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Distance from Satellite to Earth Question

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data
    A satellite in a circular orbit around Earth has a speed of 7.15x103 m/s. Determine, in terms of Earth's radius (radius of earth= 6.38 x106m):

    a) the distance the satellite is from Earth's centre
    b) the altitiude of the satellite

    2. Relevant equations
    FG = GMm / r2
    Fc = mv2 / r
    G = 6.67 x 10-11

    3. The attempt at a solution
    I'm seriously unsure on how to even start on this one, because I'm not sure what they mean by 'in terms of Earth's radius.' The answer key says 1.22 rearth for a. Do you have to do this through proportionality and ratios?

    In terms of writing down the given/known:
    v = 7.15 x 103 m/s
    rearth = 6.38 x 106 m
    Mearth = 5.98 x 1024 kg
    G = 6.67 x 10-11 Nm2/kg2

    I can't figure out the force of gravity because I don't have the mass of the satellite, so that cancels out finding Fc as well since I need the mass for that too.

    Any help on how to start this would be appreciated, thank you.
  2. jcsd
  3. Nov 12, 2008 #2


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    Homework Helper

    You won't need the mass of the satellite.

    Fc = mv2/r = Fg = GMm/r2

    v2 = GM/r
  4. Nov 12, 2008 #3
    Oh, I see. But I'm still confused by "in terms of Earth's radius," what exactly do they mean by that?
    By the way, I used v2 = GM /r to find that r = 5.58 x 1010 Would that be the radius from the Earth's centre to the satellite?
    Thanks for your help
  5. Nov 12, 2008 #4


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    Staff Emeritus
    Science Advisor
    Gold Member

    In terms of Earth's radius means how many multiples of the Earth's radius is the satellite orbiting at.
  6. Nov 12, 2008 #5
    Ah, I got it now. Thanks for the help Kurdt and LowlyPion.
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