# Eccentricity

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## Definition

Any orbit in planetary dynamics can be assumed to be of conic cross-section shape. The eccentricity of this conic section, the orbit's eccentricity, is an important parameter of the orbit that defines its absolute shape. Eccentricity may be interpreted as a measure of how much this shape deviates from a circle.

Eccentricity ($e\,\!$ ) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:

• for circular orbits: $e=0\,\!$ ,
• for elliptic orbits: $0 ,
• for parabolic orbits: $e=1\,\!$ ,
• for hyperbolic orbits: $e>1\,\!$ .

## Calculation

For elliptic orbits, eccentricity can be calculated from distance at periapsis and apoapsis:

$e={{d_{a}-d_{p}} \over {d_{a}+d_{p}}}$ $=1-{\frac {2}{(d_{a}/d_{p})+1}}$ where:

• $d_{p}\,\!$ is distance at periapsis (closest approach),
• $d_{a}\,\!$ is distance at apoapsis (farthest approach).