This equation produces the norm of the Eccentricity Vecotor, →e→e, with input being the components of the orbital radius vector, →r→r and the components of the velocity vector, →v→v.
Notes
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
This equation, Eccentricty ||→e||||→e||, references 2 pages