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September 22, 2014

September 22, 2014

Posted by **Joan** on Tuesday, March 11, 2008 at 10:37pm.

How long (inseconds) does it take the satellite to make one complete orbit around planet.

I just can't seem to get the correct answer - Please show me step by step.

Thanks

- Physics Honors -
**drwls**, Wednesday, March 12, 2008 at 1:54amYou need to set the gravitational force equal to the centripetal force. The period will be independent of the satellite's mass (m when it is small compared to the planet mass M.

GMm/R^2 = mV^2/R

m cancels out, so

GM/R = V^2

The period P is related to the Orbit radius R and velocity V by

V P = 2 pi R

Therefore

(2 pi R)^2/P^2 = GM/R

R^3 * (4 pi^2/GM)= P^2

G is the universal constant of gravity,

6.67*10^-11 m^3 kg^-1 s^-2

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