# Eccentricity

 This article is based on a Wikipedia article prior to 15 June 2009 and is controlled by version 1.2 of the the GNU Free Documentation License (GFDL).

## 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 (${\displaystyle e\,\!}$) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:[1]

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

## Calculation

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

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

where:

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