Earth's temperature changes until the energy it emits ($Q_{out}$) equals the energy it absorbs ($Q_{in}$).
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The energy radiated by Earth ($Q_{out}$) is governed by the **Stefan-Boltzmann law**, where energy is proportional to the fourth power of its absolute temperature ($Q ∝ T^4$). The greenhouse effect 'traps' some of this energy, reducing $Q_{out}$ and forcing the temperature to rise to find a new, warmer equilibrium.