= Resonance-overlap encounter estimate
{title2=$j_c\sim\mu^{-2/7}$}
A local weak <gravitational assist> estimate for a nonradiating circular grain gives $\delta\epsilon\simeq32\mu^2\epsilon^{-5}$, where $\mu=M_p/M_\star$. <Conjunction-longitude sensitivity to an encounter> then gives $|\delta\Lambda|\simeq128\pi\mu^2/(3\epsilon^7)$. Requiring the change to exceed one full turn and using $\epsilon\simeq2/(3j)$ gives $j_c\simeq(2/729)^{1/7}\mu^{-2/7}$. This motivates loss of coherent resonant conjunctions, rather than proving that every initial phase escapes. The coefficient depends on the encounter convention and the approximations; near-planet <Hill equations> require a consistent rotating-frame shear instead of mixing local inertial and rotating velocities.
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