= Resonant conjunction geometry
For an eccentric outer body and circular inner perturber, the exterior <resonant argument> is $\phi=(p+q)\lambda_{\rm out}-p\lambda_{\rm in}-q\varpi$. At equal <mean longitudes> $\Lambda$, <conjunction> phases are
$$
\Lambda_j=\varpi+\frac{\phi+2\pi j}{q},\qquad j=0,\ldots,q-1.
$$
The <synodic period> and coprime $p,q$ determine the visitation order, with advance $2\pi p/q$. For actual true alignment, write $x=f$ and $y=M(f)$ for the eccentric body's <true anomaly> and <mean anomaly>. Then $\phi=(p+q)y-px$ instead of $qx$. The evenly spaced directions are a leading-small-eccentricity approximation.
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