Finding the period of the satellite's orbital motion

[rwssman]

Homework Statement

I want to find the period of the satellite.

Homework Equations

mg = mv^2/r

The Attempt at a Solution

I derive the equation
mg = mv^2/r
v = sqrt(gr)
v = ωr and ω = 2π/T

T = 2π/ω = 2πr/v

Then, T = 2πr/sqrt(gr)

But the answer is 2πr/R * sqrt(r/g). I don't know why? Is there anyone can give an explanation to me why it is not correct.

 

[BvU]

Hi,

From the text: $g$ at the surface is not $g$ far away ...