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Joined 2026-09-21 Message
Incoming links: Very Large Telescope
Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 338 1 c iii Solution Created 2026-10-03 Updated 2026-10-05
Three complementary approaches replace the simple thick solid disk:
- A thin meniscus on an active optics support distributes and adjusts forces to preserve the figure despite changing gravity and temperature. The Very Large Telescope has four 8.2-metre unit telescopes of this type; the ESO active-optics account describes their controlled mirror supports.
- A lightweight telescope mirror uses a honeycomb or ribbed backing: a deep structure retains stiffness without a massive solid interior and cools more readily. The Large Binocular Telescope uses two 8.4-metre primaries; its official history describes their honeycomb construction.
- A segmented mirror constructs the aperture from manageable pieces. Support actuators and mirror segment phasing control figure, piston and tilt. Each ten-metre Keck telescope uses 36 hexagonal segments, as recorded in the observatory’s telescope description.
“Operational” and “planned” here refer to the 2018 examination date. The next generation included the 39-metre Extremely Large Telescope with 798 segments, the thirty-metre Thirty Meter Telescope with 492 segments, and the Giant Magellan Telescope using seven 8.4-metre primary mirrors. These designs extend segmentation or lightweight casting with active control, rather than simply making a thicker slab. The specifications are documented by the 2017 ELT announcement, TMT optics design and GMT primary-mirror description. Adaptive optics is also needed to exploit the large apertures against atmospheric turbulence; it corrects faster disturbances than active optics.
Thin actively supported menisci, lightweight honeycomb mirrors, and phased segmented primaries enable larger apertures.
Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 315 4 e Solution Created 2026-10-03 Updated 2026-10-05
First refine the ephemeris, planetary mass, stellar radius, and stellar variability using exoplanet transit photometry and the radial-velocity method. Then combine observations that probe different regions rather than relying on one spectrum. A present-day programme could use the following complementary measurements; in the 2019 setting of the paper, James Webb Space Telescope observations would have been a future capability.
- Exoplanet transmission spectrum at roughly – with the Hubble Space Telescope or optical ground-based spectroscopy: constrain exoplanet clouds, atmospheric haze, the scattering slope of a transmission spectrum, and sodium or potassium absorption.
- Near-infrared exoplanet transmission spectrum with NIRISS at – and NIRSpec modes covering roughly –: measure water, carbon monoxide, carbon dioxide, and methane bands, then constrain atmospheric metallicity of a giant planet and atmospheric carbon-to-oxygen ratio through a joint atmosphere model.
- Exoplanet secondary eclipses at near- and mid-infrared wavelengths with NIRSpec and MIRI, especially about – for the latter's time-series low-resolution mode: infer brightness temperatures, the vertical pressure-temperature structure, and whether an atmospheric thermal inversion turns bands into emission.
- A full-orbit exoplanet thermal phase curve in one or more infrared bands with the James Webb Space Telescope: constrain day-night heat redistribution, nightside emission, and the offset of the hottest region, with different bands probing different pressures.
- High-resolution near-infrared spectroscopy around molecular bands such as carbon monoxide near using CRIRES on the Very Large Telescope: resolve the planetary Doppler shift and seek wind velocities or rotation broadening after accounting for the orbital velocity.
- Ultraviolet transit spectroscopy with the Hubble Space Telescope, or ground-based near-infrared helium spectroscopy at : search for atmospheric escape and an extended upper atmosphere.
Together these address aerosols, molecular composition, elemental enrichment, vertical thermal structure, horizontal heat transport, winds, and escape. Repeat key events and monitor stellar activity, since stellar contamination and instrumental trends can imitate atmospheric signals. Use actual brightness, saturation limits, and predicted feature amplitudes to choose observing modes and exposure times.
The wavelength ranges and time-series capabilities are documented in the NIRISS SOSS guide, NIRSpec overview, MIRI spectroscopy guide, and ESO's CRIRES description.