Asymptotic gain model: Difference between revisions

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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.
 
==Uses==
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}}

Revision as of 13:33, 10 February 2013

Template:Multiple issues In celestial mechanics, the relative angular momentum () of an orbiting body () relative to a central body () is the moment of ()'s relative linear momentum:

where:

For a body in an unperturbed orbit about a central body, the orbital plane is stationary, and the relative angular momentum () is perpendicular to the orbital plane.
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.

Uses

In astrodynamics relative angular momentum is usually used to derive specific relative angular momentum ():

where:

See also

References

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