Eccentricity: Difference between revisions

Revision as of 22:12, 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 ( $e$ ) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:

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

==Calculation.^[1] ==

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: @@
 ==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:
@@ Line 8: / Line 8: @@
 *for [[parabolic orbit]]s: <math>e=1\,\!</math>,
 *for [[hyperbolic orbit]]s: <math>e>1\,\!</math>.
+==Calculation.<ref>[http://en.wikipedia.org/w/index.php?title=Orbital_eccentricity Wikipedia article on eccentricity.]</ref>
+==
+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).
 ==References==