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Exam review question about space shuttle orbits at differing radii

  1. May 2, 2012 #1
    1. The problem statement, all variables and given/known data

    The space shuttle makes 1 revolution around the Earth in 1.5 hours when it is in an orbit 200 km above the Earth’s surface. The radius of the Earth Re is 6.5 × 10^6m. If the shuttle moves to a new orbit such that it makes 1 revolution per day (24 hours), what is the radius of the new orbit?

    (1) 6.2Re (2) 12Re (3) 24.8Re (4) 16Re (5) 0.38Re

    2. Relevant equations

    Force_centripetal=Force_gravity

    v=(2piR)/T

    T=period

    3. The attempt at a solution

    My professor said:

    "Yes, the centripetal force is provided by gravity. The tangential velocity v=2piR/T where T is the period. Thus show that T is proportional to R^2 and solve. For orbit 2, R_2=R_1sqrt(T_2/T_1)"

    ...but I still can't understand what he's talking about. What does he mean that period T is proprtional to r^2? And what does any of this have to do with balancing the centripetal force with the force of gravity?

    Thank you. This forum is the best.
     
  2. jcsd
  3. May 2, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    welcome to pf!

    hi npersons274! welcome to pf! :smile:

    (try using the X2 and X2 buttons just above the Reply box :wink:)
    hint: what is the equation balancing the centripetal acceleration with the gravitational acceleration? :wink:
     
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