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.
Types
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.
Here, n = ⟨nx, ny, nz⟩ 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.