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Homework Help: Show that the satellite's orbital period P at large distances (r a) is given by

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data

    Assuming that the satellite's orbit is circular, show that its orbital period P at large distances (r>>a) is given by the expression:

    P=[(4pi/GM)^(1/2)] r^(3/2) (1-(3/4)((a^2)/(4r^2)) J(subscript2))

    Comment on the behavious of P in the limits as r approaches infinity

    2relevant equations

    g=(GM/(a^2))[-1-(3/2) J(subscript2)]

    3. The attempt at a solution

    omega^2 r =(GM/(a^2))(-1-(3/2)J(subscript 2))

    (2pi/T)^2=(GM/(a^2))(-1-(3/2)J(subscript 2))

    T=((4pi^2)/GM)^(1/2) sqrt [((a^2)r)/(m-(3/2)J2 -1)]
     
  2. jcsd
  3. Dec 7, 2011 #2
    Re: show that the satellite's orbital period P at large distances (r>>a) is given by.

    sorry I meant

    T=((4pi^2)/GM)^(1/2) sqrt [((a^2)r)/(-(3/2)J2 -1)]

    the 'm' in what I wrote before is not supposed to be there
     
  4. Dec 7, 2011 #3
    Re: show that the satellite's orbital period P at large distances (r>>a) is given by.

    behaviour typo
     
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