Solving the angular momentum equation
where h is the specific angular momentum, G is the gravitational constant, M is the mass of the central body, and a is the semimajor axis Eric Weisstein's World of Math of the orbit, for the eccentricity e gives
Plugging the gravitational energy equation
where m is the mass of the orbiting body, into (2) gives
Circular Orbit, Eccentricity Perturbations, Elliptical Orbit, Hyperbolic Orbit, Parabolic Orbit
