Satellite Subsystems Quiz

Core fact. Only the propulsion subsystem stores reaction mass and ejects it to change the spacecraft's velocity: apogee/orbit raising, east–west and north–south station-keeping, momentum-dumping support and the final re-orbiting (graveyard) manoeuvre. In Tsiolkovsky terms, it is the subsystem that “owns” the mission ΔV budget.

Why the others are wrong:

• A (ADCS) controls orientation (pointing), changing the direction of the velocity vector rather than its magnitude — wheels and torquers produce torques, not translational ΔV. (Thrusters are shared hardware, but the ΔV function belongs to propulsion.)
• B (CDH) is the computing/autonomy layer — it commands the manoeuvre but provides no thrust.
• D (Thermal) manages temperatures; it has no momentum-exchange or mass-expulsion capability.

Connected idea. Satellite lifetime is usually terminated by propellant exhaustion, not electronics failure — a central theme of mission economics.

Core fact. NiH₂ has been the GEO comsat standard for decades: 60–80 Wh/kg, excellent cycle life at 30–40% DOD, tolerance to overcharge, and a pressure vessel that doubles as its housing — with tens of thousands of cells flown and space-qualified.

Why the others are wrong:

• A (Lead–acid) has poor energy density and cycle life; it is not used in operational spacecraft.
• C (Li-ion) is a strong challenger (higher energy density, now dominant on LEO/CubeSats), but the question's qualifier — “traditionally… valued for very long cycle life” — identifies NiH₂.
• D (Supercapacitors) deliver power but negligible energy density — incapable of carrying a GEO satellite through a 72-minute eclipse.

Trade-off anchor. Battery selection = energy density vs. cycle life vs. heritage vs. mass; the eclipse energy requirement (P × T_ecl) fixes the minimum, DOD fixes the lifetime.

Core fact. A reaction wheel is a motorised flywheel: commanding a torque on the wheel produces an equal and opposite torque on the spacecraft (conservation of angular momentum). Control is precise (arc-minute class), continuous, and consumes only electrical power — no propellant.

Why the others are wrong:

• A (Magnetic torquer) is propellant-free but works only where a magnetic field exists (LEO), produces torque only perpendicular to the local field, and cannot dump momentum about the field axis.
• C (Thruster) consumes propellant — directly violating the question's condition.
• D (Gravity-gradient boom) is passive, provides only 2-axis control, and yields coarse pointing — unsuitable for antenna-pointing-class accuracy.

Connected idea. Wheels' price for precision is momentum saturation (Q8): environmental torques integrate into stored momentum, requiring periodic dumping.

Core fact. The transparent transponder chain is: receive antenna → LNA → down-converter → IMUX channel filter → high-power amplifier (TWTA or SSPA) → OMUX → transmit antenna. The HPA sets the downlink EIRP and is the largest DC-power consumer in the payload.

Why the others are wrong:

• A (LNA) amplifies the received uplink by ~50–60 dB at the input; it deliberately handles microvolt signals, not transmit power.
• B (IMUX) is passive — it only filters the channel out of the FDM spectrum; it adds loss, not gain.
• C (Mixer) shifts frequency using a local oscillator; a passive frequency translation contributes no power amplification.

Design anchor. TWTA choice (100–250 W, 60–70% efficiency at saturation, but poor linearity) vs. SSPA (linear, lower per-device power) is a payload-level business decision revisited in Q17.

Core fact. MLI comprises 10–20 layers of aluminised polymer (Kapton/Mylar) separated by netting. Radiative exchange between successive layers is suppressed because each highly reflective surface has very low emissivity toward the next; conduction through the netting spacers is minimal. The stack's effective conductivity drops to ~0.03–0.06 W/m·K — orders of magnitude better than any single sheet.

Why the others are wrong:

• B describes phase-change thermal storage — a different technology entirely.
• C is doubly false: MLI works in hard vacuum (no air to convect), and its purpose is to suppress heat flow, not enhance it.
• D misses the mechanism: a single sheet radiates from both faces and conducts well; multi-layer separation is what defeats radiation.

Direction matters. MLI keeps warm equipment warm (reducing losses to space); identical blankets on propellant tanks keep cryogenic/liquid propellant cold — the physics is bidirectional.

Concept. TT&C is the spacecraft's lifeline: it downlinks the telemetry that reveals what failed and receives the commands that effect recovery. Design practice therefore hard-separates TT&C from the payload: omnidirectional antennas (link closes in any attitude), an essential power bus, redundant cross-strapped transponders, and survival heaters. Safe mode is defined precisely as: payload off, TT&C alive.

Failure-mode logic: if TT&C depended on the payload and the payload failed (HPA short, antenna deployment jam, power converter fault), the satellite would go silent with no diagnosis and no recovery path — an avoidable total loss of a ~15-year asset.

Why the others fail: A — antennas and cooling are unrelated to TT&C survival; B — ITU obligations exist but are not the engineering rationale; D — reverses causality (the EPS powers TT&C, not the reverse).

Concept — energy balance. Orbit-averaged power balance for the bus: array energy generated over daylight = load energy over the full orbit. During eclipse the array generates nothing, so the battery must carry 100% of the load alone: E_bat = P_load × T_ecl (plus recharge inefficiency). In daylight the array powers the load and restores the charge.

Eclipse duration is thus the sizing case: GEO worst case ≈ 72 min (equinox), LEO at 400 km ≈ 35 min × 16 orbits/day. This is why Q11's battery sizing uses 1.2 h, and why the array is separately sized to recharge that energy over the daylight fraction.

Why the others fail: A — charge rate is set by the array/regulator, not capacity; C — degradation is continuous, not eclipse-gated; D — false in every practical orbit (daylight ≥ eclipse; GEO worst case is 72/24 = only 5%).

Concept — momentum bookkeeping. Wheels absorb disturbance torque by changing speed: ΔL_wheel = −∫τ_distdt. On a GEO comsat the steady torques are gravity-gradient and solar-radiation pressure (~10^-5 N·m class), plus momentum bias from antenna articulation. Integrating a tiny torque over weeks produces large accumulated momentum; each wheel eventually hits its speed ceiling, after which it cannot accept more torque in that direction — control authority is lost.

Recovery. Dumping applies an external torque against the wheel: magnetic torquers (LEO; free) or thruster couples (GEO; costs propellant). The wheel is simultaneously driven back toward nominal speed, transferring its momentum to the environment/plume.

Why the others fail: A — bearings are life-limited but unloading is a momentum operation, not a mechanical reset; B — temperature affects drag torque marginally, not the scheduling; D — friction is a disturbance, and wheels normally spin continuously anyway.

Concept — the surface balance. A radiator's steady temperature follows εσAT⁴ = αSA_proj + Q_internal: it must reject Q_internal while absorbing as little sunlight as possible. The ratio α/ε is the master surface parameter:

• Low α/ε (≈ 0.1–0.3, white paint/OSR): absorbs little Sun, radiates freely → cold radiator → electronics reject heat effectively.
• High α/ε (≈ 0.8–0.9, solar cells, black anodise): absorbs strongly, radiates poorly → warm — good for cold-biased units.

Why the others fail: B — reverses the requirement (a radiator's job is rejection, not collection); C — α/ε are optical properties, unrelated to strength; D — high emissivity is exactly what helps during eclipse.

Concept — degradation physics. Array output falls roughly 2–3% per year from: (i) UV darkening of cover glasses, (ii) displacement damage from electrons/protons (including the Van Allen transit on the way to GEO), (iii) micrometeoroid pitting, (iv) contamination. Over 15 years this compounds to ~25–35% loss (design factor often 0.7–0.8 EOL/BOL).

Design consequence. The array is sized so that degraded power still meets the EOL load — meaning at BOL the array is intentionally oversized and its excess is shunted/dissipated. Batteries similarly fade, so the eclipse case is checked at EOL too.

Why the others fail: A — mass is fixed at launch; B — array rotation is attitude-controlled and independent of age; C — battery voltage falls with age as internal resistance grows.

Step-by-step:

Checks. Two 70–80 Ah strings with margin is the flight configuration. Option A (67 Ah) results from forgetting the discharge efficiency (or using DOD = 80%); C (200 Ah) from omitting DOD; D (267 Ah) from omitting both efficiency and DOD.

Error watch. The classic slips are: using minutes instead of hours, dividing by DOD twice, and mixing Wh with Ah without the bus voltage.

Step-by-step:

Interpretation. Well over half the spacecraft mass at GTO injection is propellant for this single 1.8 km/s manoeuvre — the economic engine of electric propulsion (Q19), which cuts this fraction to ~9% at I_sp = 2,000 s.

Checks. Option A (28%) comes from halving ΔV (900 m/s); B (44%) is the final-to-initial mass ratio misread as the propellant fraction — a classic sign-error trap; D (78%) results from using natural log of the mass ratio incorrectly or double-counting.

Step-by-step:

Interpretation & margin. Real radiators operate warmer (radiators sized for ~40–60 °C equipment reject more per m² since flux ∝ T⁴), suffer view-factor losses to Earth and the Sun, and degrade — flight practice adds 25–50% margin (Q20's satellite would fly ~0.8–1.0 m²).

Checks. Option A (0.32) results from omitting the factor 2 for two faces; C (1.28) from doubling the area by mistake; D (2.56) from also halving the flux.

Step-by-step:

System meaning. A 0.75° beam covers a country-sized footprint from GEO — narrow enough to reuse the same Ku-band frequencies in a neighbouring beam (spatial frequency reuse), which is how high-throughput satellites multiply capacity. The same dish at C-band (6 GHz) would beam ~2.6°: beamwidth scales inversely with frequency for fixed D.

Checks. Option B (1.5°) results from using D = 1 m; C (3.0°) from a 0.5 m dish; D (6.0°) from confusing the 70λ/D rule with the 3 dB / null-to-null (~140λ/D) beamwidths or from a wavelength error (using 6 GHz gives 1.75°, closest to B).

Step-by-step:

Interpretation. In a 36 MHz channel this is C/N = 98.1 − 10log(36×10⁶) = 98.1 − 75.6 = 22.5 dB — an enormous clear-sky margin over typical thresholds (~8–12 dB). That margin is deliberately spent on rain fade at Ku/Ka band (10–15 dB), pointing loss, and ageing.

Checks & error watch. The 228.6 figure is 10log(k) with k in J/K — using 228.6 as a multiplier or dropping the minus sign on L_fs are the classic slips. Option A (78.1) subtracts 228.6 instead of adding; B (88.1) uses G/T = 20 dB/K; D (108.1) adds L_fs instead of subtracting.

Cycle-count analysis. GEO eclipse seasons occur around the equinoxes (two seasons/year, ~45 days each, one 72-minute eclipse per day): ≈ 90 eclipses/year × 15 years ≈ 1,350 deep discharge cycles. The battery must also sit charged for 15 years at ~28–40% DOD. Mass matters (launch cost ∝ mass) but cycle life at GEO duty dominates.

• NiH₂: purpose-built for exactly this — decades of GEO heritage, robust to overcharge, ~60–80 Wh/kg → correct answer.
• Li-ion: viable and increasingly flown, but requires careful thermal management and DOD control for calendar life; “traditionally” and the heritage qualifier point to NiH₂.

Why the others fail: A — primary cells cannot be recharged, dead after the first eclipse; C — supercapacitors store seconds–minutes of energy (Wh-class), not 2.4 kWh; D — lead–acid fails on cycle life and energy density, and is not flown on GEO comsats.

Linearity physics. FDMA places many carriers in one amplifier. A non-linear device generates intermodulation (IM) products at sums/differences of carrier frequencies; when the amplifier saturates, IM products rise sharply and fall on adjacent channels as interference (IM3, IM5…). Linear systems tolerate multi-carrier operation with small back-off.

• TWTA: excellent saturated efficiency (~65%) but soft compression → for multi-carrier it must back off ~6–10 dB, where its efficiency advantage collapses and IM still limits channel loading.
• SSPA (GaN): harder compression curve and better IM performance → smaller back-off suffices; the linearity-per-watt metric favours SSPA for FDMA/multi-carrier despite lower peak efficiency.

Why the others fail: A — TWTA efficiency is a single-carrier saturated advantage, inverted for multi-carrier; B — harmonics are out-of-band interference to be filtered, never beneficial; D — SSPAs draw DC power proportional to RF output plus bias; multi-carrier operation draws more power.

Cycle analysis. 16 eclipses/day × 365 × 5 years ≈ 29,200 cycles — two orders of magnitude beyond GEO duty (Q16). Battery cycle life scales steeply with DOD (roughly, life ∝ 1/DOD² for Li-ion), so shallow DOD is the lever. Li-ion at ~100–160 Wh/kg and 30% DOD achieves several thousand cycles and fits a mass-constrained LEO bus; NiH₂, though superb at GEO cycling, carries too much mass per delivered Wh for this duty.

Design consequence. Capacity must be ~3× the eclipse energy (1/0.3), and cell balancing, thermal control and state-of-charge management become first-order design items — this is why modern LEO buses (CubeSats included) are Li-ion with conservative DOD limits.

Why the others fail: B — NiCd at 80% DOD would survive only hundreds of cycles, dying in the first year; C — primary batteries make an orbital imaging mission absurd (one eclipse = mission over); D — night passes are exactly when imaging-power and downlink-load peaks occur.

Quantitative trade. GTO→GEO requires ≈ 1,800 m/s. Applying Tsiolkovsky to a 3,000 kg dry spacecraft:

Electric saves ~1,085 kg — ~25% of launch mass — or buys that much additional payload/transponder capacity. Costs: ~5 months of transfer (revenue delay + prolonged radiation-belt exposure, driving array/total-dose requirements), multiple long spirals through the Van Allen belts, and power diverted from payload to thrusters during raising.

Verdict logic. There is no universal winner — the correct answer analyses both sides. High-value GEO slots with impatient revenue streams favour chemical; mass-constrained missions and electric-friendly operators (all-electric comsats such as recent Boeing/Lockheed platforms) favour Hall/ion. A and C assert single-parameter dominance; D contradicts Tsiolkovsky outright (same ΔV, different I_sp → different mass ratio).

FDIR escalation analysis. With wheels saturated and gyro bias diverging, Earth-pointing is already lost; the spacecraft is power-negative risk (arrays off-Sun) and thermally drifting. The autonomous priority hierarchy is: (1) survive — guaranteed energy, (2) communicate — maintain the lifeline, (3) recover, (4) resume mission last.

1. Payload off: removes the largest power/thermal load and eliminates RF hazard during tumbling.
2. Sun-pointing using Sun sensors: the only attitude reference that works without gyros or Earth lock; restores positive power within one rotation period.
3. Momentum unloading with thrusters: restores wheel authority so the attitude loop can be re-engaged.
4. Omni TT&C beacon: works in any attitude, letting ground diagnose the gyro bias and upload recovery commands.

Why the others fail: A — transmitting while unpointed wastes power, interferes with other satellites, and accelerates the energy crisis; B — blind continuous thrust without attitude reference wastes propellant and can spin the vehicle up; C — rebooting the CDH kills the very autonomy managing the crisis (watchdog reboots are a last resort, and never while tumbling uncontrolled).