1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook