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.
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.
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
// pass requires every computed case inside -20 °C … 50 °C
Hot case
// full sunlight — solar + albedo + Earth IR + internal.
-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.
-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.
// equilibrium temperature vs survival limit
// ai-generated breakdown of what these numbers mean — with diagrams.
Common questions
How hot does a CubeSat get in orbit?
It depends far more on surface finish and eclipse than on electronics power. The black-painted CubeSat preset (α 0.95, ε 0.88, 15 W internal, 420 km) reaches about +47 °C in full sun and falls to about −54 °C in eclipse — swinging straight through the representative −20 to +50 °C survival band on both sides. That orbit-period swing, not the average temperature, is what spacecraft thermal design has to tame.
How does a satellite shed heat in vacuum?
Radiation only. With no air there is no convection and nothing to conduct into, so the sole exit path is grey-body infrared emission, Q = ε·σ·A·T⁴, to the 3 K background of deep space. Equilibrium is simply the temperature at which that outflow matches everything coming in — absorbed sunlight, albedo, Earth IR, and the electronics' own waste heat.
What do absorptivity and emissivity actually control?
Solar absorptivity (α) sets how much shortwave sunlight the surface captures; IR emissivity (ε) sets how readily it radiates heat away. Their ratio decides where the balance lands: white paint or optical solar reflectors (low α/ε) run cold — the white-radiator smallsat preset equilibrates around −26 °C even in full sun — while bare or black surfaces run hot. Cold-biased designs then make up eclipse with heater power, a transient effect this steady-state tool deliberately does not model.
How do I size a spacecraft radiator?
Invert the hot-case balance: find the radiating area at which the full-sun equilibrium sits at your target temperature — exactly what the tool's radiator figure reports. The black CubeSat preset needs ~0.24 m² to hold +40 °C, more than its entire 0.22 m² radiating surface — a clear signal that the fix is a lower-α/ε finish, not more area. When the current area already suffices, the tool says so instead of inventing a requirement.
Why is eclipse the cold case?
In shadow, the two solar terms — direct sunlight and Earth-reflected albedo — switch off together, leaving only Earth's own IR glow (scaled by the Earth-disc view factor) and internal dissipation. The higher the orbit, the smaller that view factor, so eclipse gets colder with altitude. How long each eclipse lasts, and on which day of the year it is longest, comes from the Eclipse & Beta-Angle Timeline.
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.
