= Angular-momentum kicks to nearly radial orbits
{title2=$q\simeq h^2/(2GM)$}
For a nearly radial <Kepler orbit>, $q\simeq h^2/(2GM)$, so modest changes in <specific angular momentum> can strongly change <pericentre>. A planetary <torque> acting for a reference orbital time gives $\delta h\sim(m_p/M)\sqrt{GMa_p}$. Coherent kicks change $q$ by order itself after $N\sim(M/m_p)\sqrt{q/a_p}$ orbital-scale encounters, whereas uncorrelated kicks require an order-$N^2$ random-walk count. Both estimates are conditional on encounter geometry: a close encounter with a smaller <impact parameter> can give a much larger kick.
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