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,[tex]L=\sqrt{\frac{a(1-e^{2})}{m_{1}+m_{2}}},[/tex] 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 [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.

Alexrey

Thanks very much.