Finding the Density of a Planet using Time

[lanzjohn]

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 = 2.52 hours.
What is density (mass/volume) of the planet? Assume that the planet has a uniform density.

Hint: "very close to the surface" means that Rorbit = Rplanet

Homework Equations

please look at image below

The Attempt at a Solution

[PLAIN]http://img692.imageshack.us/img692/4624/34096608.png

Where did I go wrong. I feel like its my terrible algebra skillzz?

Thanks guys

 

[D H]

Check your units. What are the units of $(4\pi T^2)/(4/3G)$?

 

[lanzjohn]

ohh I just have to change hours to seconds? Well that would make sense then my number won't be as big, which is a good sign. Okay thanks. ill try that orr maybe not..

Why would I have to change the units of G? T I understand.

 

[D H]

Yes, you have to do that, but that is not what I was talking about. You have as an answer

$$\rho = \frac{4\pi T^2}{G 4/3}$$

Numbers such as 3, 4, and pi are unitless. So let's throw them away:

$$\rho \propto \frac{T^2}{G}$$

The left-hand side is supposed to be a density with units of mass / volume = mass / length³ = mass * length^-3. To have a consistent result, the right-hand side must have the same units. The period T has units of time while the gravitational constant G has units of length³/(mass*time²). Thus T²/G has units of time²/(length³/(mass*time²)) or mass*time⁴*length^-3. Those are not the units of density.

Your units are inconsistent. That always means your result is garbage. Always.

 

[lanzjohn]

Ok bare with me here,

So are you saying that my

d=t^2/G is wrong? I understand now how the units don't match up. But where did I go wrong?

 

[willem2]

At your second step you have M T^2 = (something)

At the bottom of the first column you have M = (something) T^2
You can just divide both sides of the first equation by T^2 instead of whatever
it is you did