At full phase immediately before an <exoplanet secondary eclipse>, reflected and thermal light give
$$
\boxed{
\frac{F_p}{F_*}(\lambda)
=A_g(\lambda)\left(\frac{R_p}{a_{\rm orb}}\right)^2
+\left(\frac{R_p}{R_*}\right)^2
\frac{B_\lambda(T_p)}{B_\lambda(T_*)}}.
$$
The phase function equals one at secondary eclipse. For the stated model, the first term is constant below $1\,\mu\mathrm m$ and negligible above it. The $600\,\mathrm K$ thermal component is tiny in the visible, rises through the infrared, and peaks near $4.8\,\mu\mathrm m$ in $B_\lambda$, while the contrast continues to improve toward the mid-infrared because the stellar spectrum falls more rapidly.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 315 / 2 / a / i / Solution

{wiki=Methods_of_detecting_exoplanets#Secondary_eclipse}

During secondary eclipse the planet passes behind its star. The lost system light measures the planet-star flux ratio from reflected starlight and planetary thermal emission.


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 Incoming links: Exoplanet secondary eclipse