= Tisserand periapsis bound
{c}
{title2=$q\ge q_{\min}(T)$}
For bound <planet>-crossing <Kepler orbits>, $T=2/(q+Q)+2\sqrt{2qQ/(q+Q)}\cos I$, with the <planet> radius taken as one. At fixed $q<1$, $T$ is maximized by $I=0$ and $Q=1$. For $2<T<3$ this gives $q\ge(1-\sqrt{3-T})^2/[1+2\sqrt{3-T}-(3-T)]$. This form remains regular at $T=\sqrt8$. It is an invariant-based accessibility bound, not a guarantee that a scattering history attains it; for $0<T\le2$ it gives no positive universal <pericentre> floor.
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