# What is orbital eccentricity

1. Jul 23, 2014

### Greg Bernhardt

Definition/Summary

Eccentricity is the measure of the 'roundness' of the orbit.
For circular orbits: e=0
For elliptical orbits: 0<e<1
For parabolic trajectories: e=1
For hyperbolic Trajectories: e>1

Equations

$$e= \frac{c}{a}$$

For ellipses:
$$e = \frac{r_A-r_P}{r_a+r_P}$$

$$e = \sqrt{ 1- \left ( \frac{b}{a} \right )^2}$$

For hyperbolas:
$$e = \sqrt{ 1 + \left( \frac{b}{a} \right)^2}$$

Extended explanation

a is the semi-major axis of the orbit. For an elliptical orbit, this is equal to one half the longest length of the ellipse. For an hyperbolic path, it is equal to the distance of periapsis to to point where the asymptote lines cross (the center of the hyperbola).

b is the semi-minor axis of the orbit. For an elliptical orbit, this is equal to one half the width of the ellipse. See attached image for a hyperbolic orbit.

c is the distance between the center and the focus of the orbit.

rA is the apoapsis distance as measured from the focus.

rP is the periapsis distance as measured from the focus.

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