en>Gilliam: Reverted edits by 189.176.113.84 (talk) to last version by 195.37.61.178

2014-11-17T22:58:53Z

Reverted edits by 189.176.113.84 (talk) to last version by 195.37.61.178

en>SuperJew: Disambiguated: weak equivalence → weak equivalence (homotopy theory)

2013-11-18T20:46:26Z

Disambiguated: weak equivalence → weak equivalence (homotopy theory)

← Older revision		Revision as of 22:46, 18 November 2013
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	The ~~most common colors available are blues~~ and ~~reds~~. ~~Even if you feel~~ it is not ~~healthy~~, ~~consider taking it home~~.<br><br>~~my webpage~~ [~~http~~://~~fishtankhq~~.~~com~~/40-~~gallon~~-~~aquarium~~/ ~~fresh water fish~~]		{{Confusing\|date=July 2009}}
			[[Image:Orbit1.svg\|thumb\|right\|400px\|The longitude of the [[ascending node]].]]
			The '''longitude of the ascending node''' (☊ or Ω) is one of the [[orbital elements]] used to specify the [[orbit]] of an object in space. It is the angle from a reference direction, called the ''[[origin of longitude]]'', to the direction of the [[ascending node]], measured in a [[reference plane]].<ref>[http://www.lns.cornell.edu/~seb/celestia/orbital-parameters.html Parameters Describing Elliptical Orbits], web page, accessed May 17, 2007.</ref> Commonly used reference planes and origins of longitude include:
			* For a [[geocentric orbit]], [[Earth]]'s [[equator]]ial plane as the reference plane, and the [[First Point of Aries]] as the origin of longitude. In this case, the longitude is also called the '''right ascension of the ascending node''', or '''RAAN'''. The angle is measured eastwards (or, as seen from the [[north]], [[counterclockwise]]) from the [[First Point of Aries]] to the node.<ref name="egler" /><ref>[http://www.amsat.org/amsat/keps/kepmodel.html Keplerian Elements Tutorial], amsat.org, accessed May 17, 2007.</ref>
			* For a [[heliocentric orbit]], the [[ecliptic]] as the reference plane, and the First Point of Aries as the origin of longitude. The angle is measured counterclockwise (as seen from north of the ecliptic) from the First Point of Aries to the node.<ref name="egler">[http://www.physics.ncsu.edu/courses/astron/orbits.html Orbital Elements and Astronomical Terms], Robert A. Egler, Dept. of Physics, [[North Carolina State University]]. Web page, accessed May 17, 2007.</ref>
			* For an orbit outside the [[Solar System]], the plane through the primary perpendicular to a line through the observer and the primary (called the ''[[plane of the sky]]'') as the reference plane, and north, i.e., the [[orthographic projection\|perpendicular projection]] of the direction from the observer to the [[North Celestial Pole]] onto the plane of the sky, as the origin of longitude. The angle is measured eastwards (or, as seen by the observer, counterclockwise) from north to the node.<ref name="aitken">''The Binary Stars'', R. G. Aitken, New York: Semi-Centennial Publications of the University of California, 1918.</ref><sup>, pp. 40, 72, 137; </sup><ref name="tatum">[http://astrowww.phys.uvic.ca/~tatum/celmechs.html ''Celestial Mechanics''], [[Jeremy B. Tatum]], on line, accessed May 17, 2007.</ref><sup>, chap. 17.</sup>

			In the case of a [[binary star]] known only from visual observations, it is not possible to tell which node is ascending and which is descending. In this case the orbital parameter which is recorded is the '''longitude of the node''', Ω, which is the longitude of whichever node has a longitude between 0 and 180 degrees.<ref name="tatum" /><sup>, chap. 17;</sup><ref name="aitken" /><sup>, p. 72.</sup>

			==Calculation from state vectors==
			In [[astrodynamics]], the longitude of the ascending node can be calculated from the [[specific relative angular momentum]] vector '''''h''''' as follows:

			:<math> \mathbf{n} = \mathbf{k} \times \mathbf{h} = (-h_y, h_x, 0)</math>
			:<math> \Omega =\arccos { {n_x} \over { \mathbf{\left \|n \right \|}}}\ \ (n_y\ge 0);</math>
			:<math>\Omega =2\pi - \arccos { {n_x} \over { \mathbf{\left \|n \right \|}}}\ \ (n_y<0).</math>

			Here, '''''n'''''=<''n''<sub>x</sub>, ''n''<sub>y</sub>, ''n''<sub>z</sub>> is a vector pointing towards the [[ascending node]]. The reference plane is assumed to be the ''xy''-plane, and the origin of longitude is taken to be the positive ''x''-axis. '''''k''''' is the unit vector (0, 0, 1), which is the normal vector to the ''xy'' reference plane.

			For [[non-inclined orbit]]s (with [[orbital inclination\|inclination]] equal to zero), Ω is undefined. For computation it is then, by convention, set equal to zero; that is, the ascending node is placed in the reference direction, which is equivalent to letting '''''n''''' point towards the positive ''x''-axis.

			== See also ==
			*[[Kepler orbit]]s
			*[[Equinox]]
			*[[Orbital node]]
			*[[Orbital_perturbation_analysis_(spacecraft)#Perturbation_of_the_orbital_plane_2\|perturbation of the orbital plane]] can cause revolution of the ascending node

			==References==
			<references />

			{{orbits}}

			[[Category:Orbits]]

			[[ru:Кеплеровы элементы орбиты#Долгота восходящего узла]]

en>Agol: /* Examples */

2012-06-21T05:42:52Z

Examples

New page

The most common colors available are blues and reds. Even if you feel it is not healthy, consider taking it home.<br><br>my webpage [http://fishtankhq.com/40-gallon-aquarium/ fresh water fish]

Classifying space - Revision history

en>Gilliam: Reverted edits by 189.176.113.84 (talk) to last version by 195.37.61.178

en>SuperJew: Disambiguated: weak equivalence → weak equivalence (homotopy theory)

en>Agol: /* Examples */