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

  1. Jan 23, 2013 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations

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

    3. 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?
     
  2. jcsd
  3. Jan 23, 2013 #2

    haruspex

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