Universal Gravitation and a satellite

[Bowenj]

Homework Statement

A satellite of mass 4600 kg orbits the Earth (mass = 6.0 1024 kg) and has a period of 5500 s.
(a) Find the magnitude of the Earth's gravitational force on the satellite.
(b) Find the altitude of the satelite

Homework Equations

Kepler's Equation: R^3/T^2

Fg= GmM/R^2

Fc= m4pi^2R/T^2

The Attempt at a Solution

I tried setting Fc= Fg and solving for R. So it ended up being

R^3= GmT^2/(4pi^2)

I plugged the numbers in...

R^3= (6.67e-11)(6e24)(5500)^2/(4pi^2)

so then i solved and took the cube root and got 3.07e20 and plugged that back into the Fg equation so it was

Fg= GmM/R^2

Fg=(6.67e-11)(4600)(6e24)/(3.07e20)^2

which was like... 2.95e-23...? and I'm pretty sure that isn't right...

 

[physalpha]

Fc = m ( omega R)^2 /( R)
Fc= m (2 pi)^2 R / (T^2)
Fg= G M m /R^2

Fc=Fg
R^3 = GM T^2/ (2 pi)^2
no problem

 

[fzero]

R^3= GmT^2/(4pi^2)

I plugged the numbers in...

R^3= (6.67e-11)(6e24)(5500)^2/(4pi^2)

so then i solved and took the cube root and got 3.07e20

Those expressions are correct, but 3.07e20 is R³, not R. If you actually take the cube root, you should find the correct answer for the gravitational force.