The **longitude of the ascending node** (symbol ☊) is one of the orbital elements used to specify the orbit 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 (☊), as measured in a specified reference plane.^{ [1] } 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 orbits, Earth's equatorial plane as the reference plane, and the First Point of Aries (FPA) as the origin of longitude. In this case, the longitude is also called the
**right ascension of the ascending node**(**RAAN**). The angle is measured eastwards (or, as seen from the north, counterclockwise) from the FPA to the node.^{ [2] }^{ [3] }An alternative is the**local time of the ascending node**(**LTAN**), based on the local mean time at which the spacecraft crosses the equator. Similar definitions exist for satellites around other planets (see planetary coordinate systems). - For heliocentric orbits, the ecliptic as the reference plane, and the FPA 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.
^{ [2] } - For orbits outside the Solar System, the plane tangent to 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 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.^{ [4] }^{, pp. 40, 72, 137; }^{ [5] }^{, 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 simply labeled **longitude of the node**, ☊, and represents the longitude of whichever node has a longitude between 0 and 180 degrees.^{ [5] }^{, chap. 17;}^{ [4] }^{, p. 72.}

In astrodynamics, the longitude of the ascending node can be calculated from the specific relative angular momentum vector **h** as follows:

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. **k** is the unit vector (0, 0, 1), which is the normal vector to the *xy* reference plane.

For non-inclined orbits (with inclination equal to zero), ☊ 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.

- Equinox
- Kepler orbits
- List of orbits
- Orbital node
- Perturbation of the orbital plane can cause precession of the ascending node.

The **ecliptic** or **ecliptic plane** is the orbital plane of 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 ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.

**Right ascension** is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point in question above the Earth. When paired with declination, these astronomical coordinates specify the location of a point on the celestial sphere in the equatorial coordinate system.

In mathematics, a **spherical coordinate system** is a coordinate system for three-dimensional space where the position of a given point in space is specified by *three* numbers, : the *radial distance* of the *radial line***r** connecting the point to the fixed point of origin ; the *polar angle θ* of the

An **azimuth** is the angular measurement in a spherical coordinate system which represents the horizontal angle from a cardinal direction, most commonly north.

The **equatorial coordinate system** is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the vernal equinox, and a right-handed convention.

In astronomy, the **ecliptic coordinate system** is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets and many small Solar System bodies have orbits with only slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the vernal (March) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.

**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.

In physics, **angular velocity**, also known as **angular frequency vector**, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates around an axis of rotation and how fast the axis itself changes direction.

**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 orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics.

**Rotation** in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. A rotation is different from other types of motions: translations, which have no fixed points, and (hyperplane) reflections, each of them having an entire (*n* − 1)-dimensional flat of fixed points in a n-dimensional space.

In celestial mechanics, **true anomaly** is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse.

The **argument of periapsis**, symbolized as *ω*, is one of the orbital elements of an orbiting body. Parametrically, *ω* is the angle from the body's ascending node to its periapsis, measured in the direction of motion.

In celestial mechanics, the **longitude of the periapsis**, also called **longitude of the pericenter**, of an orbiting body is the longitude at which the periapsis would occur if the body's orbit inclination were zero. It is usually denoted *ϖ*.

**Mean longitude** is the ecliptic longitude at which an orbiting body could be found if its orbit were circular and free of perturbations. While nominally a simple longitude, in practice the mean longitude does not correspond to any one physical angle.

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.

In celestial mechanics, the **orbital plane of reference** 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 longitude of the ascending node.

**Spacecraft flight dynamics** is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and aerodynamic lift and drag.

**Orbit determination** is the estimation of orbits of objects such as moons, planets, and spacecraft. One major application is to allow tracking newly observed asteroids and verify that they have not been previously discovered. The basic methods were discovered in the 17th century and have been continuously refined.

In celestial mechanics, a **Kepler orbit** is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. A Kepler orbit can also form a straight line. It considers only the point-like gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag, solar radiation pressure, a non-spherical central body, and so on. It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem. As a theory in classical mechanics, it also does not take into account the effects of general relativity. Keplerian orbits can be parametrized into six orbital elements in various ways.

This **glossary of astronomy** is a list of definitions of terms and concepts relevant to astronomy and cosmology, their sub-disciplines, and related fields. Astronomy is concerned with the study of celestial objects and phenomena that originate outside the atmosphere of Earth. The field of astronomy features an extensive vocabulary and a significant amount of jargon.

- ↑ Parameters Describing Elliptical Orbits, web page, accessed May 17, 2007.
- 1 2 Orbital Elements and Astronomical Terms Archived 2007-04-03 at the Wayback Machine , Robert A. Egler, Dept. of Physics, North Carolina State University. Web page, accessed May 17, 2007.
- ↑ Keplerian Elements Tutorial Archived 2002-10-14 at the Wayback Machine , amsat.org, accessed May 17, 2007.
- 1 2
*The Binary Stars*, R. G. Aitken, New York: Semi-Centennial Publications of the University of California, 1918. - 1 2
*Celestial Mechanics*, Jeremy B. Tatum, on line, accessed May 17, 2007.

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