Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-315/2/a/solution

The measured mass and radius illustrate the exoplanet interior-composition degeneracy. Three plausible structures are:
An exoplanet transmission spectrum can distinguish a large-scale-height hydrogen atmosphere from compact steam or carbon-dioxide atmospheres. Molecular abundances, clouds, atmospheric mean molecular mass, and atmospheric escape constrain the envelope mass and evolution. An exoplanet emission spectrum constrains temperature, albedo, and internal cooling. A detected hydrogen-rich atmosphere favors the first scenario, a water-dominated high-molecular-weight spectrum supports the second, and a thin secondary atmosphere supports the third, although clouds can preserve degeneracies.

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