Calculating Density of a Planet Based on Close Orbit Satellite Period

[kopinator]

A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 1.94 hours. What is density of the planet? Assume that the planet has a uniform density.

density = kg/m^3
T = 2∏/ω = 2∏r/v
GMm/r^2 = (mv^2)/r
v^2 = GM/r
v = rω

So I know I need to find the radius and the mass of the planet in order to find the density. Since I don't have r or v I found ω=8.99E-4. I'm not sure where to go from here.

 

[mfb]

You don't need the radius or mass (which is a surprising result, I think). Just use r and M, and you will find some relation between those two (based on the orbit). This can be converted into a density afterwards.