Transit Radius Depth Cross-Scan - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

Three exact rows show radius ratio squaring into transit depth. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Transit depth squares the radius ratio

The checked source has radius ratio two fifths, so the depth is four twenty-fifths.

\text{depth}=\left(\tfrac{2}{5}\right)^{2}=\tfrac{4}{25}

Radius ratio changes are squared in the depth

The rows show that increasing radius ratio from one fifth to three fifths changes depth from one twenty-fifth to nine twenty-fifths.

\begin{array}{c|c}r&r^{2}\\\frac{1}{5}&\frac{1}{25}\\\frac{2}{5}&\frac{4}{25}\\\frac{3}{5}&\frac{9}{25}\\\end{array}