Case Study 24.2 — Designing the Thermal Subsystem of a 150 kg Earth-Observation Microsatellite

"The average temperature is the one number that never kills you. The extremes are." — a thermal engineer's rule of thumb

Executive Summary

Where Case Study 24.1 analyzed a finished spacecraft, here we design one from scratch. Our vehicle is "Terra-Scout," a $150\ \text{kg}$ Earth-observation microsatellite in a $600\ \text{km}$ sun-synchronous low Earth orbit. Its job is to keep a $120\ \text{W}$-class electronics stack and a lithium-ion battery alive through roughly $5{,}500$ eclipse cycles a year, holding electronics within $-20$ to $+50\ ^\circ\text{C}$ and the battery within $0$ to $+30\ ^\circ\text{C}$. We will build the thermal subsystem the way a real design proceeds: characterize the orbit's loads, bracket the worst-case hot and cold, choose coatings, size a radiator for the hot case, size the heaters the cold case then demands, and end by listing what we are least sure of. The recurring lesson — that the conflict between the hot and cold cases is the design, not a detail — drives every choice.

Skills applied - Loads in low Earth orbit: solar, albedo, planetary IR, eclipse (§24.1) - Equilibrium temperature and radiator sizing from radiative balance (§24.2, §24.4) - Coating selection by $\alpha/\varepsilon$; MLI and thermal mass (§24.3) - Heater sizing and the hot/cold conflict; worst-case brackets (§24.4, §24.6) - Handing a heater-power line to the power budget (bridge to Ch. 25)

Background

Terra-Scout is a $0.6 \times 0.6 \times 0.8\ \text{m}$ box, three-axis stabilized, nadir-pointing (its camera looks down at Earth). Its sun-synchronous orbit crosses the equator at a fixed local time; we assume a mid-morning ($\sim 10\text{:}30$) crossing, so it spends part of each $\sim 97$-minute orbit in Earth's shadow — up to about $35$ minutes of eclipse. During eclipse the payload is off and internal dissipation falls from $120\ \text{W}$ to about $40\ \text{W}$ (housekeeping only). The battery, charged in sunlight and discharged in eclipse, is the most temperature-sensitive component aboard.

The orbit gives us the loads of Section 24.1: direct sun at $1361\ \text{W/m}^2$, albedo up to $\sim 400\ \text{W/m}^2$ on the nadir (Earth-facing) side near the subsolar region, and Earth IR of $\sim 230\ \text{W/m}^2$ from below at all times. All hardware limits below are representative (Tier 2).

Phase 1 — Pick the surfaces and their jobs

Thermal design begins by assigning each external face a role, because geometry decides which loads a face sees.

• The nadir face (looking at Earth) always sees albedo and Earth IR. It carries the camera aperture; we keep it thermally quiet, not a radiator.
• The sun-tracking faces swing through direct sunlight. We wrap them in MLI so the sun's $1361\ \text{W/m}^2$ mostly bounces off and does not drive the interior.
• The anti-sun / anti-nadir face — the one that most often looks at cold, empty space — is where we put the radiator. Keeping the radiator out of the Sun is the single most important choice, exactly as Section 24.4 argued: a shaded radiator pays no $\alpha S$ penalty and can run small.

For the radiator surface we choose an optical solar reflector (OSR): $\alpha \approx 0.10$, $\varepsilon \approx 0.80$. Even if stray sunlight or albedo grazes it, its low $\alpha$ keeps the absorbed load modest, while its high $\varepsilon$ dumps heat efficiently. The rest of the exterior is MLI (effective $\varepsilon^{*} \approx 0.03$) so that only the radiator, not the whole box, exchanges heat with space.

Phase 2 — Bracket the hot and cold cases

Now the two calculations that are the design. We size the radiator so the hot case stays under the electronics limit, then see what the cold case does to the same radiator.

SIGMA = 5.670e-8

def eq_temp(q_absorbed, A, eps):
    """Equilibrium temperature (K) of a radiator absorbing q_absorbed (W) over area A (m^2)."""
    return (q_absorbed / (eps * SIGMA * A)) ** 0.25

eps, A = 0.80, 0.35        # OSR radiator, 0.35 m^2, on the anti-sun face

# HOT case: 120 W internal + ~15 W stray environment (albedo/IR grazing the panel)
t_hot = eq_temp(120 + 15, A, eps)
# COLD case: eclipse, 40 W internal + ~3.5 W residual Earth IR, unheated
t_cold = eq_temp(40 + 3.5, A, eps)
# Survival heater to hold the electronics at 253 K (-20 C) in eclipse:
q_needed = eps * SIGMA * A * 253**4
heater = q_needed - (40 + 3.5)

print("hot-case electronics:", round(t_hot - 273.15, 1), "C")
print("cold-case (unheated):", round(t_cold - 273.15, 1), "C")
print("survival heater:", round(heater, 1), "W")
# Expected output:
# hot-case electronics: 30.5 C
# cold-case (unheated): -44.4 C
# survival heater: 21.6 W

Read the result. A $0.35\ \text{m}^2$ OSR radiator holds the electronics near $+30\ ^\circ\text{C}$ in the hot case — comfortably under the $+50\ ^\circ\text{C}$ limit. But that same radiator, in eclipse with the payload off, would drag the electronics to $-44\ ^\circ\text{C}$ — well past the $-20\ ^\circ\text{C}$ survival floor. The radiator sized for the hot case over-cools in the cold case. This is the central tension of Section 24.6 made concrete, and there is no way to paint it away: a surface big enough to dump $120\ \text{W}$ when hot is far too big when only $40\ \text{W}$ remains.

Sanity check. In the hot case the panel absorbs $135\ \text{W}$ and, at $303.7\ \text{K}$, emits $\varepsilon\sigma A T^4 = 0.80 \times 5.67\times10^{-8}\times 0.35 \times (303.7)^4 = 135\ \text{W}$ — balanced, as it must be. The arithmetic closes.

Phase 3 — Resolve the conflict: heaters versus a louver

Two standard fixes close the gap between the hot-case radiator and the cold-case floor.

1. Survival heaters. Accept the oversized radiator and add electrical heaters that switch on in eclipse. From the code, holding $-20\ ^\circ\text{C}$ needs about $22\ \text{W}$ of heater power; holding a more comfortable $0\ ^\circ\text{C}$ would need about $45\ \text{W}$. Heaters are simple and reliable but that power is stolen from the battery precisely when the battery is discharging — a real cost we hand to Chapter 25.
2. A louver over the radiator. A bimetallic louver (Section 24.4) closes as the panel cools, cutting its effective emittance from $\sim 0.8$ (open, hot case) to $\sim 0.12$ (shut, cold case) with no power. That nearly seven-fold reduction largely eliminates the eclipse over-cooling, at the cost of louver mass, moving parts, and a new failure mode.

For a $150\ \text{kg}$ microsatellite where simplicity usually wins, we choose survival heaters and budget $\sim 22\ \text{W}$ of eclipse heater power for the electronics zone, while noting the louver as the option if the power budget cannot bear it. This is a judgment call, and we flag it as one.

Phase 4 — Protect the battery separately

The battery has the tightest limits ($0$ to $+30\ ^\circ\text{C}$) and its own survival stakes, so we isolate it thermally: mount it on a lightly conductive standoff, wrap it in its own MLI ($\varepsilon^{*} \approx 0.05$, presented area $\sim 0.1\ \text{m}^2$), and give it a dedicated thermostatically controlled heater. From the Section 24.4 method, holding the battery at $0\ ^\circ\text{C}$ ($273\ \text{K}$) against its MLI-suppressed radiative loss needs only $$ Q = \varepsilon^{*}\sigma A T^4 = 0.05 \times 5.67\times10^{-8}\times 0.1 \times (273)^4 \approx 1.6\ \text{W}, $$ plus a small allowance for conduction down the standoff — call it $\sim 3\ \text{W}$ of battery heater in eclipse. The MLI is what makes this number small; without it the same box would need tens of watts. We add a little thermal mass here deliberately: the battery's own mass, plus its mounting plate, gives it enough thermal inertia to coast through the $35$-minute eclipse with the modest heater trimming the low end rather than fighting a fast plunge.

One subtlety deserves a flag: the camera is not merely a survival problem but a stability one. An Earth-observation instrument must hold its focus and pointing to a fraction of a pixel, and an optic that expands and contracts as the spacecraft swings from sunlight to eclipse will smear its images even if it never approaches a temperature limit. So the camera bench gets its own treatment — a low-expansion mounting, generous MLI, and a small operational heater that holds it not just above a survival floor but within a tight band (say $\pm 2\ ^\circ\text{C}$) so its dimensions barely change. This is a different job from the survival heaters of Phase 3: those keep hardware alive; this one keeps it accurate. Budget another few watts for it, and note that "thermal control" quietly includes "dimensional control" whenever optics or precise structures are aboard.

Phase 5 — Assemble the bracket and state the margins

Collecting the design into the worst-case table that a review board would demand:

Total eclipse survival-heater load: $\sim 25\ \text{W}$, the number that now flows into the power budget. Note that we ran the hot case with end-of-life surface properties (a degraded radiator) and the cold case with minimum internal power, following Section 24.6 — designing for the average would have hidden both failures. We keep a temperature margin of at least $10\ ^\circ\text{C}$ to each limit; formalizing how large that margin should be is the subject of Chapter 29.

Discussion Questions

1. The radiator that is right for the hot case is wrong for the cold case. Explain why this tension is fundamental to any spacecraft with variable internal power, not a flaw in our particular numbers.
2. We chose survival heaters over a louver for simplicity, at a cost of $\sim 22\ \text{W}$ in eclipse. Under what mission conditions (orbit, power margin, lifetime) would the louver become the better choice?
3. Why did we isolate the battery in its own MLI-wrapped, separately heated enclosure rather than let it share the electronics zone's thermal environment?
4. The external structure swings from $\sim +90$ to $\sim -70\ ^\circ\text{C}$ every orbit, thousands of times a year. Connect this to the fatigue discussion of Chapter 23: what does it demand of the joints and coatings?

Your Turn: Extensions

• Option A (re-size). Suppose the mission moves to a dawn–dusk sun-synchronous orbit with almost no eclipse. Redo Phase 2's cold case: with continuous sunlight and steady internal power, does the survival heater shrink or vanish? What new hot-case worry appears instead?
• Option B (trade). Re-run the Phase 2 code with a radiator of $0.45\ \text{m}^2$. How does the hot case improve, and how much more eclipse heater power does the larger radiator now demand? Use the result to argue that "bigger radiator" is not a free choice.
• Option C (deep-space variant). Re-imagine Terra-Scout as an asteroid-rendezvous probe (Track D) at $2.5\ \text{AU}$. Recompute the solar flux, and explain qualitatively how the whole design inverts — from a heat-rejection problem to a heat-retention problem — and what that does to the heater budget.

Key Takeaways

• The design is the hot/cold conflict: a radiator sized to dump $120\ \text{W}$ in sunlight over-cools badly in a $40\ \text{W}$ eclipse, and closing that gap (heaters or a louver) is the central engineering choice.
• Keep radiators out of the Sun (here, the anti-sun face) so they pay no $\alpha S$ penalty and stay small; wrap everything else in MLI so only the radiator talks to space.
• Isolate the most temperature-sensitive item (the battery) in its own MLI enclosure with a dedicated heater and some thermal mass — MLI is what keeps that heater a couple of watts instead of tens.
• Size the hot case with degraded end-of-life surfaces and the cold case with minimum power; the $\sim 25\ \text{W}$ eclipse heater total is the thermal subsystem's bill to the power budget of Chapter 25.