Finding Density of a Planet Using Period of Orbit

[surferdud3]

Homework Statement

A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is T = 1.78 hours.
What is density (mass/volume) of the planet? Assume that the planet has a uniform density.

Homework Equations

T$$^{2}$$=4*PI^2*r^3/G*M
Density = Mass/Volume
Volume of Sphere = 4/3*PI*r^2

The Attempt at a Solution

I converted T into seconds, which I get 6408 seconds,

I have tried to solve for a single variable, but when I put it back into the equation, everything cancels out...

What should I do, I'm just super confused... :(

 

[rock.freak667]

So we have


$$T^2=\frac{4\pi^2 r^3}{GM}$$

and we know $V=\frac{4}{3}\pi r^3$


So if we divide the equation with T₂ by 3, can we somehow factor out (4/3)πr³?