= Coplanar transit limit
{title2=$P_2/P_1<[(1+k_2)/b_1]^{3/2}$}
For two exactly coplanar <circular orbits> around the same <star>, <transit impact parameters> scale as <semi-major axis>, hence as $P^{2/3}$. Any overlap by the outer <planet> requires $b_2<1+k_2$. In the point-planet limit the period ratio is bounded by $b_1^{-3/2}$. Tangency has zero duration, so this is a geometric supremum; practical detection also requires sufficient <signal-to-noise ratio> and survey coverage.
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