= Total duration of a circular planetary transit
{title2=$T_{14}=\frac P\pi\arcsin\sqrt{\frac{(1+k)^2-b^2}{(a/R_\star)^2-b^2}}$}
The first-to-fourth-contact duration of an <exoplanet transit> by a spherical opaque <planet> of <radius> ratio $k=R_p/R_\star$ on a <circular orbit>. The <transit impact parameter> is $b=(a/R_\star)\cos i$. The formula includes finite planet size and orbital curvature; it reduces to the <transit duration of a small planet> when $k\to0$ and $R_\star/a\ll1$. It describes contact geometry, not a uniquely specified light-curve threshold in the presence of <limb darkening>.
Back to article page
