LEO Satellite Systems Quiz — ECE 521E Radar & Satellite Engineering

Instructions to Candidates

This quiz contains 20 multiple-choice questions covering the first four levels of Bloom's taxonomy (Remember, Understand, Apply, Analyse).
Select the best answer for each question, then press "Check Answers" for instant marking with explanations, or consult the Post-Test Answer Key at the end.
Constants: μ = 3.986×10⁵ km³/s², R_E = 6 371 km, FSPL = 92.45 + 20log f(GHz) + 20log d(km), c = 3×10⁵ km/s.
Total time: 45 minutes (indicative).

Level 1
Remember (Q1–5)

Level 2
Understand (Q6–10)

Level 3
Apply (Q11–15)

Level 4
Analyse (Q16–20)

Level 1 — Remember (Q1–Q5)

1

The altitude range conventionally defining Low Earth Orbit (LEO) is:Remember

(a) 100 – 1 000 km (b) Approximately 180 – 2 000 km (c) 2 000 – 35 786 km (d) Exactly 35 786 km

Explanation: LEO spans roughly 180 km (lowest survivable orbits) to 2 000 km (below the inner Van Allen belt). Option (c) is MEO; (d) is GEO.

2

A satellite in a circular orbit at 550 km altitude has an orbital period of approximately:Remember

(a) 24 hours (b) 4 hours (c) 95 minutes (d) 12 hours

Explanation: T = 2π√(a³/μ) with a = 6 921 km gives ≈ 5 730 s ≈ 95.5 min — typical of LEO. Only GEO has 24 h (option a); half-sidereal-day orbits (12 h, option d) are MEO territory.

3

An inter-satellite link (ISL) is:Remember

(a) A radio or optical cross-connection between satellites of a constellation, forming an orbital mesh (b) The feeder link between a satellite and its ground gateway (c) The downlink from satellite to user terminal (d) A backup cable deployed between two satellites

Explanation: ISLs interconnect satellites (Iridium's RF mesh; Starlink's optical links), letting traffic cross oceans in space. Options (b) and (c) are feeder and service links — satellite-to-ground, not satellite-to-satellite.

4

The elevation mask (minimum elevation angle) of a LEO constellation primarily determines:Remember

(a) The satellite's orbital period (b) The transponder bandwidth (c) The launch vehicle selection (d) The usable footprint size and therefore the constellation size

Explanation: The mask ε_min sets the service footprint radius via ρ = arccos((R_E/(R_E+h))cos ε_min) − ε_min: higher mask → smaller footprint → more satellites for the same coverage. It does not affect orbital mechanics (option a).

5

In Walker constellation notation (i : T/P/F), the parameter P denotes:Remember

(a) The number of satellites per plane (b) The number of orbital planes (c) The phasing between planes (d) The orbital period in minutes

Explanation: Walker notation (i : T/P/F): T = total satellites, P = number of planes, F = relative phasing factor between adjacent planes. Example: Iridium ≈ 86.4°:66/6/… — 66 satellites in 6 polar planes.

Level 2 — Understand (Q6–Q10)

6

LEO satellite links achieve millisecond-level latency primarily because:Understand

(a) Signals travel faster at low altitude (b) LEO satellites move faster, reducing transit time (c) The short slant range (hundreds of km vs 35 786 km) gives ~2–4 ms one-way vacuum delay versus ~120 ms from GEO (d) LEO links bypass the atmosphere entirely

Explanation: Latency is propagation distance ÷ c: 550 km gives ~1.8 ms one-way; GEO's 35 786 km gives ~119 ms. Options (a) and (b) are physical nonsense (c is constant in vacuum); (d) is false — LEO signals traverse the atmosphere twice.

7

Altitudes around 550 km are described as "fail-safe" for mega-constellations because:Understand

(a) Atmospheric drag removes dead satellites passively within years, bounding collision exposure without propulsion (b) There is no space debris below 600 km (c) Satellites at 550 km cannot collide with each other (d) Solar radiation pushes debris out of 550 km automatically

Explanation: At 550 km a dead satellite decays in ~5–25 years (solar-cycle dependent) — nature provides free disposal, so a propulsion failure is recoverable by physics. At 1 200 km the same failure persists for centuries. Debris exists at all LEO altitudes (b); collisions are avoided by maneuvering, not altitude (c).

8

Phased-array antennas are the standard LEO payload because they:Understand

(a) Consume no DC power (b) Eliminate the need for an elevation mask (c) Work only at optical frequencies (d) Steer beams electronically in microseconds with no moving parts — essential for tracking users and executing frequent handovers

Explanation: With passes lasting minutes and handovers constantly required, mechanical gimbals would wear out; electronic beam steering re-points instantly and supports thousands of simultaneous beams. Phased arrays draw significant DC power (a is false) and are used at RF (c is false).

9

Starlink flies inclined shells near 53° while Iridium uses near-polar planes (86.4°) because:Understand

(a) 53° requires fewer satellites for the same coverage (b) Inclined shells concentrate satellite dwell over populated mid-latitudes; polar planes are needed only when pole-to-pole coverage is a mission requirement (c) Polar orbits are impossible below 1 000 km (d) Inclination has no effect on which latitudes are best served

Explanation: Coverage quality peaks near the orbital inclination's latitude band. Broadband demand lives at 30–60° N/S — served best by 53° shells; Iridium's aviation/military/maritime mandate required the poles, which only near-polar planes reach. Inclination is a coverage design variable (d false), and polar LEO is routine (c false).

10

Adding optical inter-satellite links to a LEO broadband constellation primarily improves:Understand

(a) The satellite's orbital lifetime (b) The elevation mask over oceans (c) Latency and reach: traffic crosses oceans in vacuum (faster than fiber's ⅔-c) and serves regions far from gateways (d) Rain-fade margins on the user downlink

Explanation: ISLs turn the constellation into a mesh: long-haul traffic stays in vacuum at full c (beating terrestrial fiber on some routes) and mid-ocean users no longer need a nearby gateway. ISLs are space-to-space links — they do nothing for the atmosphere-crossing user link (d) or orbital decay (a).

Level 3 — Apply (Q11–Q15)

11

The orbital velocity of a satellite at 550 km altitude is approximately:Apply

(a) 3.07 km/s (b) 7.59 km/s (c) 11.2 km/s (d) 1.63 km/s

Explanation: v = √(μ/r) = √(3.986×10⁵/6 921) ≈ 7.59 km/s. Option (a) is GEO's velocity; (c) is Earth's escape velocity; (d) is a HEO apogee velocity.

12

For a satellite at 550 km with a minimum elevation mask of 10°, the service coverage half-angle ρ and the minimum number of satellites for one equatorial ring are:Apply

(a) ρ ≈ 15°, ring minimum ≈ 12 satellites (b) ρ ≈ 23°, ring minimum ≈ 8 satellites (c) ρ ≈ 8.5°, ring minimum ≈ 21 satellites (d) ρ ≈ 33°, ring minimum ≈ 5 satellites

Explanation: ρ = arccos((6371/6921)·cos10°) − 10° = arccos(0.9065) − 10° ≈ 25.0° − 10° = 15.0°; ring minimum = 360°/(2×15°) = 12. Option (b) is the answer for a 0° (horizon) mask; (c) corresponds to a 25° mask.

13

The free-space path loss of a LEO downlink at 11 GHz over 550 km is approximately:Apply

(a) 205 dB (b) 182 dB (c) 168 dB (d) 154 dB

Explanation: L_FS = 92.45 + 20log(11) + 20log(550) = 92.45 + 20.8 + 54.8 = 168.1 dB — about 37 dB below GEO at the same frequency (option a is GEO at Ku). This 37 dB is the entire economic foundation of consumer LEO terminals.

14

The maximum Doppler shift experienced on a 1.6 GHz L-band link from a 550 km satellite (v ≈ 7.6 km/s) is approximately:Apply

(a) ±1.5 kHz (b) ±400 Hz (c) ±4 kHz (d) ±40 kHz

Explanation: Δf = (v/c)f₀ = (7.6/3×10⁵) × 1.6×10⁹ ≈ ±40.5 kHz. Option (c) ≈ the MEO/GNSS value (±4 kHz); (a) is GEO's negligible shift. At Ku (11 GHz) the same pass gives ±280 kHz — receivers need wide capture range and fast acquisition.

15

Using the single-fold coverage estimate N ≈ 4.84/sin²(ρ) with ρ = 10°, the minimum constellation for continuous single-fold LEO coverage is approximately:Apply

(a) 160 satellites (b) 66 satellites (c) 24 satellites (d) 8 satellites

Explanation: N ≈ 4.84/sin²10° = 4.84/0.0302 ≈ 160 satellites. Real broadband constellations exceed this by 10–100× because multi-fold capacity — not geometry — drives the count. Option (b) is Iridium's count (polar geometry, different design point).

Level 4 — Analyse (Q16–Q20)

16

A constellation operator finds satellites deployed at 320 km need re-boost every few weeks and still decay within months, wrecking the business case. The correct analysis and remedy:Analyse

(a) The satellites need bigger solar arrays (b) The satellites must be launched to GEO instead (c) Atmospheric density grows exponentially below ~400 km, so drag at 320 km is enormous; the constellation must move to ~450–550 km where drag is manageable yet passive decay still complies with debris rules (d) The problem is Van Allen belt drag; raising perigee above 2 000 km will fix it

Explanation: The altitude-dependence of drag (∝ρv² with ρ exponential in −h) is the diagnosis: 320 km sits in the regime where the ISS needs regular re-boost. The fix is the industry-standard 450–600 km band: drag still cleans up dead sats (years), but living sats survive with modest propellant. Solar arrays don't fight drag (a); GEO solves decay but destroys the LEO link economics (b); radiation belts exert no drag (d).

17

A regulator challenges a proposed 1 200 km constellation: "Every failed satellite you leave is a collision seed for centuries." The operator's strongest technically-grounded defence is:Analyse

(a) At 1 200 km, drag still removes debris within the 25-year rule (b) The satellites carry electric propulsion and an autonomous de-orbit mode, so disposal is active and rapid even though natural decay takes centuries — reliability plus mandatory de-orbit plans, not physics, carries the compliance (c) 1 200 km is above all space debris, so collisions are impossible (d) The constellation is small, so debris is not a regulatory matter

Explanation: Above ~700 km natural decay fails the 25-year rule (at 1 200 km: centuries) — so compliance must come from engineering: propulsion reliability statistics, autonomous passivation/de-orbit, and conjunction management. Option (a) is factually false; (c) is false (debris exists at all altitudes, and OneWeb-class sats at 1 200 km cross many shells); (d) is false (regulators license constellations precisely on debris terms).

18

Comparing handover regimes in a LEO constellation: intra-plane handovers are routine, but inter-plane handovers at a polar constellation's seam (where adjacent planes counter-rotate) are historically troublesome. The analysis is:Analyse

(a) Intra-plane handovers are harder because the next satellite is farther away (b) Seam handovers are rare, so they don't matter to network design (c) The seam problem is caused by rain fade at the poles (d) In one plane, the next satellite follows a predictable, identical path (steady-state relay); at the seam, satellites in adjacent planes move in opposite directions, so relative geometry, pointing and link budgets change rapidly — demanding tight choreography and ISL cross-links

Explanation: Same-plane geometry repeats almost exactly each orbit — the handover is a solved steady-state problem. At the polar seam, counter-rotating planes make the successor's approach direction and Doppler reverse sign relative to the setting satellite, so beam pointing and routing tables must switch aggressively; Iridium solves it with cross-plane ISLs. Options (a), (b), (c) are factually wrong.

19

A Ka-band rain-fade study shows a GEO link (12 GHz, 35 786 km) needs 12 dB of margin in a tropical climate, while the same-band LEO link (550 km) shows negligible fade impact. The correct quantified analysis:Analyse

(a) LEO's FSPL is ~36 dB lower (168.8 vs 205.1 dB), so the rain fade is absorbed inside the link's huge clear-weather margin — GEO must instead buy margin with power or ACM because it starts from a 200+ dB path (b) Rain falls only below 600 km altitude, so LEO signals pass under the weather (c) The LEO satellite moves so fast that raindrops cannot attenuate its signal (d) Ka-band rain fade is identical at all altitudes; the study must be wrong

Explanation: Rain attenuation is (to first order) path-integrated and frequency-dependent — not altitude-dependent. What differs is the starting margin: LEO's 36 dB FSPL advantage means a 10 dB rain fade barely dents the C/N, while GEO's budget has no such cushion and must spend on ACM, site diversity, or power. Options (b) and (c) are physical nonsense; (d) ignores the budget context.

20

An IoT terminal with G/T = −15 dB/K and a 2 GHz LEO downlink (EIRP 25 dBW, 550 km, misc 2 dB) claims reliable 10 kHz-bandwidth reception. An auditor doubts the negative G/T. The verification:Analyse

(a) The auditor is right: negative G/T makes any reception impossible regardless of other parameters (b) The link only works because LEO satellites transmit 1 MW of power (c) C/N₀ = 25 − 15 − 153.3 − 2 + 228.6 ≈ 83 dBHz; over 10 kHz that is C/N ≈ 43 dB — the tiny bandwidth need combined with LEO's low path loss closes the link with huge margin, which is exactly why low-power IoT terminals work in LEO but not via GEO (d) Negative G/T is normal and means the antenna has gain; the claim needs no verification

Explanation: G/T decomposes as G − 10log T_sys: a small antenna (low G) plus a warm receiver (high T_sys) easily gives negative dB/K. What matters is the complete budget: C/N₀ ≈ 83 dBHz against a 10 kHz (40 dBHz) need → C/N ≈ 43 dB. GEO's extra ~35 dB path loss would destroy the same budget — the negative G/T itself is unremarkable. Option (d) is complacent (a budget is always verified, never assumed).

Post-Test Answer Key & Summary

Q	Key	Bloom Level	Concept Tested
1	b	Remember	LEO altitude regime
2	c	Remember	LEO orbital period
3	a	Remember	Inter-satellite link definition
4	d	Remember	Elevation mask → footprint → constellation size
5	b	Remember	Walker notation T/P/F
6	c	Understand	LEO latency physics
7	a	Understand	Passive debris compliance at 550 km
8	d	Understand	Phased arrays vs mechanical steering
9	b	Understand	Inclination choice: 53° vs polar
10	c	Understand	Optical ISL benefits
11	b	Apply	Orbital velocity 7.59 km/s
12	a	Apply	Coverage half-angle 15°, ring 12
13	c	Apply	FSPL 168 dB at Ku
14	d	Apply	Doppler ±40 kHz at L-band
15	a	Apply	Rider estimate ≈ 160 sats
16	c	Analyse	Drag diagnosis at 320 km
17	b	Analyse	Active disposal at 1 200 km
18	d	Analyse	Polar-seam handover geometry
19	a	Analyse	Rain margin from FSPL advantage
20	c	Analyse	Negative G/T budget verification

Grading guide: 18–20 = Excellent (constellation-ready understanding); 14–17 = Good; 10–13 = Fair — revisit coverage geometry and link budgets; <10 = Review the LEO Satellite Systems study guide before re-attempting.