In vacuum there is no air, so a spacecraft cannot lose heat by convection — the only path is thermal radiation, governed by the Stefan–Boltzmann law: radiated power P = ε·σ·A·T⁴, where σ is the Stefan–Boltzmann constant and T is absolute temperature. Because power depends on the fourth power of temperature, a modest rise in radiator temperature lets each square metre reject dramatically more heat.
Rearranged for a fixed waste-heat load Q that must be rejected at equilibrium: A = Q / (ε·σ·T⁴). Double the temperature and the required area falls by roughly a factor of sixteen. That is the entire tradeoff: a large, cool radiator is gentle on nearby sensors and structures but heavy and bulky; a small, hot radiator saves mass and area but forces the connected hardware — and the radiator material itself — to tolerate much higher temperatures.
- Waste-heat load — total power the spacecraft must shed to hold thermal balance.
- Radiator temperature — the surface temperature the panel is allowed to run at.
- Required area — recomputed live from the T⁴ relationship for the same heat load.