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Regarding Gravitation and Gravitational Fields

  1. May 12, 2008 #1
    1. The problem statement, all variables and given/known data

    A satellite is designed to orbit Earth at an altitude above its surface that will place it in a gravitational field with a strength of 4.5N/kg.
    a) Calculate the distance above the surface of Earth at which the satellite must orbit.
    b) Assuming the orbit is circular, calculate the acceleration of the satellite and its direction.
    c) At what speed must the satellite travel in order to maintain this orbit?


    2. Relevant equations
    g=(G*Me)/r^2, where Me is earth's mass

    3. The attempt at a solution
    For a), I've used the above equation, with given g value(4.5) substituted into the equation, and got 3.0 x 10^3km as my final answer but b) and c) is where I have the problem. In order to calculate the acceleration for b), I believe that I need to calculate the velocity(v=sqrt(G*Me/r)) first then substitute into (a = v^2/r). However, if I end up getting an answer for part b), didn't I just do c) as well? Because for c) I need to calculate the velocity as well.. I'd like to know whether or not I was wrong about this before I get in any further.

    Thank you in advance for your comments.
     
  2. jcsd
  3. May 12, 2008 #2

    Chi Meson

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    Hint:
    orbital motion is "free-fall." What is the acceleration of free fall?
     
  4. May 12, 2008 #3
    The way you calculated b) is not wrong, and it will work. However, how did you arrive at your equation for velocity? To derive it, you would start by equating centripetal force with gravitational force. What is the centripetal acceleration? Can you figure it out without first calculating velocity?
     
  5. May 12, 2008 #4
    acceleration in free-fall is 9.8m/s/s right?
     
  6. May 12, 2008 #5
    Only near the surface of the earth, because the gravitational force is GMm/r2 = mg = 9.8m on the surface.
     
  7. May 13, 2008 #6

    Chi Meson

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    only where g is 9.8 N/kg
     
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