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=(nx, ny, nz) 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.
Read more about this topic: Longitude Of The Ascending Node
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