Radius Ratio Squares to Depth - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

A transit depth starts as the square of one radius ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A radius ratio becomes an area ratio by squaring

The planet-to-star radius ratio is 1/5.

r=\tfrac{1}{5}

The transit depth is the checked square

Squaring the radius ratio gives depth 1/25.

\text{depth}=\left(\tfrac{1}{5}\right)^{2}=\tfrac{1}{25}