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Satellite Energy and Orbit problem

  1. Dec 2, 2014 #1
    1. The problem statement, all variables and given/known data
    A spy satellite of mass m is in a circular orbit with radius R and velocity v around
    the earth. One of the satellites thrusters suddenly fires giving it an additional
    velocity v in the outward radial direction (same v). What is the new total energy
    of the satellite? What is the new orbit of the satellite?

    2. Relevant equations
    mv^2/r
    GMm/r^2
    -K=.5U
    2K+U=0

    3. The attempt at a solution
    I honestly don't really have an idea how to even set up the problem. From what I understand mv^2=GMm/r^2 for circular orbit which should I could then use to find the energy, but I don't know how the velocity increasing radially will affect this. Any helpful nudge in the right direction would be greatly appreciated.
     
  2. jcsd
  3. Dec 2, 2014 #2

    haruspex

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    I think you mistyped the left hand side. As a result you have energy on the left and a force on the right.

    What is the initial KE?
    What is the initial PE?
    How much energy was added?
     
  4. Dec 2, 2014 #3
    So initially I got my K=1/2GMm/r and my U=-GMm/r

    Since we are adding another V, which is Sqrt[GM/r], i get that my new total energy = -.5GMm/r+.5GMm/r=0

    however, this doesn't seem right
     
  5. Dec 2, 2014 #4

    haruspex

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    It's right :). Remember, the total energy beforehand was negative.
    So what do you get for the new orbit?
     
  6. Dec 2, 2014 #5
    AH, infinite radius? so we get an open orbit? Thanks a ton. Didn't think it would be so simple
     
  7. Dec 2, 2014 #6

    haruspex

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    That's it. So what general rule do you deduce for vertical escape velocity from a given orbit?
     
  8. Dec 2, 2014 #7
    Hmm, it must be equal to or greater than tangential velocity?
     
  9. Dec 2, 2014 #8

    haruspex

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    Equal. ("Escape velocity" means the minimum necessary to escape the gravitational field.)
     
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