Longitude of the ascending node

﻿
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. [ [http://www.lns.cornell.edu/~seb/celestia/orbital-parameters.html Parameters Describing Elliptical Orbits] , web page, accessed May 17, 2007.] Commonly used reference planes and origins of longitude include:
* For a geocentric orbit, Earth's equatorial 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. [ [http://www.amsat.org/amsat/keps/kepmodel.html Keplerian Elements Tutorial] , amsat.org, accessed May 17, 2007.]
* 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. [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.]
* 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 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."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, accessed May 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, &Omega;, 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 from orbital state vectors as follows:

:$Omega =arccos \left\{ \left\{n_x\right\} over \left\{ mathbf\left\{left |n ight |\right\} \left(n_yge 0\right);$:$Omega =2pi - arccos \left\{ \left\{n_x\right\} over \left\{ mathbf\left\{left |n ight |\right\} \left(n_y<0\right).$Here, "n"=("n"x, "n"y, "n"z) 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.

For non-inclined orbits (with inclination equal to zero), &Omega; 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

*Equinox
*Orbital node

Wikimedia Foundation. 2010.

Look at other dictionaries:

• Longitude of the periapsis — In astrodynamics, the longitude of the periapsis (symbolized varpi) of an orbiting body is the longitude (measured from the point of the vernal equinox) at which the periapsis (closest approach to the central body) would occur if the body s… …   Wikipedia

• Node — In general, a node is a localised swelling (a knot ) or a point of intersection (a vertex). Node may refer to: In mathematics Node (autonomous system), behaviour for an ordinary differential equation near a critical point Node (graph theory), a… …   Wikipedia

• Orbital node — The ascending node. An orbital node is one of the two points where an orbit crosses a plane of reference to which it is inclined. An orbit which is contained in the plane of reference (called non inclined) has no nodes …   Wikipedia

• Secular variations of the planetary orbits — The Secular Variations of the Planetary Orbits (French: Variations Séculaires des Orbites Planétaires, abbreviated as VSOP) is a semi analytic theory describing the long term changes (secular variation) in the orbits of the planets Mercury to… …   Wikipedia

• Orbit of the Moon — Not to be confused with Lunar orbit in the sense of a selenocentric orbit, that is, an orbit around the Moon The Moon completes its orbit around the Earth in approximately 27.3 days (a sidereal month). The Earth and Moon orbit about their… …   Wikipedia

• Mean longitude — In astrodynamics or celestial dynamics, mean longitude is the longitude at which an orbiting body could be found if its orbit were circular, and free of perturbations, and if its inclination were zero. Both the mean longitude and the true… …   Wikipedia

• Lunar node — Dragon s Tail redirects here. For the Dragon s Tail stretch of road in North Carolina, see Deals Gap, North Carolina. The lunar nodes are the points where the moon s path in the sky crosses the ecliptic, the sun s path in the sky The lunar nodes… …   Wikipedia

• True longitude — In astrodynamics true longitude is the longitude at which an orbiting body could actually be found if its inclination were zero. Together with the inclination and the ascending node, the true longitude can tell us the precise direction from the… …   Wikipedia

• celestial mechanics — the branch of astronomy that deals with the application of the laws of dynamics and Newton s law of gravitation to the motions of heavenly bodies. [1815 25] * * * Branch of astronomy that deals with the mathematical theory of the motions of… …   Universalium

• Argument of periapsis — The argument of periapsis (or argument of perifocus) ( ω ) is the orbital element describing the angle of an orbiting body s periapsis (the point of closest approach to the central body), relative to its ascending node (the point where the body… …   Wikipedia