This equation produces the eccentricity, e, with inputs being the orbital energy, E, the angular momentum, L, the reduced mass, `m_"red"`, and the coefficient of the inverse-square law central force, `alpha`.
The orbits and trajectories that can be characterized by eccentricity are:
elliptical: circular: e = 1 parabolic trajectory hyperbolic trajectory |
0 < e < 1 e = 1 e = 1 e> 1 |