Equilibrium Temperature - Theoretical Model

Theoretical Model

Consider a spherical star and a spherical planet. The star and the planet are considered to be perfect black bodies. The planet has an albedo and only absorbs a fraction of radiation, depending on its surface characteristics. The star emits radiation isotropically according to the Stefan–Boltzmann law which travels a distance equal to the orbital distance of the planet. The planet absorbs the radiation that isn't reflected by the albedo of the surface, and heats up. Since the planet is also a black body which emits radiation according to the Stefan–Boltzmann law, it will emit radiation and lose energy. Thermal equilibrium exists when the power supplied by the star is equal to the power emitted by the planet. The temperature at which this balance occurs is the planetary equilibrium temperature and is equal to:

The equilibrium temperature is neither an upper nor lower bound on actual temperatures on a planet. Because of the greenhouse effect, planets with atmospheres will have temperatures higher than the equilibrium temperature. For example, Venus has an equilibrium temperature of 260 K, but a surface temperature of 740 K. The Moon has a black body temperature of 271 K, but can have temperatures of 373 K in the daytime and 100 K at night. This is due to the relatively slow rotation of the moon compared to its size, so that the entire surface doesn't heat evenly. Orbiting bodies can also be heated by Tidal heating, Geothermal energy which is driven by radioactive decay in the core of the planet, or accretional heating.