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

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Homework Statement

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)]

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)]

 

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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

 

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behaviour typo