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Orbital Period of satellite in terms of v and r

  1. Oct 21, 2012 #1
    1. The problem statement, all variables and given/known data
    "A satellite orbits the earth in a circular orbit of radius r. If the orbital speed of the satellite is v, what is the orbital period T of the satellite in terms of v and r? You must explain how you derive the expression for the period."


    2. Relevant equations
    Speed = distance/time
    a = v2/r

    3. The attempt at a solution
    Distance for 1 revolution of a circle is equal to the circumference. So distance = 2(pi)r
    Time to travel 1 revolution = period T

    So velocity = speed = 2(pi)r/T

    a = v2/r

    a = 2(pi)r/T * 1/T

    a = 2(pi)r / T2

    At this point I would solve for T, but I am not sure if this is valid, what I'm doing? I don't think we are supposed to have an acceleration in there, so I was wondering if there is another equation I could use that relates v and r. Btw this is not graded, it's just a sample test (that we're not turning in) to help us for the real test (on Tuesday). Thanks for any assistance.
     
    Last edited: Oct 21, 2012
  2. jcsd
  3. Oct 21, 2012 #2
    I don't think you even need to bother with the centripetal acceleration equation.

    If we have an orbital radius of r, this gives an orbital path distance of 2∏r

    T = d / v ---> T = (2∏r) / v
     
  4. Oct 21, 2012 #3
    If you know the distance per revolution, and you know the velocity, surely you can compute the time of one revolution.
     
  5. Oct 21, 2012 #4
    Oh thanks, so I could have stopped there and solved for T. I guess I made it too complicated. So that answers the question right?
     
  6. Oct 21, 2012 #5
    Yup, in general you want to use the least amount of extra variables/equations possible.
     
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