 Pericentre geometry of an exterior resonance

At pericentre, mean longitude equals longitude of periapsis, so resonant argument $\varphi =(p+q)\lambda -p{\lambda }_p-q\varpi$ becomes $\varphi =p(\varpi -{\lambda }_p)$. The pericentre angle in the planet's rotating frame is $\varphi /p$ modulo $2\pi /p$. For coprime $p,q$, there are $p$ distinct pericentre directions before the trajectory closes. Resonant-argument libration restricts these directions and supplies resonance protection.