Past exam of the mathematics course of the University of Cambridge 2015 iii Paper 59 1 c i Solution Created 2026-10-03 Updated 2026-10-06
The continuum exoplanet transit photometry depth is approximately the opaque projected area ratio, assuming a corrected or negligible limb darkening contribution:For a Sun-sized host, . The natural size analogue is Jupiter, not Earth.
The expected bulk constituent is molecular hydrogen, with helium next most abundant for a retained primary planetary atmosphere. The water band detects a strong trace absorber; it does not imply that water is the dominant gas. This interpretation assumes a conventional H/He gas giant; the measured radius by itself is not a measurement of mass or composition.
Past exam of the mathematics course of the University of Cambridge 2016 iii Paper 315 4 h Solution Created 2026-10-03 Updated 2026-10-06
A primary planetary atmosphere is gas captured from the protoplanetary nebula, typically H/He-rich. A secondary planetary atmosphere is assembled or substantially replenished after formation by outgassing, volatile delivery and processing, rather than retaining the original nebular envelope.
Jupiter, Saturn, Uranus and Neptune retain primary H/He envelopes, although their heavy-element enrichment and deep interiors differ. Venus, Earth and Mars have predominantly secondary present-day atmospheres, shaped by volcanic outgassing, impacts, escape and, on Earth, biology. Mercury has a tenuous surface-derived exosphere rather than a substantial retained primary atmosphere. The classification describes origin and evolution, not simply whether a current molecule is heavy or light.
Secondary planetary atmosphere 2026-10-06
A secondary planetary atmosphere is supplied or replenished after the original nebular-envelope stage, through outgassing, volatile delivery and processing. The present atmospheres of Earth, Venus and Mars are predominantly secondary. The distinction from a primary planetary atmosphere concerns origin, not merely current molecular weight.