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.

Calculation from state vectors

---

In astrodynamics, for elliptic orbits the longitude of the ascending node $\backslash Omega\; \backslash ,$ 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:

$\backslash Omega\; =\; \backslash arccos\; \{\; \{n\_x\}\; \backslash over\; \{\; \backslash mathbf\{\backslash left\; |n\; \backslash right\; |\}\}\}$

(if then $\backslash Omega\; =\; 2\; \backslash pi\; -\; \backslash Omega\; \backslash ,$)

where:

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

For equatorial orbits (i.e. orbits with orbital inclination equal to zero) $\backslash Omega\backslash ,$ 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 $\backslash mathbf\{n\}\; /\; \backslash mathbf\{\backslash left\; |n\; \backslash right\; |\}\; =\; (1,0,0)$ for a right-handed system with the x-axis pointing towards the vernal equinox (or other reference direction) and the z-axis pointing upwards.

See also

---

• Vernal equinox
• Ascending node

Astronomy | Astrodynamics

Дължина на възходящия възел | Longitud del node ascendent | Opstigende knudes længde | Argument des Knotens | Longitudine del nodo ascendente | 昇交点黄経 | Dĺžka výstupného uzla | Kinh độ của điểm nút lên