Deriving an expression for the radius of a satellite's orbit around Earth(?)

[AudioGeek]

Homework Statement

Derive an expression for the radius of a satellite's orbit around Earth in terms of the period of revolution, the universal gravitation constant, and Earth's mass.

Homework Equations

The final equation should be: r = \sqrt[3]{\frac{T^{2}Gm_{E}}{4\prod^{2}}}

The Attempt at a Solution

I have no idea how to do this. To be honest, I'm not even really sure what it means to derive an equation. Someone please help me with this?

 

[mgb_phys]

A satelite (or anything else) in orbit has a gravitational force inward toward Earth balanced by a centrifugal force outward.
You need the formulae for gravitational attraction (depends on the radius, mass of Earth and satellite) and the centrifugal force (depends on radius and mass of satellite)
Set the two equations equal to each other and rearrange them to get radius

 

[Delphi51]

All circular satellite calculations begin with "centripetal force = force of gravity".
Fill in the formulas for the two forces and solve for the quantity you want.
Be sure to use the centripetal force formula with period in it since that is specified in the question.

 

[AudioGeek]

All circular satellite calculations begin with "centripetal force = force of gravity".
Fill in the formulas for the two forces and solve for the quantity you want.
Be sure to use the centripetal force formula with period in it since that is specified in the question.

Once it was explained like this, it was dead easy!

Thanks a bunch =).