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Finding radius of satellite in orbit given mass and rotational period

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data

    Suppose that Captain Omega of the Imperial Space Patrol wishes to place a spy satellite in geosynchronous orbit above the mysterious Planet X, which has a mass of 5.90 x1024 kg, and a rotational period of 26.4 hours.

    (a) What should be the radius of the satellite's orbit?
    (b) What would be the orbital speed of the satellite?


    2. Relevant equations



    3. The attempt at a solution

    I used the law of periods : T2/r3 = 4∏2/GM

    So I rearranged that to get:

    r = (GMT2 / 4∏2) 1/3

    I plugged in:
    G = 6.67 e -11
    M = 5.9 e 24 kg
    T = 95040s

    I ended up with 2.06e8 m = 2.06e5 km

    But that answer isn't right and I don't understand what I'm doing wrong.
     
  2. jcsd
  3. Oct 19, 2011 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    I plug in your numbers to your formula and I get a different answer. You must have forgot a step in your arithmetic.
     
  4. Oct 19, 2011 #3
    Thank you! I'm not sure what I was doing wrong..mistake while entering in the calculator I guess!
     
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