Finding radius of satellite in orbit given mass and rotational period

[csgirl504]

Homework Statement

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?

Homework Equations

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.

 

[SteamKing]

I plug in your numbers to your formula and I get a different answer. You must have forgot a step in your arithmetic.

 

[csgirl504]

Thank you! I'm not sure what I was doing wrong..mistake while entering in the calculator I guess!