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?

 

[tomcue]

As a scientist, your first step would be to carefully check your calculations and equations to ensure they are accurate. You also need to make sure that all your units are consistent and that you are using the correct values for the constants. Once you have confirmed that your calculations are correct, you can use the equation T^2 = 4π^2r^3/GM to solve for the mass of the planet (M). Then, you can use the formula for density (density = mass/volume) to calculate the density of the planet. Remember to use the formula for the volume of a sphere (4/3πr^3) to calculate the volume of the planet.