Eccentricity: Difference between revisions

Latest revision as of 23:33, 17 December 2018

This article is based on a Wikipedia article prior to 15 June 2009 and is controlled by version 1.2 of the the GNU Free Documentation License (GFDL).

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 ( $e$ ) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:^[1]

for circular orbits: $e = 0$ ,
for elliptic orbits: $0 < e < 1$ ,
for parabolic orbits: $e = 1$ ,
for hyperbolic orbits: $e > 1$ .

Calculation

For elliptic orbits, eccentricity can be calculated from distance at periapsis and apoapsis:

e = \frac{d_{a} - d_{p}}{d_{a} + d_{p}}

= 1 - \frac{2}{(d_{a} / d_{p}) + 1}

where:

$d_{p}$ is distance at periapsis (closest approach),
$d_{a}$ is distance at apoapsis (farthest approach).

References

↑ Wikipedia article on eccentricity.

[1] Wikipedia article on eccentricity.

[1]

@@ Line 1: / Line 1: @@
+{{wikipedia-GFDL}}
 ==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.<ref>[http://en.wikipedia.org/w/index.php?title=Orbital_eccentricity Wikipedia article on eccentricity.]</ref>
+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, 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 [[circular orbit]]s: <math>e=0\,\!</math>,
-*for [[elliptic orbit]]s: <math>0<e<1\,\!</math>,
-*for [[parabolic orbit]]s: <math>e=1\,\!</math>,
-*for [[hyperbolic orbit]s]: <math>e>1\,\!</math>.
-[[category:orbital mechanics]]
+*for circular orbits: <math>e=0\,\!</math>,
+*for elliptic orbits: <math>0<e<1\,\!</math>,
+*for parabolic orbits: <math>e=1\,\!</math>,
+*for hyperbolic orbits: <math>e>1\,\!</math>.
+==Calculation==
+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>=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).
+==References==
+<references/>
+[[Category:Orbit]]