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

1. Dec 7, 2011

### blueyellow

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. Dec 7, 2011

### blueyellow

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

3. Dec 7, 2011

### blueyellow

Re: show that the satellite's orbital period P at large distances (r>>a) is given by.

behaviour typo