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Gravitation: Satellite Orbits

  1. Jan 1, 2013 #1
    1. The problem statement, all variables and given/known data
    Two satellites are launched at a distance R from a planet of negligible radius. Both satellites are launched in the tangential direction. The first satellite launches correctly at a speed v0 and enters a circular orbit. The second satellite, however, is launched at a speed .5v0. what is the minimum distance between the second satellite and the planet over the course of its orbit?

    R=launch radius, r=minimum radius, v=velocity at minimum radius

    2. Relevant equations
    F=GMm/R^2
    U= -GMm/R
    K=.5mv^2
    mvr= const. (conservation of angular momentum)
    K+U=const. (conservation of energy)

    3. The attempt at a solution

    GM= R(v0)^2
    v0R/2 = vr, v = (v0R)/(2r)
    .5m(.5v0)^2 - GM (m/R) = .5m(v^2) - GM (m/r)

    Substituting in values and solving for r doesn't lead me to the answer. Any help?
     
  2. jcsd
  3. Jan 1, 2013 #2

    TSny

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    Hi, slai13. Welcome to PF!

    Everything looks good to me. Assuming your algebra is correct, I think you should get the right answer. Can you tell us what you got?
     
  4. Jan 1, 2013 #3
    Sorry to have wasted your time.

    I worked out the quadratic equation and got R/7 and R. R/7, I'm sure, is the minimum I'm looking for. Thanks!
     
  5. Jan 1, 2013 #4

    TSny

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    No problem. Good work!
     
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