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Encyclopedia > Longitude of the ascending node

The Longitude of the ascending node (☊, also noted Ω) is one of the orbital elements used to specify the orbit of an object in space. For a Sun-orbiting body, it is the angle formed at the Sun from the First Point of Aries to the body's ascending node, measured in the reference plane (the ecliptic) and in the direct sense. In aerospace engineering, it is usually called the right ascension of the ascending node (or RAAN). The elements of an orbit are the parameters needed to specify that orbit uniquely, given a model of two ideal masses obeying the Newtonian laws of motion and the inverse-square law of gravitational attraction. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... The Sun is the star at the center of the Solar System. ... The Sun is the star at the center of the Solar System. ... The First Point of Aries, also called the vernal equinox point, is one of the two points on the celestial sphere where the celestial equator intersects the ecliptic. ... The ascending node is one of the orbital nodes, a point in the orbit of an object where it crosses the plane of the ecliptic from the south celestial hemisphere to the north celestial hemisphere in the direction of motion. ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ...

Fig. 1: The line of nodes is the green line in this diagram.

Image File history File links Orbit. ... Image File history File links Orbit. ...

## Calculation from state vectors GA_googleFillSlot("encyclopedia_square");

In astrodynamics, for elliptic orbits the longitude of the ascending node $Omega ,$ is the angle between the reference direction (e.g. the vernal equinox) and the ascending node. It can be calculated from orbital state vectors as: Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ... Two bodies with similar mass orbiting around a common barycenter with elliptic orbits. ... Illumination of Earth by Sun on the day of equinox The vernal equinox (or spring equinox) marks the beginning of astronomical spring. ... The ascending node is one of the orbital nodes, a point in the orbit of an object where it crosses the plane of the ecliptic from the south celestial hemisphere to the north celestial hemisphere in the direction of motion. ... In astrodynamics or celestial dynamics orbital state vectors (sometimes State Vectors) are vectors of position () and velocity () that together with their time (epoch) () uniquely determine the state of an orbiting body. ...

$Omega = arccos { {n_x} over { mathbf{left |n right |}}}$
(if $n_y < 0 ,$ then $Omega = 2 pi - Omega ,$)

where:

• $n_x ,$ is the x-component of $mathbf{n}$,
• $mathbf{n}$ is cartesian vector pointing towards the ascending node (i.e. the z-component of $mathbf{n}$ is zero).

For equatorial orbits (i.e. orbits with orbital inclination equal to zero) $Omega,$ is undefined. For computations it is then by convention set to zero i.e. "ascending node" is placed in the reference direction which is equivalent to setting $mathbf{n} / mathbf{left |n right |} = (1,0,0)$ for a right-handed system with the x-axis pointing towards the vernal equinox (or other reference direction) and the z-axis pointing upwards.piop Cartesian means of or relating to the French philosopher and mathematician René Descartes. ... Inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit and is the angular distance of the orbital plane from the plane of the reference (usually planets equator or the ecliptic), stated in degrees. ... The ascending node is one of the orbital nodes, a point in the orbit of an object where it crosses the plane of the ecliptic from the south celestial hemisphere to the north celestial hemisphere in the direction of motion. ...

Results from FactBites:

 Practical Astronautics (1528 words) ascending node - the point on the orbit where the spacecraft crosses the equatorial plane moving from the southern hemisphere to the northern hemisphere. 180 degrees from the ascending node is the descending node. LAN realtes the orbits orientation to the Prime Meridian.
 Orbital Elements and Astronomical Terms (1242 words) Figure 2): The angle between the plane of the orbit and the plane of the celestial equator for Earth orbiting satellites (or the plane of the ecliptic for sun orbiting satellites). * Longitude of the Ascending Node, (W in Figure 2): The angle between the vernal equinox and the ascending node, measured counter-clockwise. It is equal to the sum of the Argument of Perigee and the Longitude of the Ascending Node (W + w in figure 2).
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