- #1

kariibex

- 9

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## 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?