Eccentricity (orbit)

__NOTOC__ :''This page refers to eccentricity in astrodynamics. For other uses, see the disambiguation page eccentricity.'' In astrodynamics, under standard assumptions in astrodynamics any orbit must be of conic section shape. The eccentricity (mathematics) 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 in astrodynamics eccentricity ( $e\,\!$ ) is strictly defined for all circular orbit, elliptic orbit, parabolic trajectory and hyperbolic trajectory orbits and may take following values: *for circular orbits: $e=0\,\!$ , *for elliptic orbits: $0,
*for$ parabolic trajectory: $e=1\,\!$ , *for hyperbolic trajectory: $e>1\,\!$ . ==Calculation== Eccentricity''' of an orbit can be calculated from orbital state vectors as a magnitude (mathematics) of eccentricity vector: :

e= \left | \mathbf{e} \right |

where: *

\mathbf{e}\,\!

is eccentricity vector. ---- For elliptic orbits it can also be calculated from distance at periapsis and apoapsis: :

e={{d_a-d_p}\over{d_a+d_p}}=1-\frac{2}{\frac{d_a}{d_p}+1}=\frac{2}{\frac{d_p}{d_a}+1}-1

where: *

d_p\,\!

is distance at periapsis, *

d_a\,\!

is distance at apoapsis. ==Examples== 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 [http://www.museum.state.il.us/exhibits/ice_ages/eccentricity_graph.html]). Other values: Pluto (planet) 0.2488 (largest value among the planets of the Solar System), Mercury (planet) 0.2056, Moon 0.0554. For the values for all planets in one table, see :de:Planet (Tabelle). ==See also== *Eccentricity vector ==External links== *[http://scienceworld.wolfram.com/physics/Eccentricity.html World of Physics: Eccentricity] Astrodynamics Celestial mechanics

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Eccentricity_(orbit)