A spacecraft deep in the solar system is so far away that its direction from Earth is effectively fixed in inertial space — only its declination δ matters, not its distance. Earth spins underneath that fixed direction once every ~24 h, so a single ground antenna sees the spacecraft rise, cross the sky and set, then loses lock until Earth rotates back around.
For a station at latitude φ and local hour angle H (how far Earth has rotated since the station last faced the spacecraft), the elevation is the standard spherical-astronomy formula:
sin(elevation) = sin(φ)·sin(δ) + cos(φ)·cos(δ)·cos(H)
The polar map above looks straight down Earth's spin axis: each station orbits the centre once per simulated day at an angular rate set by H, and a station's own latitude pulls it toward the centre (radius ∝ cos φ) exactly the way a real polar map projection does. A station's dot is coloured green whenever that formula clears the elevation mask below — real antennas can't track near the horizon, where buildings, mountains and the atmosphere get in the way.
NASA's real Deep Space Network solves the single-antenna blind-spot with three antenna complexes spaced roughly 120° apart in longitude:
- Goldstone — Mojave Desert, California, USA (35.4°N, 116.9°W)
- Madrid — Robledo de Chavela, Spain (40.4°N, 4.2°W)
- Canberra — Tidbinbilla, Australia (35.4°S, 149.0°E)
Because the three sites are spaced by roughly a third of Earth's circumference, at least one of them has the spacecraft above the horizon at almost any moment, handing off tracking to the next station as the current one sets — this is what keeps deep-space missions like Voyager, Perseverance and New Horizons in constant contact. The strip chart traces each station's elevation over time; drag the declination slider toward the poles and watch coverage gaps open or close on the chart: high-latitude stations gain near-continuous view of high-declination targets, while all three can briefly lose an equatorial (δ≈0°) target if the mask is pushed up.