Longitude of The Ascending Node - Calculation From State Vectors

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:

Here, n=(n_x, n_y, n_z) 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), Ω 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.