Find period of astronaut when Normal force of ship = normal force on earth

[kariibex]

Homework Statement

If the gravitational acceleration at Earth's surface is given by: g = GMe/Re^2, show that the period of rotation of a spaceship needed to make an astronaut feel the same normal force on the ship that they would feel on Earth, when it is given by T = √[(4pi^2)(Rs)(Re^2)/GMe], where Rs is the radius of ship and Re is radius of earth.

Homework Equations

Fc = ma = m(v^2/r)
Fg = gMem/r^2
v = 2∏r/ T

The Attempt at a Solution

Normal force on Earth = normal force on ship
N = mg = m(GMe/Re^2)
Normal force ship on astronaut = mac = m(v^2/r)

Now I'm not sure what to substitute into the Period formula and how to approach this?

 

[haruspex]

Rewrite v = 2∏r/ T into the form T = ... You have an expression for v, and r = Rs. Just substitute in.