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| In [[celestial mechanics]], the '''eccentricity vector''' of a [[Kepler orbit]] is the [[vector (geometric)|vector]] that points towards the [[periapsis]] and has a magnitude equal to the orbit's scalar [[orbital eccentricity|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 orbit|osculating]] eccentricity vector to change continuously. For the eccentricity and [[argument of periapsis]] parameters, eccentricity zero (circular orbit) corresponds to a singularity.
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| ==Calculation==
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| The '''eccentricity vector''' <math> \mathbf{e} \,</math> can be calculated<ref>{{cite book |title=The Kepler Problem |first=Bruno |last=Cordani |page=22 |location= |publisher=Birkhaeuser |year=2003 |isbn=3-7643-6902-7 }}</ref>
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| :<math> \mathbf{e} = {\mathbf{v}\times\mathbf{h}\over{\mu}} - {\mathbf{r}\over{\left|\mathbf{r}\right|}}</math>
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| where:
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| *<math> \mathbf{v}\,\!</math> is [[velocity vector]]
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| *<math>\mathbf{h}\,\!</math> is [[Specific relative angular momentum|specific angular momentum vector]] (equal to <math>\mathbf{r}\times\mathbf{v}</math>)
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| *<math>\mathbf{r}\,\!</math> is [[position vector]]
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| *<math>\mu\,\!</math> is [[standard gravitational parameter]]
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| or equivalently:
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| :<math> \mathbf{e} = {\mathbf{\left |v \right |}^2 \mathbf{r} \over {\mu}} - {(\mathbf{r} \cdot \mathbf{v} ) \mathbf{v} \over{\mu}} - {\mathbf{r}\over{\left|\mathbf{r}\right|}}</math>
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| ==See also==
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| *[[Kepler orbit]]
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| *[[Orbit]]
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| *[[Eccentricity (orbit)|Eccentricity]]
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| *[[Laplace–Runge–Lenz vector]]
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| ==References==
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| {{Reflist}}
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| {{DEFAULTSORT:Eccentricity Vector}}
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| [[Category:Orbits]]
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| [[Category:Vectors]]
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Revision as of 22:40, 25 February 2014
The title of the writer is Nestor. His working day job is a cashier and his wage has been truly satisfying. The preferred pastime for my kids and me is playing crochet and now I'm trying to earn cash with it. He presently lives in Arizona and his mothers and fathers live nearby.
My web-site: monsterpest.com