Suppose that Captain Omega of the Imperial Space Patrol wishes to place a spy satellite in geosynchronous orbit above the mysterious Planet X, which has a mass of 5.90 x1024 kg, and a rotational period of 26.4 hours.
(a) What should be the radius of the satellite's orbit?
(b) What would be the orbital speed of the satellite?
The Attempt at a Solution
I used the law of periods : T2/r3 = 4∏2/GM
So I rearranged that to get:
r = (GMT2 / 4∏2) 1/3
I plugged in:
G = 6.67 e -11
M = 5.9 e 24 kg
T = 95040s
I ended up with 2.06e8 m = 2.06e5 km
But that answer isn't right and I don't understand what I'm doing wrong.