Editing Longitude of the ascending node (section)

==Calculation from state vectors==
In [[astrodynamics]], the longitude of the ascending node can be calculated from the [[specific relative angular momentum]] vector '''h''' as follows:

:<math>\begin{align}
  \mathbf{n} &= \mathbf{k} \times \mathbf{h} = (-h_y, h_x, 0) \\
      \Omega &= \begin{cases}
                  \arccos { {n_x} \over { \mathbf{\left |n \right |}}},      &n_y \ge 0; \\
                  2\pi-\arccos { {n_x} \over { \mathbf{\left |n \right |}}}, &n_y < 0.
                \end{cases}
\end{align}</math>

Here, '''n''' = ⟨''n''<sub>x</sub>, ''n''<sub>y</sub>, ''n''<sub>z</sub>⟩ 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 orbit]]s (with [[orbital inclination|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.