The longitude of the ascending node (☊ or Ω) is one of the
orbital elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same ...
used to specify the
orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a ...
of an object in space. It is the angle from a specified reference direction, called the ''
origin of longitude'', to the direction of the
ascending node
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes.
Planes of reference
Common planes of reference ...
, as measured in a specified
reference plane
In celestial mechanics, the plane of reference (or reference plane) is the plane used to define orbital elements (positions). The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longi ...
. The ascending node is the point where the orbit of the object passes through the plane of reference, as seen in the adjacent image. Commonly used reference planes and origins of longitude include:
* For
geocentric orbit
A geocentric orbit or Earth orbit involves any object orbiting Earth, such as the Moon or artificial satellites. In 1997, NASA estimated there were approximately 2,465 artificial satellite payloads orbiting Earth and 6,216 pieces of space debri ...
s,
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface ...
's
equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can al ...
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
Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the earth.
When paired w ...
of the ascending node (RAAN). The angle is measured eastwards (or, as seen from the
north
North is one of the four compass points or cardinal directions. It is the opposite of south and is perpendicular to east and west. ''North'' is a noun, adjective, or adverb indicating direction or geography.
Etymology
The word ''north'' is ...
,
counterclockwise
Two-dimensional rotation can occur in two possible directions. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back up to the top. The opposite s ...
) from the
First Point of Aries to the node.
Keplerian Elements Tutorial
amsat.org, accessed May 17, 2007. An alternative is the local time of the ascending node (LTAN), based on the local mean time
Local mean time (LMT) is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude. This measurement of time was used for everyday use during the 19th century before time zones ...
at which the spacecraft crosses the equator. Similar definitions exist for satellites around other planets (see planetary coordinate systems).
* For heliocentric orbit
A heliocentric orbit (also called circumsolar orbit) is an orbit around the barycenter of the Solar System, which is usually located within or very near the surface of the Sun. All planets, comets, and asteroids in the Solar System, and the Sun i ...
s, the ecliptic
The ecliptic or ecliptic plane is the orbital plane of the Earth's orbit, Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the e ...
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.[Orbital Elements and Astronomical Terms](_blank)
, Robert A. Egler, Dept. of Physics, North Carolina State University
North Carolina State University (NC State) is a public land-grant research university in Raleigh, North Carolina. Founded in 1887 and part of the University of North Carolina system, it is the largest university in the Carolinas. The university ...
. Web page, accessed May 17, 2007.
* For orbits outside the Solar System
The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
, the plane tangent to the celestial sphere
In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...
at the point of interest (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
The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at ...
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; [''Celestial Mechanics''](_blank)
Jeremy B. Tatum, on line, accessed May 17, 2007., chap. 17.
In the case of a binary star
A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in w ...
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 simply labeled longitude of the node, Ω, and represents the longitude of whichever node has a longitude between 0 and 180 degrees., chap. 17;, p. 72.
Calculation from state vectors
In astrodynamics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
, the longitude of the ascending node can be calculated from the specific relative angular momentum
In celestial mechanics, the specific relative angular momentum (often denoted \vec or \mathbf) of a body is the angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear ...
vector h as follows:
:
Here, n = ⟨''n''x, ''n''y, ''n''z⟩ is a vector pointing towards the ascending node
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes.
Planes of reference
Common planes of reference ...
. 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
A near-equatorial orbit is an orbit that lies close to the equatorial plane of the object orbited. Such an orbit has an inclination near 0°. On Earth, such orbits lie on the celestial equator, the great circle of the imaginary celestial sphere on ...
s (with inclination
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.
For a satellite orbiting the Earth ...
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
*Equinox
A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and set ...
*Kepler orbits
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of ...
*List of orbits
Summary
A simple list of just the common orbit abbreviations.
List of abbreviations of common Earth orbits
List of abbreviations of other orbits
Classifications
The following is a list of types of orbits:
Centric classifications
* Gal ...
*Orbital node
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes.
Planes of reference
Common planes of reference ...
* Perturbation of the orbital plane can cause precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
of the ascending node.
References
{{Portal bar, Physics, Astronomy, Stars, Spaceflight, Outer space, Solar System, Science
Orbits