Past exam of the mathematics course of the University of Cambridge 2016 iii Paper 315 4 g Solution Created 2026-10-03 Updated 2026-10-06
A super-Earth is a planet more massive than Earth but below the usual ice-giant scale, conventionally about --. The term does not guarantee an Earth-like or rocky composition; water-rich planets and objects with small H/He envelopes can lie in this range.
The most direct constraints are transit radius and a mass from radial velocities or transit-timing variations, giving . Comparing these with interior models constrains the possible iron core, silicate mantle, water layer and gas envelope, but many mixtures share one mass and radius.
Additional observables include atmospheric spectra/mean molecular weight and escape signatures, which test whether a low-density envelope is H/He or heavier volatiles; stellar Fe/Mg/Si abundances as priors on refractory composition; and age, irradiation and orbital history, which control thermal expansion and envelope survival. Where measurable, a Love number or related apsidal response constrains central concentration. Mass and radius constrain families of interiors, not a unique composition; atmospheric and dynamical information can reduce this exoplanet interior-composition degeneracy.