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Angular momentum and eccentricity

  1. Jul 11, 2012 #1
    I'm trying to find the relationship between angular momentum and orbital eccentricity but so far I haven't really found anything. I did find an indirect relationship, though, which looked like it should come out to,[tex]L=\sqrt{\frac{a(1-e^{2})}{m_{1}+m_{2}}},[/tex] but I may be completely wrong. Anyone know the correct answer?
     
  2. jcsd
  3. Jul 11, 2012 #2

    mfb

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    Staff: Mentor

    Even if you remove as many variables as possible, orbits always have two degrees of freedom, they can be written as semi-major axis and eccentricity. The angular momentum will depend on both, together with the masses and the gravitational constant.

    I found this formula at wikipedia:
    a6a3c8e287edeb7d9fa7762763bce081.png

    The energy is [itex]E = \frac{-G(M+m)}{2a}[/itex]

    Therefore, [itex]e^2 = 1-\frac{c}{a} L^2[/itex] with [itex]c=\frac{M+m}{GM^2m^3}[/itex] and [itex]L=\sqrt{\frac{1-e^2}{ca}}[/itex] where c just depends on the masses.
     
  4. Jul 16, 2012 #3
    Thanks very much.
     
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