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eccentricity vector : ウィキペディア英語版
eccentricity vector
In celestial mechanics, the eccentricity vector of a Kepler orbit is the vector that points towards the periapsis and has a magnitude equal to the orbit's scalar eccentricity. The magnitude is unitless. For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously. For the eccentricity and argument of periapsis parameters, eccentricity zero (circular orbit) corresponds to a singularity.
==Calculation==
The eccentricity vector \mathbf \, is:
: \mathbf = \over} - \right|}} =
\left ( }- } \right ) \mathbf - \over} \mathbf

which follows immediately from the vector identity:
: \mathbf\times \left ( \mathbf\times \mathbf \right ) = \left ( \mathbf \cdot \mathbf \right ) \mathbf - \left ( \mathbf \cdot \mathbf \right ) \mathbf
where:
* \mathbf\,\! is velocity vector
*\mathbf\,\! is specific angular momentum vector (equal to \mathbf\times\mathbf)
*\mathbf\,\! is position vector
*\mu\,\! is standard gravitational parameter

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「eccentricity vector」の詳細全文を読む



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