 Orbital eccentricity

Orbital eccentricity $e$ measures the shape of a Kepler orbit. A circle has $e=0$, an ellipse $0<e<1$, a parabola $e=1$, and a hyperbola $e>1$ for a nonradial attractive orbit.

For a bound ellipse with semi-major axis $a$, pericentre $r_p=a(1-e)$ and apocentre $r_a=a(1+e)$ giveThus unequal turning distances measure eccentricity directly. In a perturbed orbit, osculating orbital elements can change with time; eccentricity need not remain conserved.^[ref]