 10^6 m (altitude plus radius of earth)
    G = 6.67 x 10^-11 N/kg. (Earth's gravitational field strength)

    I figured that the energy needed would be equal to the energy of the satellite in orbit minus the energy of the satellite on earth's surface....giving thus:

    E(needed) = -1/2(GMm/r2) - (-GMm/r1)

    where did I go wrong?

    Thx!
     
    Last edited: Nov 15, 2005
  2. jcsd
  3. Nov 15, 2005 #2

    Fermat

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    you have r2 as 500m instead of 500 km.
    Or, is that a typo ?
     
  4. Nov 15, 2005 #3
    uh...oops....lol, thanks man. yea that should be 500 km. i'll edit it out in the first post.
     
  5. Nov 15, 2005 #4
    alright, but it still gives me the wrong answer....the correct one is 6.7 x 10^10 J.
     
  6. Nov 15, 2005 #5

    Fermat

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    Just noticed, where did the -1/2 come from ? is that another typo ?
     
  7. Nov 15, 2005 #6
    the equation for total energy is -1/2(GMm/r2) is it not?
     
  8. Nov 15, 2005 #7

    Fermat

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    Hmm, I got 8.8 x 10^9 J.
    I'll check my working.
     
  9. Nov 15, 2005 #8

    Fermat

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    To be honest, I've never seen that expression.
    I used calculus and got,
    E(needed) = GMm(1/r1 - 1/r2)
     
  10. Nov 15, 2005 #9
    Interesting...using my method I got a similar answer to yours.

    I'm starting to think the answer given to me is wrong. Thanks a lot for all your help man!
     
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