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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-59/4/g/solution

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Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 59 / 4 / g / Solution by

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

For typical well-mixed structures, the dominant processes are:

Gas giant interiors: efficient convection through most of the deep fluid envelope; radiative transfer releases the heat near the photosphere.
Rocky interiors: slow solid-state mantle convection over geological time, with heat conduction dominant across the rigid lithosphere. A liquid core can also convect; being solid does not prevent creep-driven heat transport in the mantle.
Weakly irradiated giant atmospheres at $0.1$ – $10 bar$ : usually convection in the planetary troposphere, becoming radiative near and above the tropopause. The transition pressure and cloud or compositional effects vary between planets.
Strongly irradiated hot Jupiter atmospheres at $0.1$ – $10 bar$ : usually a stable radiative region; the deep radiative-convective boundary can lie at substantially larger pressure. Atmospheric winds also redistribute energy horizontally.

Representative temperatures must specify the level: Earth has about $288 K$ at the surface (about

255 K

effective emission temperature); Jupiter has about $165 K$ near one bar (about

125 K

effective temperature); hot Jupiters commonly have photospheric temperatures of order $1000$ – $2500 K$ ; and the Sun's photosphere is about $5800 K$ . Upper layers, nightsides, deep interiors and the solar corona have different temperatures. These are characteristic values, not constant temperatures throughout each atmosphere.

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