Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 315 / 2 / c / Solution

At exoplanet secondary eclipse, the full-phase planet-star flux ratio is the sum of reflected and thermal light. Approximating both bodies as unresolved blackbodies and taking wavelength-independent geometric albedo,The first term is a flat reflected-light level under the stated constant-albedo assumption. At short wavelength the cool planet lies in the Wien limit, so thermal emission is exponentially suppressed and reflection dominates. At long wavelength both spectra enter the Rayleigh-Jeans law, givingThe sketch therefore starts on the reflected plateau, rises where planetary blackbody radiation becomes important, and asymptotically approaches the long-wavelength plateau. This neglects spectral albedo features, phase dependence, stellar lines, and a nonisothermal planetary photosphere.