Satellite Coverage

Satellite Ground Coverage (space-systems/orbit-mechanics/satellite-coverage)

Use when the task is satellite ground coverage and access analysis: compute the instantaneous access circle from the orbital altitude and the minimum elevation angle, estimate the swath width and the coverage fraction, or evaluate the access time per pass, the revisit time, and the off-nadir and elevation geometry at a ground station.

Domain quick reference

• Spherical Earth model: Re = 6371 km, orbit radius r = Re + altitude_km. Coverage numbers shift only a few percent against an oblate (WGS84) Earth, which matters for precise station masks, not for first-order coverage sizing.
• Minimum elevation angle eps (deg) is the mask at the ground point; eps = 0 is horizon access, typical masks run 5-10 deg to clear terrain and atmosphere.
• Earth central angle eta (deg) of the access circle edge: eta = 90 - eps - asin((Re / r) * cos(eps)). This is the angular radius at the Earth center of the circle of ground points that see the satellite at or above eps.
• Maximum off-nadir angle theta_max = asin((Re / r) * cos(eps)) is the look angle at the satellite to the access circle edge. The limb triangle closes with eta + eps + theta_max = 90 deg.
• Swath width: the full access strip across nadir, the spherical arc W = 2 * Re * eta_rad. The access circle ground radius is Re * eta_rad.
• Global coverage fraction of one access circle over the whole sphere: (1 - cos(eta_rad)) / 2. A geostationary satellite at horizon access covers 42.4% of the globe; a 400 km satellite covers 2.95% at any instant.
• Worked anchors: 400 km altitude with eps = 0 gives eta = 19.79 deg, swath 4401.7 km; 500 km with eps = 10 deg gives eta = 14.06 deg, swath 3126.0 km; GEO (35786 km) with eps = 5 deg gives eta = 76.34 deg, swath 16977.5 km.
• Access time per pass (first-order): T_orbit * (2 * eta_deg / 360) for a ground point crossing the access circle center; off-center crossings give shorter times, and the fraction is exact only for a polar pass over the subsatellite track.
• Revisit time is set by the orbit repeat cycle and the constellation phasing: a single satellite revisits after the repeat cycle from ground-track-repeat; adding planes and phasing in a Walker-delta constellation shortens the worst-case gap to the constellation revisit time.

Workflow

1. Take the orbital altitude in km and the minimum elevation angle in degrees (0 to 90, usually 5-10).
2. Compute the access circle with central_angle and access_circle_radius_km.
3. Estimate the ground coverage width with swath_width and the off-nadir limit with max_off_nadir.
4. Evaluate the coverage fraction with coverage_fraction_global for globe coverage or coverage_fraction_region for a target region.
5. Convert to access time per pass with access_time_per_pass using the orbital period; compare the revisit time against the orbit repeat cycle for the mission gap requirement.
6. For constellations, treat the Walker-delta pattern (N satellites, P planes, F phasing) as a coverage ensemble: each satellite carries its own access circle and the joint coverage fraction rises toward 1.0 as the circles overlap, with the revisit gap set by the largest hole between circles.

Pitfalls

• Routing link-budget questions here: EIRP, path loss, C/N0, Eb/N0, and margin belong to communication-link-budget; coverage analysis sizes geometry, not the radio link.
• Routing repeat-cycle questions here: nodal period, revolutions per day, and integer repeat cycles belong to ground-track-repeat; the revisit time read from this leaf assumes the repeat cycle is already known.
• Routing shadow questions here: beta angle, shadow fraction, and eclipse duration belong to eclipse-time; an access circle is about visibility geometry, not sunlight.
• Using degrees in the arc formulas: swath and radius take eta in radians; feeding the degree value in directly overstates the swath by a factor of pi / 180.
• Forgetting the elevation mask: the access circle shrinks fast with eps (500 km: 19.2 deg at eps = 0, 14.1 deg at eps = 10), so a horizon assumption overstates coverage.
• Treating swath as chord instead of arc: the spherical arc length 2 * Re * eta_rad is the ground distance; the straight-line chord is shorter and is not the covered strip.
• Summing coverage fractions: instantaneous single-satellite fractions overlap; global coverage over time needs the ensemble geometry, not a per-satellite sum.
• Using the solar day instead of the orbital period for access time: access time per pass scales with the orbital period, not 86400 s.

Behavior contract (gate 3)

The access circle central angle, swath width, off-nadir angle, access circle radius, coverage fractions, and access time per pass logic is exercised by the gate 3 contract test: scripts/test_satellite_coverage.py against scripts/satellite_coverage_logic.py (stdlib unittest, offline). Run: python3 scripts/test_satellite_coverage.py

Compliance

• Standards referenced, not reproduced: ECSS series text is copyright ESA; the access circle, swath, and coverage fraction geometry is common astrodynamics, summary-only per standards-map.yaml (ecss is a free ESA download).
• compliance: STANDARDS-REF, gated: false.