Orbital eccentricity

Examples of four orbital trajectories with different eccentricities

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

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

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

Finding eccentricity

Here is a formula to find eccentricity:

[math]\displaystyle{ e_{obj}=\frac {r_a-r_p} {r_a+r_p} }[/math]

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.