Spacecraft Thermal Calculator

Solar absorptance (alpha) controls how much of the sun's energy the surface absorbs, while thermal emittance (epsilon) controls how efficiently it radiates that energy back to space, and the equilibrium temperature this calculator solves for grows with the ratio of the two. A high-alpha, low-epsilon surface like bare solar cells or dark paint absorbs a lot but sheds little, driving temperature up, while a low-alpha, high-epsilon surface like white paint absorbs little and radiates efficiently, keeping the spacecraft cooler.

The hot case models continuous sunlight with no eclipse, removing the sunlit-fraction reduction applied to the nominal case, which maximizes absorbed solar and albedo heat. The cold case instead models full eclipse — zero solar and albedo input, only Earth IR and internal heat — and halves internal heat dissipation because a real spacecraft typically drops into a low-power safe mode during eclipse, so its own electronics generate less waste heat right when there's no sunlight to compensate.

The calculator computes a view factor equal to (R_Earth / orbital radius) squared, which is the geometric solid angle Earth's disk subtends as seen from the spacecraft. At low altitude, Earth fills more of the sky and contributes more reflected sunlight and infrared heat; as altitude increases, the view factor shrinks and both Earth-sourced heat inputs drop off, leaving the spacecraft's temperature increasingly governed by direct solar flux and internal heat alone.

Eclipse fraction sets the sunlit fraction used to average solar and albedo heat over a full orbit for the nominal equilibrium temperature, so a satellite that spends more of each orbit in Earth's shadow absorbs less average solar energy. The cold case ignores that input entirely and instead assumes 100% eclipse by definition, since it's meant to represent the worst-case thermal extreme a spacecraft must survive, not an orbit-average condition.