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In [[celestial mechanics]], the '''relative angular momentum''' (<math>\mathbf{H_{{2}/{1}}}\,\!</math>) of an [[orbiting body]] (<math>m_2\,\!</math>) relative to a [[central body]] (<math>m_1\,\!</math>) is the [[moment (physics)|moment]] of (<math>m_2\,\!</math>)'s relative [[linear momentum]]:
:<math>\mathbf{H_{{2}/{1}}}=\mathbf{r}\times m_2\mathbf{v}\,\!</math>
where:
*<math>\mathbf{r}\,\!</math> is the [[orbital position vector]] of the orbiting body relative to the central body,
*<math>\mathbf{v}\,\!</math> is the [[orbital velocity vector]] of the orbiting body relative to the central body,
*<math>m_2\,\!</math> is mass of the orbiting body.


For a body in an unperturbed orbit about a central body, the orbital plane is stationary, and the relative angular momentum (<math>\mathbf{H_{{2}/{1}}}\,\!</math>) is [[perpendicular]] to the [[Orbital plane (astronomy)|orbital plane]]. <br>
For perturbed orbits where the orbital plane is in motion, the relative angular momentum vector is perpendicular to the (osculating) orbital plane at only two points in the orbit.


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In astrodynamics '''relative angular momentum''' is usually used to derive [[specific relative angular momentum]] (<math>\mathbf{h}\,\!</math>):
:<math>\mathbf{h}=\mathbf{H_{{2}/{1}}}/m_2\,\!</math>
where:
*<math>m_2\,\!</math> is mass of the orbiting body.
 
==See also==
*[[Angular momentum]]
*[[Specific relative angular momentum]]
*[[Linear momentum]]
*[[Momentum]]
 
==References==
{{reflist}}
 
[[Category:Orbits]]
 
{{physics-stub}}
{{astronomy-stub}}

Latest revision as of 19:57, 6 January 2015


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