Angular momentum and eccentricity

[Alexrey]

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?

 

[mfb]

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.

 

[Alexrey]

Thanks very much.