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Energy required to transfer an object to a higher orbit

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data
    A spaceship of mass m circles a planet (mass = M) in an orbit of radius R. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?

    2. Relevant equations

    3. The attempt at a solution
    I had no idea how to do this problem. I thought about subtracting the total final energy from the total initial energy to get the energy input required, but I didn't know how to find v. The two equations I could think of for find v are listed above

    It would be nice if you guys could at least give me a hint as to how to solve this test problem, since I get to have a second try at it tomorrow.
  2. jcsd
  3. Jan 19, 2010 #2

    D H

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    What force is needed to keep something in uniform circular motion? How does this relate to the gravitational force that makes a the spaceship orbit the planet?
  4. Jan 19, 2010 #3
    That would be the centripetal force, which is mv^2/r
    And that's equal to the gravitational force, GMm/r^2

    Which leads me to v^2 = GM/r
    I substituted that into the equations I had and got -GMm/3r for a final answer. Jeez, the solution was that simple??? Thank you very much for helping me! :)
  5. Jan 19, 2010 #4

    D H

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    That simple. However -- are you sure about the sign of your result? Does that make sense?
  6. Jan 19, 2010 #5
    Dang... you're right. It doesn't make sense since the energy should be greater at the higher orbit. And all the answer choices are positive anyways.

    I see where I went wrong now. Thanks for the heads up!
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