= Conjunction-longitude sensitivity to an encounter
{title2=$\delta\Lambda=\Lambda'(\epsilon)\delta\epsilon$}
For an exterior circular grain with <radiation-pressure coefficient> $\beta$, set $q=\sqrt{1-\beta}$ and $\epsilon=a/a_p-1$. Its next <conjunction> occurs after the <synodic period>, during which the planet's unwrapped <mean longitude> advances by $\Lambda=2\pi/[1-q(1+\epsilon)^{-3/2}]$. A weak <planetary scattering> encounter changes this by $\delta\Lambda\simeq-3\pi q(1+\epsilon)^{-5/2}\delta\epsilon/[1-q(1+\epsilon)^{-3/2}]^2$. Unwrapped longitude counts turns; reducing it modulo $2\pi$ before comparison would erase this measure of timing sensitivity.
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