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Trouble working out the GM product of Earth: u = GM.

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Don't laugh! I am scratching my head. Somewhere I am doing something very stupid, but I just don't know where. My problem is that my result of G*M of Earth is different than the accepted result of G*M.

    Accepted value of G*M: μ = 398600 km^3 s^-2



    2. Relevant equations

    μ = GM

    G = 6.673*10^-11 N m^2 kg^-2

    M (Earth) = 5.977*10^24 kg



    3. The attempt at a solution

    μ = GM = 6.673*10^-11 * 5.977*10^24 = 3.9884521*10^14

    So my results show μ = 3.9884521*10^14, while the accepted results give 3.986*10^8 (after allowing for the km to m conversion)

    Where have all my extra zeros come from??! I am sure this is something really stupid.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 4, 2012 #2
    It looks like a conversion error. Wikipedia gives 398,600.44 km3s−2. To get the value in m3s−2 you need to multiply by (1000 m/km)3. I suspect you forgot the cube.
     
  4. Feb 4, 2012 #3

    D H

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    There are 1000 meters in a kilometer, so 10002=106 square meters in a square kilometer, 10003=109 cubic meters in a cubic kilometer.

    You are dividing by 106 when you should be dividing by 109.
     
  5. Feb 4, 2012 #4
    Ah, ok, so my problem here appears to lie with my grappling with the units. My answer comes out as 3.9884521*10^14 m^3 s^-2 (metres!) so, if I converted that into km^3 s^-2 I would have to divide that by 1000^3, thereby ending up with the accepted value! This would explain my confusion... schoolboy error...:rolleyes:

    Thanks a lot guys!
     
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