Goldilocks

A planet’s surface can hold liquid water only if it gets the right amount of starlight. The game uses the habitable zone model of Kopparapu et al. (2014), built on Kopparapu et al. (2013): climate calculations give the starlight, S_eff, at each edge as a polynomial in the star’s temperature, and the distance is d = √(L / S_eff) in AU, with L the star’s luminosity in Suns. The conservative zone runs from the runaway greenhouse limit, where oceans would boil away, to the maximum greenhouse limit, where even a thick carbon dioxide atmosphere cannot keep water liquid. The optimistic zone stretches from the “recent Venus” to the “early Mars” limits, two empirical edges: Venus seems to have had no liquid water on its surface for at least the last billion years, while Mars had water flowing on its surface about 3.8 billion years ago, when the young Sun was fainter. Red stars shift the zone to lower starlight because their light is absorbed more by water vapor and carbon dioxide and scattered less.

Simplifications: the edges are for an Earth-mass planet with an Earth-like atmosphere, on a circular orbit, and the model is fitted for stars from 2,600 to 7,200 K (TRAPPIST-1, at 2,566 K, uses the 2,600 K values). Clouds are the biggest uncertainty: 3D climate models suggest that slowly rotating planets around red dwarfs could stay temperate under much more starlight, and put the Sun’s inner edge as close as 0.93 AU instead of 0.95 AU (Kopparapu et al. 2014 summarize them). Distances are drawn to scale within each level, but the scale changes between levels.

Data: the Sun’s temperature (5,772 K) and the orbits of Venus, Earth and Mars come from the NASA planetary fact sheets. Star and planet values come from the NASA Exoplanet Archive (Planetary Systems Composite Parameters, October 2026); the game computes each planet’s starlight from the star’s luminosity and the orbit size. The typical stars in level 3 are from Mamajek’s dwarf star sequence (Pecaut and Mamajek 2013), and their lifetimes use the rough rule 10 billion years × mass / luminosity, which underestimates red dwarfs. The Sun’s brightening follows Gough’s (1981) formula, L = 1 / (1 + 0.4 (1 − t / 4.57 billion years)), which gives about 10% per billion years; the game keeps the Sun’s temperature fixed.

Being in the habitable zone is not the same as being habitable. Mars sits inside the Sun’s zone today, yet it is frozen, and its air pressure is less than 1% of Earth’s. A planet also needs enough mass to hold an atmosphere, the right mix of gases, and probably a magnetic field and a way to recycle carbon. For most exoplanets in the zone, none of that has been measured yet.