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This page refers to eccentricity in astrodynamics. For other uses, see the disambiguation page eccentricity.

In astrodynamics, under standard assumptions any orbit must be of conic 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.

Under standard assumptions eccentricity ($e\backslash ,\backslash !$) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:

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

Calculation

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Eccentricity of an orbit can be calculated from orbital state vectors as a magnitude of eccentricity vector:

$e=\; \backslash left\; |\; \backslash mathbf\{e\}\; \backslash right\; |$

where:

• $\backslash mathbf\{e\}\backslash ,\backslash !$ is eccentricity vector.

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For elliptic orbits it can also be calculated from distance at periapsis and apoapsis:

$e==1-\backslash frac\{2\}\{\backslash frac\{d\_a\}\{d\_p\}+1\}=\backslash frac\{2\}\{\backslash frac\{d\_p\}\{d\_a\}+1\}-1$

where:

• $d\_p\backslash ,\backslash !$ is distance at periapsis,
• $d\_a\backslash ,\backslash !$ is distance at apoapsis.

Examples

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For example, the eccentricity of the Earth's orbit today is 0.0167. Through time, the eccentricity of the Earth's orbit slowly changes from nearly 0 to almost 0.05 as a result of gravitational attractions between the planets (see graph ^*).

Other values: Pluto 0.2488 (largest value among the planets of the Solar System), Mercury 0.2056, Moon 0.0554. For the values for all planets in one table, see de:Planet (Tabelle).

See also

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• Eccentricity vector

External links

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• World of Physics: Eccentricity
• The NOAA page on Climate Forcing Data includes (calculated) data from Berger (1978), Berger and Loutre (1991) and Laskar et al. (2004) on Earth orbital variations, including eccentricity, over the last 50 million years and for the coming 20 million years
• The orbital simulations by Varadi, Ghil and Runnegar (2003) provide another, slightly different series for Earth orbital eccentricity, and also a series for orbital inclination

Astrodynamics | Celestial mechanics

Excentricité orbitale | Excentricitás (csillagászat) | Eccentricità (orbita) | Excentriciteit (astronomie) | Excentricitatea (orbită) | Dışmerkezlik (gökbilim)