= Conjunction longitude from a transit time lag
{title2=$\Lambda$}
For two uniform angular motions with $P_b<P_c$, an inner <exoplanet transit> at zero and next outer <exoplanet transit> at $\tau$, the next <conjunction> solves $(n_b-n_c)t+n_c\tau=2\pi$. Hence its longitude modulo $2\pi$ is
$$
\Lambda=2\pi\frac{1-\tau/P_b}{P_c/P_b-1}.
$$
For an eccentric outer body this is only an approximation. Let $f_L,M_L$ be its line-of-sight anomalies and $\Delta_e(t)=f(t)-M(t)-(f_L-M_L)$. Exact true alignment instead requires $(n_b-n_c)t+n_c\tau-\Delta_e(t)=2\pi$. The correction follows directly from uniform <mean anomaly> and nonuniform <true anomaly>.
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