Past exam of the mathematics course of the University of Cambridge 2015 iii Paper 59 4 g Solution 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 –: 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 –: 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 at the surface (about effective emission temperature); Jupiter has about near one bar (about effective temperature); hot Jupiters commonly have photospheric temperatures of order –; and the Sun's photosphere is about . Upper layers, nightsides, deep interiors and the solar corona have different temperatures. These are characteristic values, not constant temperatures throughout each atmosphere.
Planetary stratosphere 2026-10-06
An upper atmospheric region above the tropopause in which shortwave heating can produce an atmospheric thermal inversion. Ozone on Earth, and methane and aerosols on giant planets, are examples of absorbers that help heat it. Its positive altitude temperature gradient makes it stable against homogeneous-gas thermal convection.
Planetary troposphere 2026-10-06
The lower part of a planetary atmosphere where temperature generally decreases outward and convection can carry intrinsic or surface heat. Its upper boundary is a tropopause. Stellar irradiation, composition gradients and clouds affect the extent of this region; pressure alone does not universally identify it.