Habitable Zone + Climate Toy

Determining a habitable zone necessitates computing the stringent thermal equilibrium of a planetary body. By integrating stellar luminosity, albedo, and greenhouse effect parameters, one calculates the effective temperature using the Stefan-Boltzmann law. The boundaries of liquid water stability are mathematically constrained by inverse-square flux degradation. This systemic thermodynamic equation strictly dictates habitability potentials, devoid of arbitrary assumptions about biological adaptability.

A planet keeps warming until it radiates away exactly as much heat as it absorbs from its star — that balance point is the equilibrium temperature this toy computes. Orbit distance sets the incoming flux, albedo sets how much bounces straight back, and the greenhouse offset traps part of the outgoing heat. Concrete takeaway: bare-rock Earth would sit near 255 K (-18°C), below freezing; its greenhouse blanket adds about 33 K to reach the 288 K (15°C) we actually enjoy.

The equation returns a single temperature, but real climate can have two stable states at the same orbit. Raise the albedo and the planet cools; a cooler planet grows more ice, which reflects even more light — a runaway loop called ice-albedo feedback. Around 700 million years ago Earth fell into exactly this trap: a "Snowball Earth" with ice reaching the tropics, a frozen state that persisted long after the original trigger was gone.