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Universal Gravity Circular Orbit

  1. Nov 7, 2012 #1
    1. The problem statement, all variables and given/known data
    What is the radius of a circular orbit about the earth where the acceleration is 0.1g?

    2. Relevant equations
    g=9.8m/s^2
    F=(Gmm)/r^2
    Radius of Earth= 6.38x103 km
    Mass of Earth= 5.98x10^24 m/s

    3. The attempt at a solution
    I said 1/(2^x)=1/10 then did log2(10)=x and solved for x getting 3.3 earth radiuses. I multiplied that by the radius of the earth and got 21,000 m. This was obviously the wrong method.
     
  2. jcsd
  3. Nov 8, 2012 #2
    Your method seems correct, but the equations seems all messed up (not sure why you use logs to the base 2?):
    r2 = 10 R2
    so that
    r = √10 R
    Your answer seems sligthly off.
    Also Halliday and Resnick lists R as 6.37 which then gives r as 20 x 106 m.
     
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