Difference between revisions of "Eccentricity"
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==Definition== | ==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. | + | 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: | ||
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*for [[parabolic orbit]]s: <math>e=1\,\!</math>, | *for [[parabolic orbit]]s: <math>e=1\,\!</math>, | ||
*for [[hyperbolic orbit]]s: <math>e>1\,\!</math>. | *for [[hyperbolic orbit]]s: <math>e>1\,\!</math>. | ||
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| + | ==Calculation.<ref>[http://en.wikipedia.org/w/index.php?title=Orbital_eccentricity Wikipedia article on eccentricity.]</ref> | ||
| + | == | ||
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| + | For [[elliptic orbit]]s, eccentricity can be calculated from distance at [[periapsis]] and [[apoapsis]]: | ||
| + | :<math>e={{d_a-d_p}\over{d_a+d_p}}</math> | ||
| + | ::<math>=1-\frac{2}{(d_a/d_p)+1}</math> | ||
| + | where: | ||
| + | *<math>d_p\,\!</math> is distance at [[periapsis]] (closest approach), | ||
| + | *<math>d_a\,\!</math> is distance at [[apoapsis]] (farthest approach). | ||
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==References== | ==References== | ||
Revision as of 13:12, 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:
- for circular orbits: ,
- for elliptic orbits: ,
- for parabolic orbits: ,
- for hyperbolic orbits: .
==Calculation.[1] ==
For elliptic orbits, eccentricity can be calculated from distance at periapsis and apoapsis:
where:
