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Energy principle and circular/ellipse orbits

  1. Feb 3, 2012 #1
    Question is as follows:
    How much energy do i need when i move an object with a mass M from a circular orbit with a radius of R_1 to an ellipse orbit with aphelion radius of R_2.

    I'm assuming energy principle is the way to go here but it leads to a question i'd like someone to help me out with.

    Do i need to assume the perihelion radius of the new orbit (aphelion radius R_2) is the circular orbit's radius R_1?

    Thanks in advance.
     
  2. jcsd
  3. Feb 3, 2012 #2

    gneill

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    Staff: Mentor

    You can assume anything you like; The answer you get will depend upon your assumptions :smile:

    The Total Specific Mechanical Energy, [itex] \xi [/itex], of an orbit is inversely proportional to the size of its major axis. Thus [itex] \xi = -\frac{\mu}{2 a} [/itex] . The length of the major axis, in turn, is the sum of the perihelion and aphelion distances. Specific Mechanical Energy is the energy per unit mass; Multiply by mass of the orbiting object to get the energy.

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  4. Feb 3, 2012 #3
    Yea, i presumed as much. To get the energy change needed i'd have to go

    [itex]\Delta E = -\frac{GMm}{2a} - \frac{1}{2}mv_1^2 + \frac{GMm}{R_1}[/itex]

    So basically ellipse orbit total energy minus circular orbit total energy. Since i wasn't given the semi-major axis but only the aphelion radius of the ellipse orbit, i would think i'd need to assume the perihelion radius is the R_1. Either way, i think i'm going with this.
    Whatever the case, thanks for the reply!
     
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