# orbital angular momentum and the longitude of ascending node

Consider the motion of a planet around an oblate star. Because of the oblateness the star has a non-zero quadrupole moment which causes the orbital angular momentum of the planet to precess around the symmetry axis of the oblate star. My naive question is: is this precession rate exactly the same as the precession rate of the longitude of the ascending node or are there subtle differences between the two?

They're the same, assuming the star's equator is the principal plane of the coordinate system. One way to calculate the longitude of ascending node as $\Omega = \arctan(h_x, -h_y)$, where $\arctan(a,b)$ is the two-argument inverse tangent function and $h_x$ and $h_y$ are the x and y components of angular momentum vector.