Thermal balance

Spacecraft Thermal Balance

How hot does a satellite run? No air, no convection — only absorbed sunlight in, radiated infrared out. Solve the 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.

AI explainer Run the numbers, then let ENKI break down what they mean — diagrams and all.
How this model works & what it omits

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.

// pick a configuration, then dial surface optics / power / altitude.

Surface optics

// α absorbs shortwave; ε emits IR. white paint α≈0.2, black α≈0.95.

Spacecraft

// internal electrical dissipation becomes heat.

Orbit & case

// altitude sets the Earth-disc view factor for albedo + Earth IR.

Thermal balance

// single-node steady state · survival range -20 °C to 50 °C

Outside survival range

// pass requires every computed case inside -20 °C … 50 °C

Hot case

// full sunlight — solar + albedo + Earth IR + internal.

Within survival range

-9.8 °C

Equilibrium temp

263.3 K

Equilibrium temp (K)

// absorbed-heat breakdown — total 463 W

  • Solar 204 W · 44.1%
  • Albedo 53 W · 11.4%
  • Earth IR 87 W · 18.7%
  • Internal 120 W · 25.9%

Cold case

// eclipse — Earth IR + internal only, no solar/albedo.

Outside survival range

-58.0 °C

Equilibrium temp

215.2 K

Equilibrium temp (K)

// absorbed-heat breakdown — total 207 W

  • Solar 0.0 W · 0.0%
  • Albedo 0.0 W · 0.0%
  • Earth IR 87 W · 41.9%
  • Internal 120 W · 58.1%

—

Radiator area for 40 °C

-9.8 °C

Hot equilibrium

-58.0 °C

Cold equilibrium

86.0%

Earth view factor

// no radiator growth needed

The hot-case equilibrium temperature already sits at or below the 40 °C target — the current radiating area is sufficient. If anything, the cold case may need heaters or a smaller effective radiator.

// shareable URL encodes every input. no backend.

// ai-generated breakdown of what these numbers mean — with diagrams.

References

  • // Wertz, J. R., Everett, D. F., Puschell, J. J. (eds.) (2011). Space Mission Analysis and Design (SMAD), Ch. 11 — Spacecraft Subsystems / Thermal.
  • // Gilmore, D. G. (ed.) (2002). Spacecraft Thermal Control Handbook, Vol. 1 — Fundamental Technologies. The Aerospace Press.
  • // Gilmore, Ch. 2 — the orbital thermal environment (solar, albedo, Earth IR, view factors).
  • // Kopp, G., Lean, J. L. (2011). A new, lower value of total solar irradiance. GRL 38, L01706.
  • // Incropera, F. P., DeWitt, D. P. — Fundamentals of Heat and Mass Transfer, Stefan-Boltzmann radiation and grey-body emission.