Post-Test Quiz: Introduction to Satellite Engineering

Q1 — Answer (a). LEVEL 1
GPS is a GNSS (Global Navigation Satellite System) — a system of satellites providing positioning, navigation, and timing. GEO, LEO, and MEO in options (b)–(d) are orbit classes, not navigation systems; interestingly, GPS itself flies in MEO.

Q2 — Answer (b). LEVEL 1
A transponder is the core communications payload: it receives the uplink at one frequency, amplifies the very weak signal, converts it to the downlink frequency, amplifies again to high power, and retransmits toward Earth. Options (a), (c), and (d) describe the attitude control, power, and propulsion subsystems respectively.

Q3 — Answer (b). LEVEL 1
Kepler's first law (law of orbits): satellites travel in elliptical paths with the Earth's center at one focus. A circular orbit is the special case where both foci coincide — GEO is a near-circular equatorial orbit.

Q4 — Answer (b). LEVEL 1
GPS satellites fly in MEO at about 20,200 km altitude with a period of about 11 h 58 min. This gives a good compromise: high enough for wide coverage with 24+ satellites, low enough for manageable signal power and Doppler. LEO would need hundreds of satellites for the same coverage; GEO would not provide the geometry needed for accurate positioning at high latitudes.

Q5 — Answer (b). LEVEL 1
Downlink = satellite → ground station; uplink = ground station → satellite. The two use different frequency bands (e.g., C-band uplink near 6 GHz, downlink near 4 GHz) so both directions can operate simultaneously.

Q6 — Answer (b). LEVEL 2
Three conditions must hold together: (1) orbital period = Earth's rotation period (≈ 24 h), which fixes the altitude at 35,786 km; (2) a circular orbit so the speed is constant; (3) an equatorial, prograde orbit (inclination ≈ 0°) so the satellite has no north–south drift. The satellite and the Earth then rotate with the same angular velocity, and the satellite hangs fixed over one longitude. Thrusters only correct small drift, and gravity is never zero at GEO (it is about 0.22 g).

Q7 — Answer (b). LEVEL 2
Two effects combine: the low altitude makes the orbital speed very high (≈ 7.5 km/s, period ≈ 90–100 min), so the satellite crosses the sky in minutes; and geometry limits the horizon-to-horizon visibility (the footprint) to roughly 10–15 minutes and a region of only about 1,000–2,000 km across. Continuous global service therefore needs many satellites (e.g., 66 in the original Iridium design) with handover from one to the next.

Q8 — Answer (b). LEVEL 2
The received uplink at the satellite is extremely weak (tens to hundreds of femtowatts) while the satellite simultaneously transmits tens of watts of downlink power. Transmitting and receiving on different frequencies lets filters separate the two, enabling full-duplex operation without self-interference — the same reason mobile phones use different transmit and receive frequencies.

Q9 — Answer (a). LEVEL 2
A GEO relay path is about 2 × 35,786 km, i.e. ≈ 240 ms one-way (≈ 480 ms round trip). Conversational turn-taking becomes awkward, and the speaker hears their own delayed voice as echo. GEO telephone systems therefore include echo cancellers, while low-latency services (telephony, gaming, financial trading) prefer fiber or LEO constellations.

Q10 — Answer (a). LEVEL 2
Solar arrays are the primary power source, but a satellite passes through the Earth's shadow (an eclipse) once per orbit — for GEO up to about 70 minutes per day around the equinoxes. During eclipse the panels produce nothing, so rechargeable batteries (historically Ni–H₂, now mostly Li-ion) maintain power until the satellite re-emerges into sunlight.

Q11 — Answer (c). LEVEL 3
t = d/c = 35.786×10⁹ m / 3×10⁹ m/s ≈ 0.119 s ≈ 120 ms
Note this is the minimum possible value, when the ground station is on the satellite's sub-satellite point; slant ranges to the edge of coverage are longer (up to about 41,000 km).

Q12 — Answer (b). LEVEL 3
t = 2 × 120 ms = 240 ms (one way, A → satellite → B)
A listener's reply takes another 240 ms to return, giving a round-trip delay of ≈ 480 ms — the origin of the echo and "walkie-talkie" feel of GEO telephone calls.

Q13 — Answer (c). LEVEL 3
L_fs = 92.45 + 20log(36,000) + 20log(4) = 92.45 + 91.13 + 12.04 ≈ 196 dB
Equivalently, L_fs = (4πdf/c)². This enormous loss (the satellite's downlink signal arrives at roughly 10⁻²⁰ of the transmitted power) explains the need for high-power amplifiers on the satellite, large ground antennas, and low-noise receivers.

Q14 — Answer (c). LEVEL 3
v = √(μ/r) = √(3.986×10⁹⁴ / 6.871×10⁹) = √(5.80×10⁷) ≈ 7,615 m/s ≈ 7.6 km/s
The lower the orbit, the stronger the gravity and the higher the required orbital speed. 11.2 km/s is the escape velocity at the surface — a satellite at that speed would leave Earth entirely.

Q15 — Answer (b). LEVEL 3
T = 2π√(r³/μ) = 2π√((7.171×10⁹)³/3.986×10⁹⁴) ≈ 6,040 s ≈ 100 min
This is the typical LEO period. Kepler's third law shows the strong altitude dependence: the period grows with r^3/2, reaching 24 h only at the GEO radius of 42,164 km.