Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 315 / 3 / b / i / Solution

A deep ultraviolet transit and asymmetric light curve are signatures of an extended, escaping atmosphere rather than the optical planetary disc. Neutral hydrogen and ionized or neutral metals can form a comet-like tail, while interaction with the stellar wind can create an asymmetric bow shock.

For $R_{\ast }=0.5R_{\odot }$ and transit depth $D=0.5$, the absorbing radius isabout ten Neptune radii. This scale directly demonstrates that the ultraviolet absorber is gravitationally extended.