Consider planet mass of 4.98 E 21 kilograms with a satellite orbitting it at distance of 3.11 E 6 meters from planet's center. Satellite has mass of 369 kilograms.

Question

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

drwls · Answer

You 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