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Can this gravity problem be solved without using the Earth's mass

  1. Mar 15, 2017 #1
    1. The problem statement, all variables and given/known data
    A satellite orbits the Earth in a geosynchronous orbit around the equator, meaning that its period is 24 hours and it stays above the same location on earth at all times. (G = 6.67 x 10⁻¹¹ Nm²/kg².) What is the radius of its orbit?

    2. Relevant equations
    GM/r2 = v2/r = w2r

    3. The attempt at a solution
    I can solve this if the mass of Earth is given but since it isn't I'd like to know if there is a way to solve this without using Earth's mass
     
  2. jcsd
  3. Mar 15, 2017 #2

    kuruman

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    Sometimes you may have to look things up.
     
  4. Mar 15, 2017 #3
    You know that g = GM/re2, rearrange this to give you the expression for M then go from there
     
  5. Mar 15, 2017 #4

    kuruman

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    Sure, but then re needs to be looked up.
     
  6. Mar 16, 2017 #5
    This is true enough and in general I think that re is given in data tables rather than M.(certainly in A level reference tables)
    Also the combination GM usually crops up on both side of gravitational equations and therefore cancel out
    In this example for the Earth gE = GME/rE2 and for the satellite gs = GME/rs2
    This gives gErE2 = gsrs2
    knowing that gs = v2/rs and further substitution enables rs to be calculated.
    If re is not given then an answer can still be obtained in terms of re
     
  7. Mar 17, 2017 #6

    kuruman

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    This is, of course, correct. Perhaps the problem should have asked
    to make things clear.
     
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