Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 8E / c / Solution

The orbital plane has normal parallel to the conserved angular momentum. If its inclination to the equatorial plane is $\psi$, then $L_z=L\cos \psi$. ThereforesoIt vanishes when $\sin \theta =|\cos \psi |$, equivalently at the greatest northern and southern latitudes reached by the inclined orbit. These are the turning points of the polar motion.