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Period of an orbiting object?

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data
    At what distance about Earth would a satellite have a period of 125 min?
    G=6.673x10^-11
    T=125 Min
    Mass=5.97x10^24
    Radius of Earth=6.38*10^6
    2. Relevant equations
    T=2pi*Square root of (R^3/constant*mass)


    3. The attempt at a solution
    125=2*3.14*Square root of ((6.38x10^6)^3+R^3/6.673x10^-11*5.97x10^24)
    I got a negative #.... Which i know is wrong!
     
  2. jcsd
  3. Dec 4, 2008 #2

    mgb_phys

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    Put the units in - it will help !
     
  4. Dec 4, 2008 #3
    I did that, but still got an unreasonable answer: 2.6x10^26
     
  5. Dec 4, 2008 #4

    mgb_phys

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    T=2pi*sqrt(R^3/GM)
    so T/2pi = sqrt(R^3/GM)
    Square both sides (T/2pi)^2 = R^3/GM
    Finally R = cube root ( GM * (T/2pi)^2 )

    Check the units (m^3 kg^01 s^-2 * kg * s^2)^1/3 = (m^3 )^1/3 = m
     
  6. Dec 4, 2008 #5
    Is the answer 106.6 KM? Thanks so much for the explanations by the way!
     
  7. Dec 4, 2008 #6

    mgb_phys

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    I think you have a slight mistype there, do you have T in seconds?
    Remember that the result is the radius of the orbit from the centre of the Earth - if you want the altitude you need to subtract the radius of the Earth.
     
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