The science
Orbit. A circular orbit of radius a = RE + h has period T = 2π√(a³/μ) (μ = 3.986×1014 m³/s²): 95.5 min and 7.6 km/s at h = 550 km. The lab uses exact circular Kepler motion on a spherical Earth and converts to an Earth-fixed frame by rotating at 7.292×10-5 rad/s.
Walker delta i: T/P/F. T satellites in P equally spaced planes (RAAN 360°p/P), S = T/P per plane equally spaced in anomaly, and plane p phase-shifted by 360°·F·p/T. A single shell at inclination i covers latitudes up to about i plus the footprint radius; satellites linger near ±i, so density peaks there.
Visibility. A satellite must be above a minimum elevation ε. The Earth central angle of the coverage cap is λ = arccos(R cosε / (R+h)) − ε (8.5°, about 940 km radius, for 550 km and 25°). The slant range is d = √((R+h)² − R²cos²ε) − R sinε, between 550 km (overhead) and 1123 km (at 25°).
Mean visible count. For uniform time sampling the satellite latitude obeys sinφs = sin i sin u with u uniform and longitude uniform, so the expected number visible from latitude φ is N/π² ∫ arccos(clamp((cosλ − sinφ sinφs)/(cosφ cosφs))) du. Its globe average is N(1 − cosλ)/2. The latitude sweep compares this with a brute-force count.
Latency. One-way radio delay is d/c: 1.8 ms overhead and 3.7 ms at 25° elevation at 550 km. A bent-pipe user-satellite-gateway round trip is about 4d/c plus processing when the gateway sees the same satellite. Laser inter-satellite links travel at c in vacuum; fibre carries light at about 0.67c along a route longer than the great circle, so beyond a crossover distance a path up, along the shell and down can win. The route model uses arc length at radius R+h times a stretch factor and a per-hop delay.
Handover. A satellite crosses the sky in at most 2λ/n ≈ 4.5 min (about π/4 of that for a random chord). Policies: re-pick the highest satellite every slot (publicly described networks reconfigure on a fixed interval of order 15 s), stay until lost, or choose the satellite visible longest (look-ahead propagation).
Doppler. Range rate ρ̇ = (r−ru)·v/|r−ru| in the rotating frame gives fd = −f ρ̇/c. At 11.7 GHz the peak here is about ±240 kHz (range rate up to about 6 km/s); it scales with carrier frequency (about ±400 kHz at 20 GHz).
Link budget. Free-space loss FSPL = 20 log10(4πdf/c) (168.6 dB at 550 km, 11.7 GHz). C/N0 = EIRP − FSPL − Arain − Agas − L + G/T + 228.6 dB-Hz; C/N = C/N0 − 10 log10B. Spectral efficiency is Shannon with an implementation gap, η = log2(1 + SNR/Γ), capped at 5.5 bit/s/Hz, zero below −3 dB. Rain loss follows the power law γ = kRα dB/km (ITU-R P.838-style coefficients) over a slant path below a 3 km rain height with a horizontal reduction factor (simplified ITU-R P.618).
Capacity. Cell capacity = satellites serving the cell × channels × channel bandwidth × η; users share it. Per active user = capacity / (users × activity), limited by the terminal peak rate. This is a contention model, not a scheduler.
Not modelled: collision probability and debris (the Kessler effect), orbital decay and J2 precession, station keeping, eclipses, antenna patterns and beam interference, gateway placement and routing congestion, weather other than the rain slider. The route calculation is analytic, not a full shortest-path search through the satellite grid. Publicly reported figures: shells near 550 km and 53°, thousands of satellites, 25° minimum elevation and 15 s scheduling intervals in publicly described networks; all link parameters here are the lab's own illustrative values.
Independent educational model, not affiliated with or endorsed by any company named here; trademarks belong to their owners. Numbers are textbook-level/publicly reported approximations.