Orbital eccentricity

In astrodynamics, orbital eccentricity shows how much the shape of an object's orbit is different from a circle.

Examples of four orbital trajectories with different eccentricities

Eccentricity (${\displaystyle e\,\!}$) is defined for all circular, elliptic, parabolic and hyperbolic orbits. It can take the following values:

• for circular orbits: ${\displaystyle e\,\!}$ is equal to zero,
• for elliptical orbits: ${\displaystyle e\,\!}$ is more than zero but less than 1,
• for parabolic trajectories: ${\displaystyle e\,\!}$ is equal to 1,
• for hyperbolic trajectories: ${\displaystyle e\,\!}$ is more than 1.

Finding eccentricity

Here is a formula to find eccentricity:

${\displaystyle e_{obj}={\frac {r_{a}-r_{p}}{r_{a}+r_{p}}}}$

Where e_obj is the eccentricity, r_a is the apoapsis (far point) of the object's orbit, and r_p is the periapsis (near point) of the object's orbit. The near and far points are the apsides.