= Transit duration of a small planet
{title2=$D\simeq PR_\star\sqrt{1-b^2}/(\pi a)$}
For a small <planet> on a nearly circular <Kepler orbit>, a stellar chord at normalized <transit impact parameter> $b$ has length $2R_\star\sqrt{1-b^2}$. Dividing by transverse orbital speed $2\pi a/P$ gives the duration. A central transit has the longest duration within this approximation. Eliminating $a$ with <Kepler's third law> yields $P/D^3\ge\pi^2G\rho_\star/3$ for known mean stellar <mass density>. Finite planet radius, appreciable <orbital eccentricity>, and $R_\star/a$ corrections change the bound.
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