A spacecraft deep in the solar system is so far away that its direction from Earth is effectively fixed in inertial space (only its right ascension / declination matter, 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, the elevation of a target at declination δ and local hour angle H is the standard spherical-astronomy formula:
sin(elevation) = sin(φ)·sin(δ) + cos(φ)·cos(δ)·cos(H)
This simulator computes that dot product directly in 3D: each station's local "up" (zenith) vector rotates with Earth, the spacecraft direction stays fixed, and elevation = arcsin(up · direction). A station is "locked" whenever its elevation clears the elevation mask (real antennas can't track near the horizon — buildings, mountains and 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. Drag the declination slider toward the poles and watch coverage gaps open or close: high-latitude stations gain nearly continuous view of high-declination targets, while all three can briefly lose an equatorial (δ≈0°) target if the mask is pushed up.