Spacecraft Thermal Balance

single-node steady-state energy balance. absorbed solar + albedo + Earth IR + internal power = epsilon·sigma·A·T^4. hot case (full sun) and cold case (eclipse). radiator sizing + survival-range check. trade-study accuracy, not a nodal thermal model.

This spacecraft thermal balance calculator solves the single-node steady-state energy balance - absorbed sunlight (1361 W/m² solar constant), Earth-reflected albedo (0.30), Earth infrared (IR, 237 W/m²), and internal electronics power against ε·σ·A·T⁴ grey-body radiation (Space Mission Analysis and Design (SMAD) ch. 11; Gilmore) - for a full-sun hot case and an eclipse cold case. It then sizes the radiator area that holds a target temperature and flags both equilibria against a representative −20 to +50 °C electronics survival band. First-order CubeSat thermal analysis for a trade study - flight design needs a nodal model with orbit-resolved fluxes.

A spacecraft sits in vacuum. With no air there is no convection and no conduction to the environment - the only way it sheds heat is by radiating infrared to the 3 K background of deep space. At the same time it is constantly absorbing heat: direct sunlight, sunlight reflected off the Earth (albedo), the Earth's own infrared glow, and the waste heat of its own electronics. The equilibrium temperature is the temperature at which the heat radiated out exactly equals the heat absorbed and generated.

This tool uses the single-node steady-state energy balance - the standard first-order treatment for a thermal trade study (SMAD Ch. 11; Gilmore, Spacecraft Thermal Control Handbook, Vol. 1). The spacecraft is treated as an isothermal lumped mass with one external surface: Q_solar + Q_albedo + Q_earthIR + Q_internal = ε·σ·A·T⁴, which inverts to T = ( Q_total / (ε·σ·A) )^(1/4). The shortwave-absorbing projected area is taken as A/4 - the mean projected area of a convex body (for a sphere, exactly πr² against a total surface 4πr²). Albedo and Earth-infrared (IR) loads are scaled by the Earth-disc view factor F = (R / (R + h))², which approaches 1 near the surface and falls toward 0 at high altitude.

Two cases bracket the mission. The hot case is full sunlight: solar, albedo, Earth IR, and internal power all load the spacecraft. The cold case is eclipse: solar and albedo switch off, leaving only Earth IR and internal dissipation. The two surface optical properties drive everything - solar absorptivity α sets how much shortwave flux is captured, IR emissivity ε sets how readily heat radiates away. A low α/ε ratio (white paint, optical solar reflectors) runs cold; a high ratio (bare or black surfaces) runs hot. The tool also sizes the radiator area needed to hold the hot case at or below a target temperature, and flags each equilibrium against a representative electronics survival range.

What this tool does not capture: transient thermal response and thermal mass (it is steady-state only), internal temperature gradients and multi-node conduction, multilayer-insulation (MLI) blanketing, heater duty cycles, view-factor detail for non-convex geometry, beta-angle and seasonal solar-constant variation, and end-of-life degradation of optical coatings (α typically drifts upward over years of UV and atomic-oxygen exposure). Flight thermal design needs a nodal model (Thermal Desktop / ESATAN) with orbit-resolved environmental fluxes.