Larger Planet Makes Deeper Transit - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

Because depth scales as radius squared, a larger planet blocks a bigger patch of the stellar disk and makes a deeper transit. Doubling the planet radius quadruples the dip, holding the star fixed. The clean scaling holds for the ideal uniform-disk model; measured depths also shift with limb-darkening, inclination, and contamination.

Changing only radius ratio changes the checked 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

Only the radius ratio changes

With radius ratio 2/5, the planet is larger relative to the star.

r=\tfrac{2}{5}

The depth becomes four twenty-fifths

The squared ratio is 4/25, so the dip is deeper.

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