F4IOZOlivier · radio amateur · JN18FS

LEO satellites low orbit, step by step

Height, period, ground track, footprint, AOS and LOS, elevation and azimuth, TLEs: with Kepler, understand how low satellites go round, and how to catch them. All tutorials

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The tutorial's formulas

Period: T = 2π √(a³/μ), with a = 6,371 km + the height and μ = 398,600.4418 km³/s².
Speed on a circular orbit: v = √(μ/a). At 400 km: 7.67 km/s, 92.4 minutes.
Track shift: 360° × T / 86,164 s (the sidereal day) westwards each orbit, about 23° for the ISS.
Footprint above an elevation ε: a circle of angular radius acos(R cos ε / a) − ε.
TLE: period (min) = 1,440 / mean motion; semi-major axis a = (μ / n²)^(1/3), n in radians a second.

The model Circular orbits, a spherical Earth held still during a pass, a fixed orbital plane: enough to understand and to be right within a few per cent. Tracking software (SatMe, for one) goes further with the SGP4 model and recent TLEs.

The sources

The tutorial's figures and advice rest on these references:

ESA, « Types of orbits » — low orbit: below 2,000 km, about 90 minutes, about 7.8 km/s
NASA, « Space Station Facts and Figures » — the ISS: 16 orbits in 24 hours, about one every 90 minutes
AMSAT, « Keplerian Two Line Element Set Format » — the TLE's columns, the 2004 ISS example, the modulo 10 checksum
AMSAT, « Working Satellites » (W2JV, WD9EWK) — pick passes above 30° to start with, hand-held antenna
AMSAT, Satellite Gen 255 — the longest passes when the satellite goes nearly overhead, the shortest near the horizon