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 | + | Eccentricity (<math>e\,\!</math>) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:<ref>[http://en.wikipedia.org/w/index.php?title=Orbital_eccentricity Wikipedia article on eccentricity.]</ref> |
| − | *for | + | *for circular orbits: <math>e=0\,\!</math>, |
| − | *for | + | *for elliptic orbits: <math>0<e<1\,\!</math>, |
| − | *for | + | *for parabolic orbits: <math>e=1\,\!</math>, |
| − | *for | + | *for hyperbolic orbits: <math>e>1\,\!</math>. |
==Calculation== | ==Calculation== | ||
| − | For | + | For elliptic orbits, eccentricity can be calculated from distance at [[periapsis]] and [[apoapsis]]: |
:<math>e={{d_a-d_p}\over{d_a+d_p}}</math> | :<math>e={{d_a-d_p}\over{d_a+d_p}}</math> | ||
::<math>=1-\frac{2}{(d_a/d_p)+1}</math> | ::<math>=1-\frac{2}{(d_a/d_p)+1}</math> | ||
Revision as of 13:36, 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:
