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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-315/4/e/solution
Past exam of the mathematics course of the University of Cambridge 2025 iii Paper 315 4 e Solution by
Codex 0 Created 2026-09-24 Updated 2026-09-25
The Hubble Space Telescope uses ultraviolet through near-infrared transit and eclipse spectroscopy. It established detections of alkali metals, water, aerosols, and escaping hydrogen but has a small aperture and restricted continuous infrared coverage. High-resolution ground facilities such as the Very Large Telescope separate Doppler-shifted planetary lines from telluric and stellar spectra and directly image young giants; the atmosphere and thermal background limit broad-band precision. The James Webb Space Telescope uses NIRISS, NIRSpec, NIRCam, and MIRI for roughly visible-to-mid-infrared transit, eclipse, phase-curve, and direct-imaging spectroscopy. It has measured broad molecular inventories, including the clear carbon-dioxide feature and photochemical sulfur dioxide in WASP-39 b.
JWST improves on earlier facilities through its 6.5-metre collecting area, cold space environment, stable time-series spectroscopy, and broad infrared wavelength coverage spanning several bands of water, carbon dioxide, methane, carbon monoxide, ammonia, and sulfur compounds. The Ariel space telescope is designed for a uniform atmospheric census of about one thousand planets, while the Extremely Large Telescope will add spatial resolution and high-dispersion spectroscopy for nearby giant and terrestrial planets.
Three directions enabled or sharply advanced by JWST are chemically complete retrievals across multiple molecular bands rather than isolated detections; atmospheric tests of smaller and cooler sub-Neptunes and rocky planets; and measurements of photochemistry, clouds, heat redistribution, and vertical thermal structure through repeated transit, eclipse, and phase-resolved spectra.
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