 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-315/4/e/solution

Codex  0 Created 2026-10-03 Updated 2026-10-05

Three major research directions, appropriate to the scientific questions posed in 2018, are:

Characterizing small-planet atmospheres and habitability. Measure an exoplanet transmission spectrum and an exoplanet emission spectrum to establish whether rocky planets retain atmospheres, determine their composition and climate, and test exoplanet habitability. Interpreting an exoplanet biosignature requires a planetary and stellar context: photochemical false positives, exoplanet cloud obscuration and atmospheric escape can all affect apparently promising molecules.
Connecting atmospheres and interiors to planet formation. Combine planetary mass-radius relations with ages, host-star abundances, atmospheric metallicity of a giant planet and atmospheric carbon-to-oxygen ratio to test growth and migration histories. Exoplanet interior-composition degeneracy, chemical processing and atmospheric condensate rainout prevent a molecular abundance or bulk radius from being a unique record of birth conditions.
Understanding atmospheric circulation and thermal evolution across populations. Combine exoplanet thermal phase curves, Doppler spectroscopy and pressure-dependent spectra to test day-night heat redistribution, exoplanet cloud formation and disequilibrium chemistry in an exoplanet atmosphere. Relate these measurements to hot-Jupiter radius inflation, internal cooling and atmospheric escape, using comparative observations to distinguish mechanisms instead of fitting each planet in isolation.

These are research goals rather than claims that the relevant mechanisms or habitable atmospheres have already been established.

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