# Longitude of the ascending node

The

**longitude of the ascending node**(☊ or Ω) is one of theorbital elements used to specify theorbit of an object in space. It is the angle from a reference direction, called the "origin of longitude ", to the direction of theascending node , measured in areference plane . [*[*] Commonly used reference planes and origins of longitude include:*http://www.lns.cornell.edu/~seb/celestia/orbital-parameters.html Parameters Describing Elliptical Orbits*] , web page, accessedMay 17 ,2007 .

* For ageocentric orbit ,Earth 'sequator ial plane as the reference plane, and theFirst 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 thenorth ,counterclockwise ) from the First Point of Aries to the node. [*[*]*http://www.amsat.org/amsat/keps/kepmodel.html Keplerian Elements Tutorial*] , amsat.org, accessedMay 17 ,2007 .

* For aheliocentric orbit , theecliptic 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. [*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, accessedMay 17 ,2007 .]

* For an orbit outside theSolar 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 perpendicular projection of the direction from the observer to theNorth 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."The Binary Stars", R. G. Aitken, New York: Semi-Centennial Publications of the University of California, 1918.]^{, pp. 40, 72, 137; }[*http://astrowww.phys.uvic.ca/~tatum/celmechs.html "Celestial Mechanics"*] , J. B. Tatum, on line, accessedMay 17 ,2007 .]^{, chap. 17.}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.^{, chap. 17;}^{, p. 72.}**Calculation from state vectors**In

astrodynamics , the longitude of the ascending node can be calculated fromorbital state vectors as follows::$Omega\; =arccos\; \{\; \{n\_x\}\; over\; \{\; mathbf\{left\; |n\; ight\; |\}\; (n\_yge\; 0);$:$Omega\; =2pi\; -\; arccos\; \{\; \{n\_x\}\; over\; \{\; mathbf\{left\; |n\; ight\; |\}\; (n\_y<0).$Here,

**"n**"=("n"_{x}, "n"_{y}, "n"_{z}) is a vector pointing towards theascending node . The reference plane is assumed to be the "xy"-plane, and the origin of longitude is taken to be the positive "x"-axis.For

non-inclined orbit s (with 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.**References****See also***

Equinox

*Orbital node

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