\frac{Brightness of planet}{Brightness of star} = \frac{B_{p}}{B_{s}} = \frac{surface area of planet}{surface area of star}

= \frac{4πR_{p}^{2}}{4πR_{s}^{2}}

= (\frac{R_{p}}{R_{s}} )^{2}

\frac{Brightness of planet}{Brightness of star} = \frac{B_{p}}{B_{s}} = \frac{surface area of planet}{surface area of orbit}

= \frac{4πR_{p}^{2}}{4πr_{orb}^{2}}

= (\frac{R_{p}}{r_{orb}} )^{2}