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

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

Finding eccentricity

Here is a formula to find eccentricity:

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

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.

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Orbital eccentricity

Finding eccentricity

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