Difference between revisions of "Eccentricity"
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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. | 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 (<math>e\,\!</math>) is strictly defined for all [[circular orbit|circular]], [[elliptic orbit|elliptic]], [[parabolic orbit|parabolic]] and [[hyperbolic orbit|hyperbolic]] orbits and may take following values: | + | Eccentricity (<math>e\,\!</math>) is strictly defined for all [[circular orbit|circular]], [[elliptic orbit|elliptic]], [[parabolic orbit|parabolic]] and [[hyperbolic orbit|hyperbolic]] orbits and may take following values:<ref>[http://en.wikipedia.org/w/index.php?title=Orbital_eccentricity Wikipedia article on eccentricity.]</ref> |
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*for [[circular orbit]]s: <math>e=0\,\!</math>, | *for [[circular orbit]]s: <math>e=0\,\!</math>, | ||
*for [[elliptic orbit]]s: <math>0<e<1\,\!</math>, | *for [[elliptic orbit]]s: <math>0<e<1\,\!</math>, | ||
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*for [[hyperbolic orbit]]s: <math>e>1\,\!</math>. | *for [[hyperbolic orbit]]s: <math>e>1\,\!</math>. | ||
| − | ==Calculation== | + | ==Calculation== |
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For [[elliptic orbit]]s, eccentricity can be calculated from distance at [[periapsis]] and [[apoapsis]]: | For [[elliptic orbit]]s, eccentricity can be calculated from distance at [[periapsis]] and [[apoapsis]]: | ||
Revision as of 13:13, 6 October 2007
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 () is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:[1]
- for circular orbits: ,
- for elliptic orbits: ,
- for parabolic orbits: ,
- for hyperbolic orbits: .
Calculation
For elliptic orbits, eccentricity can be calculated from distance at periapsis and apoapsis:
where:
