= Solution
For each point $(\Delta\phi_1,e)$, sample $\delta\in[-\Delta\phi_1,\Delta\phi_1]$ and the three conjunction branches
$$
M_{c,k}=\frac{\pi+\delta+2\pi k}{3}.
$$
For every branch, solve <Kepler's equation> for the <eccentric anomaly>, evaluate $r=a(1-e\cos E)$, and minimize the planet-planetesimal separation over $\delta$ and $k$. Mark the point as encounter-capable when this minimum is below a chosen $R_{\rm enc}$, naturally the <Hill radius> for strong scattering. Repeating this calculation on a grid traces the boundary in the $\Delta\phi_1$--$e$ plane.
Direct integrations of the <circular restricted three-body problem> can then refine the geometric map by allowing the <resonant argument>, eccentricity, and conjunction kicks to evolve self-consistently. The integrations distinguish merely orbit-crossing initial data from trajectories that actually enter the encounter region, and reveal chaotic layers near the boundary.
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