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

1. Mar 29, 2009

### AudioGeek

1. The problem statement, all variables and given/known data
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.

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

3. 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?

2. Mar 29, 2009

### 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

Last edited: Mar 30, 2009
3. Mar 29, 2009

### 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.

4. Mar 29, 2009

### AudioGeek

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

Thanks a bunch =).