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 specified reference direction, called the origin of longitude, to the direction of the ascending node, as measured in a specified reference plane. 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 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 First Point of Aries to the node. 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 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. 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., pp. 40, 72, 137; , 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, Ω, and represents the longitude of whichever node has a longitude between 0 and 180 degrees.

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Longitude of the ascending node

Orbital pole

An orbital pole is either point at the ends of the orbital normal, an imaginary line segment that runs through a focus of an orbit (of a revolving body like a planet, moon or satellite) and is perpendicular (or normal) to the orbital plane. Projected onto the celestial sphere, orbital poles are similar in concept to celestial poles, but are based on the body's orbit instead of its equator. The north orbital pole of a revolving body is defined by the right-hand rule.

Orbital plane

The orbital plane of a revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane. A common example would be the positions of the centers of a massive body (host) and of an orbiting celestial body at two different times/points of its orbit. The orbital plane is defined in relation to a reference plane by two parameters: inclination (i) and longitude of the ascending node (Ω).

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