## Angular momentum and eccentricity

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,$$L=\sqrt{\frac{a(1-e^{2})}{m_{1}+m_{2}}},$$ but I may be completely wrong. Anyone know the correct answer?

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 Recognitions: Homework Help Science Advisor 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: The energy is $E = \frac{-G(M+m)}{2a}$ Therefore, $e^2 = 1-\frac{c}{a} L^2$ with $c=\frac{M+m}{GM^2m^3}$ and $L=\sqrt{\frac{1-e^2}{ca}}$ where c just depends on the masses.
 Thanks very much.