Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 315 / 1 / d / Solution

For $R_p=R_{\oplus }$, $R_{\ast }=0.1R_{\odot }$, $T_p=600\mathrm{K}$, and $T_{\ast }=3500\mathrm{K}$, the same thermal eclipse depth at $17\mu \mathrm{m}$ isThus a $100\mathrm{ppm}$ uncertainty givesThis assumes one independent eclipse measurement with that precision, negligible reflected light in the infrared, no atmosphere, and blackbody emission from the bare surface.