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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

[tex]e= \frac{c}{a}[/tex]

For ellipses:

[tex]e = \frac{r_A-r_P}{r_a+r_P}[/tex]

[tex]e = \sqrt{ 1- \left ( \frac{b}{a} \right )^2}[/tex]

For hyperbolas:

[tex]e = \sqrt{ 1 + \left( \frac{b}{a} \right)^2}[/tex]

Extended explanation

ais 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).

bis 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.

cis the distance between the center and the focus of the orbit.

ris the apoapsis distance as measured from the focus._{A}

ris the periapsis distance as measured from the focus._{P}

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# What is orbital eccentricity

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