Ground-to-satellite line-of-sight and coverage

Visibility from the ground is the bread and butter of practical satellite tracking. "When can I see the ISS from my backyard?" "Will Starlink overfly me tonight?" "Does my ground station have line-of-sight to GOES-19?" All three reduce to the same geometric question: given a satellite ephemeris and an observer location, when is the satellite above the observer's horizon, and at what direction (azimuth) and how high (elevation) in the sky?

Azimuth and elevation

From any point on Earth's surface, a satellite's position relative to you can be described by two angles:

• Azimuth — the compass direction in the horizontal plane, measured from true north (0°) clockwise. Due east is 90°, due south is 180°, due west is 270°.
• Elevation — the angle above the horizontal plane. 0° is the horizon; 90° is directly overhead (zenith); negative values are below the horizon.

A satellite is "visible" when its elevation is greater than zero. For practical purposes (atmospheric absorption, trees, buildings), most ground stations consider visibility to start at ~10° elevation. Astronomy observations often require >30° elevation to escape atmospheric turbulence.

Pass geometry

A satellite pass has three key moments:

1. Rise (AOS — acquisition of signal) — the satellite crosses 0° elevation from below.
2. Culmination (TCA — time of closest approach) — the satellite reaches its maximum elevation during the pass.
3. Set (LOS — loss of signal) — the satellite returns to 0° elevation and disappears.

For an ISS pass, the entire cycle takes 4–10 minutes depending on geometry. A "great" pass has a culmination >70°; an unusable pass culminates <10°.

Computing this with skyfield

from skyfield.api import load, wgs84

ts = load.timescale()
iss = EarthSatellite(line1, line2, "ISS", ts)
observer = wgs84.latlon(40.7128, -74.0060)  # NYC

# Look for events in next 24 hours
t0 = ts.now()
t1 = ts.tt_jd(t0.tt + 1.0)
times, events = iss.find_events(observer, t0, t1, altitude_degrees=10.0)
# events: 0=rise, 1=culminate, 2=set
for t, ev in zip(times, events):
    alt, az, _ = (iss - observer).at(t).altaz()
    print(f"{t.utc_iso()} event={ev} alt={alt.degrees:.1f}° az={az.degrees:.1f}°")

Line-of-sight

Pass visibility assumes nothing blocks the line of sight. For a real ground station, you also need to account for:

• Atmospheric refraction — the atmosphere bends light, making satellites appear ~0.5° higher than their geometric position near the horizon. skyfield handles this if you ask for topos.altaz(refraction=True).
• Terrain horizon — a mountain to your west blocks satellites at low westward elevation. Real ground stations build a "horizon mask" with the local skyline.
• Building obstructions — for urban deployments, the local horizon mask is built from building footprints + height.

Coverage cone

From the satellite's perspective, the inverse question is: which observers can see me right now? The answer is a circular "footprint" on Earth's surface. For a LEO satellite at 400 km altitude with a 5° minimum elevation, the footprint radius is ~2,100 km — a circle covering most of the eastern United States.

The lab takes a user-supplied lat/lon and finds the next visible ISS pass within the next 24 hours, outputting AOS time, TCA time + max elevation, and LOS time as JSON. This is the same logic that powers launchdetect.com/satellite-tracker/'s "next visible pass" feature.