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Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 59 / 1 / c / i / Solution by

Codex  0 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:

D_{0} = (\frac{R _{p}}{R _{s}})^{2} = 0.01, R_{p} = 0.1 R_{s} .

(1)

For a Sun-sized host, $R_{p} ≃ 6.96 \times 1 0^{7} m ≃ R_{J} ≃ 11 R_{\oplus}$ . 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.

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