LearnPlanetary scienceBuilds on the rest
Equilibrium temperature
The temperature a world settles at when the sunlight it absorbs exactly balances the heat it radiates away.
Why it matters
It is the first thing anyone calculates about a newly found planet, and the reason the habitable zone is where it is. It also shows, by failing, how much atmospheres matter.
The maths, in layers
1 · Intuition
Absorbed power depends on the disc the planet presents to the Sun; radiated power depends on its whole surface. Setting the two equal fixes the temperature.
2 · The equation
T_eq = T_star · √(R_star / 2d) · (1 − A)^(1/4)
- A
- bond albedo — the fraction reflected
- d
- distance from the star
- R_star, T_star
- the star's radius and surface temperature
3 · Where it comes from
Note the fourth root on the albedo term. Even a large change in reflectivity moves the temperature only modestly, which is why albedo alone never explains Venus.
What people usually get wrong
Venus is hottest because it is closest to the Sun after Mercury.
Its equilibrium temperature is about 230 K — cooler than Earth's, because its clouds reflect 70% of the sunlight straight back. The surface sits at 737 K entirely because of the greenhouse effect, and the 500 K gap between prediction and reality is the measure of it.
In practice
Compare the mean temperatures in this site's planetarium against this formula. Earth, Mars and Mercury land close; Venus is out by 500 K, and that discrepancy is the point.
Rests on
- AlbedoThe fraction of incident sunlight a surface reflects rather than absorbs.
- The inverse-square law of brightnessThe apparent brightness of a source falls off as the square of its distance, because the same light is spread over an expanding sphere.
- Blackbody radiationThe characteristic spectrum any warm, opaque object emits, whose shape depends only on its temperature.
Leads to
Nothing here builds on it yet.