Past exam of the mathematics course of the University of Cambridge 2015 iii Paper 59 4 e Solution Created 2026-10-03 Updated 2026-10-06
The circumstellar habitable zone is the range of orbital distances where a terrestrial planet with a specified atmospheric inventory can retain liquid water at its surface. It is a conditional climate criterion, not a guarantee of life or a requirement for every possible subsurface habitat.
Four influential factors are:
- The incident stellar energy and spectrum, including orbital distance and long-term stellar evolution.
- Atmospheric pressure and composition, greenhouse effect, Bond albedo and clouds, which set the relation between absorbed light and surface temperature.
- The water and volatile inventory, together with planetary mass and the ability to retain or replenish an atmosphere.
- Internal and surface evolution, including plate tectonics, outgassing and the carbonate-silicate cycle, which can regulate climate over geological time.
For a Sun-like present-day star and an Earth-like planet, a useful conservative range is approximately –. The inner limit depends on the adopted moist or runaway greenhouse condition, and the outer limit on the maximum greenhouse outer habitable-zone limit. More restrictive water-loss choices put the inner edge near . Empirical optimistic limits based on past Venus and Mars are about –. These are model conventions rather than exact universal boundaries.
Past exam of the mathematics course of the University of Cambridge 2025 iii Paper 315 3 b Solution Created 2026-09-24 Updated 2026-09-25
For an Earth-mass planet with a nitrogen-carbon-dioxide-water atmosphere, commonly quoted conservative Solar boundaries are approximatelyThe inner edge is governed by moist-greenhouse water loss and ultimately the runaway greenhouse. The outer edge is the maximum greenhouse outer habitable-zone limit, where additional carbon dioxide condenses or increases reflected light faster than it increases infrared trapping. Optimistic empirical boundaries, based on recent Venus and early Mars, are broader, roughly to . The values depend on clouds, planetary mass, atmospheric inventory, and climate assumptions.