Sunlight in, heat out.
Balance the sunlight a planet absorbs against the heat it radiates away and you get its temperature — no atmosphere required. For Earth's real reflectivity that gives 255 K (−18°C). Earth's real surface averages 288 K (15°C). That 33° gap is the greenhouse effect.
Sunlight in · 1361 W/m²
Heat radiated out
Albedo α
α↑ → T↓
0.0 · asphalt-dark0.9 · fresh snow
Equilibrium temperature
273 K · freezing
288 K · Earth’s real average
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This is the idealized greenhouse model's equilibrium temperature, found from the Stefan–Boltzmann law: sunlight absorbed over the planet's cross-section (πR²) must equal heat radiated from its whole surface (4πR²), which is where the 4 in the denominator comes from. S = 1361 W/m² is the solar constant at Earth's distance and σ = 5.67×10⁻⁸ W/m²K⁴ is the Stefan–Boltzmann constant — both fixed. This equation deliberately ignores atmospheric composition entirely: no CO&sub2;, no water vapour, no greenhouse gases of any kind — that omission is the whole point. Whatever gap remains between this bare number and a planet's real measured temperature is, by definition, what its atmosphere is doing. For Earth that gap is 33°C. Venus's real surface is about 735 K (462°C) — not because it's closer to the Sun (its high albedo of 0.65 reflects away more sunlight than Earth does), but because its thick CO&sub2; atmosphere traps heat far more aggressively than Earth's, an even more extreme version of the same missing mechanism.