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Finding the radius of a satellite

  1. Oct 1, 2009 #1
    Just realized how horrible the thread title is. Sorry, I meant the radius of a satellite's *orbit*

    1. The problem statement, all variables and given/known data

    Two satellites revolve around the Earth. Satellite A has mass m and has an orbit of radius r. Satellite B has mass 6m and an orbit of unknown radius rb. The forces of gravitational attraction between each satellite and the Earth is the same. Find rb.
    Express your answer in terms of r.


    2. Relevant equations

    F=(G(m1m2))/r2

    3. The attempt at a solution

    F1 = F2, where F1 and F2 are the forces of gravity acting on satellite A and B, respectively.

    I equated the formulas for the force of gravity for both satellites because the information given states they are equivalent. I then negated every variable I could - G, m, andmearth, leaving r and rb. It looked like this:

    1/r = 6/rb

    So I multiplied r and rb into the numerators, getting rb=6r. I don't see what I did wrong here, but clearly it isn't right. Please help set me on the right path, and thanks for at least taking the time to read all of this :)
     
  2. jcsd
  3. Oct 1, 2009 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Check your algebra:

    [tex]GMm_a/r_a^2 = GMm_b/r_b^2[/tex]

    does not reduce to 1/ra = 6/rb where mb = 6ma

    AM
     
  4. Oct 1, 2009 #3
    Gah, I see. Radical(6)r

    Thanks a lot for your help
     
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