Impact parameter from total transit duration
= Impact parameter from total transit duration
{title2=$b^2=[(1+k)^2-A^2s^2]/(1-s^2)$}
For a circular orbit, define $k=R_p/R_\star$, $A=a/R_\star$ and $s=\sin(\pi T_{14}/P)$. Inverting contact geometry gives $b^2=[(1+k)^2-A^2s^2]/(1-s^2)$. The inferred value is conditional on the stellar scale, the total-duration convention and the orbital model; it must satisfy $0\leq b<1+k$. A non-grazing complete crossing additionally has $b<1-k$.