Planetary Equilibrium Temperature
The temperature a planet would settle at from sunlight alone, before greenhouse warming.
Formula
Variables
Example
Earth: Tₑ ≈ 255 K (−18°C) before greenhouse gases
How it works
This formula gives the temperature a planet would have if it simply absorbed sunlight and radiated energy back into space as a blackbody, with no greenhouse effect, internal heat source, or atmospheric heat transport. It comes from an energy balance: the planet intercepts solar power over a disk area, but it emits thermal radiation over its whole spherical surface, which is why the factor of 4 appears. Lower albedo means more absorbed sunlight and a higher equilibrium temperature; a larger solar constant also raises the temperature, while the Stefan–Boltzmann law links emitted power to the fourth power of temperature.
When to use it
Use this when estimating the baseline temperature of a planet, moon, or exoplanet from stellar irradiation and reflectivity alone. It is also useful as the starting point for climate models, habitability estimates, and for comparing how bright/dark surfaces or different orbital distances affect planetary temperature.
Worked example, step by step
Estimate the equilibrium temperature of Mars using S = 590 W/m², α = 0.25, and σ = 5.67 × 10^-8 W/m²/K^4. Step 1: Compute absorbed flux: S(1 − α) = 590(1 − 0.25) = 590 × 0.75 = 442.5 W/m² Step 2: Divide by 4σ: 442.5 / (4 × 5.67 × 10^-8) = 442.5 / 2.268 × 10^-7 ≈ 1.95 × 10^9 Step 3: Take the fourth root: T_e = (1.95 × 10^9)^(1/4) ≈ 210 K Final answer: T_e ≈ 210 K, which is about −63°C
Common mistakes to avoid
- Forgetting the factor of 4 from averaging sunlight over a spherical surface
- Using the planet's actual surface temperature instead of the no-greenhouse equilibrium temperature
- Mixing units or using a solar constant that does not match the planet's distance from its star
Did You Know?
The 33°C gap between this and Earth’s real 15°C average is the greenhouse effect.
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