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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/iii/paper-315/4/j/solution

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Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 315 / 4 / j / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-06

Three research directions natural in the 2017 setting are:

Atmospheric characterization of small planets, extending beyond bright hot Jupiters to super-Earth-sized and terrestrial bodies. The aim is to determine whether they retain light envelopes or heavier secondary atmospheres and to understand exoplanet habitability. Potential exoplanet biosignatures require a chemical and stellar context because abiotic processes can mimic individual molecules; future infrared observatories such as the then-planned James Webb Space Telescope offered a route to better spectra, without guaranteeing a biological interpretation.
Connecting measured composition to planet formation and planetary migration. Atmospheric metallicity of a giant planet, atmospheric carbon-to-oxygen ratio, orbital architecture and bulk mass-radius measurements can constrain accretion of gas and solids. Atmospheric condensate rainout, disequilibrium chemistry in an exoplanet atmosphere and exoplanet interior-composition degeneracy make a one-to-one mapping from a measured ratio to a birth location unreliable; comparative samples and coupled models are needed.
Resolving atmospheric structure in space and time. Exoplanet thermal phase curves, repeated spectra, high-resolution planetary spectroscopy and exoplanet direct imaging can test day-night heat redistribution, winds, patchy exoplanet clouds, atmospheric escape and chemical heterogeneity. The challenge is to distinguish actual variability or circulation from changes in stellar light and instrumental calibration.

Small-planet atmospheres, formation through composition, and atmospheric dynamics/variability provide three concrete emerging directions. The examples describe research aims as of the paper's date, rather than treating later discoveries or later operating missions as established in 2017.

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