Sub-solar Point and Terminator
Where it's noon on a planet at this instant, and the line dividing day from night.
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Stand at the equator at solar noon. The Sun is directly overhead. Wherever you are at that moment defines the sub-solar point — the single longitude where the Sun's rays hit the surface perpendicularly. As the planet rotates eastward, the sub-solar point sweeps westward across the surface. As the planet orbits the Sun and its tilt swings the hemispheres into and out of sunlight, the sub-solar latitude also changes — on Earth it oscillates between 23.4°N and 23.4°S over the year (the tropics of Cancer and Capricorn).
Ninety degrees away from the sub-solar point — in every direction — sits the terminator: the great circle separating the lit hemisphere from the dark one. Stand on the terminator and the Sun is on the horizon. East of it (in the planet's rotation sense), it's morning everywhere; west of it, sunset, then night. The terminator moves at exactly the speed of planetary rotation at the equator (about 1670 km/h on Earth, 6.5 km/h on the Moon).
On an airless body like Mercury or the Moon, the terminator is razor-sharp — sunlight versus pitch black, no twilight. With an atmosphere, the terminator becomes a gradient: Earth's atmosphere scatters sunlight forward into the night side and back into the day side, giving you civil twilight, nautical twilight, astronomical twilight — about 30 minutes of usable light after sunset at mid-latitudes. Venus's much thicker atmosphere makes the day/night transition essentially indistinguishable from above; on the surface, sunlight is so diffused that the sky is uniformly bright.
The sub-solar point's instantaneous location is calculated from three angles: the planet's rotation phase (which longitude faces the Sun right now), its axial tilt (which seasonal latitude the Sun illuminates), and its orbital position (which hemisphere is angled sunward). On Earth, the sub-solar latitude oscillates between +23.4° and −23.4° in the cycle we call seasons. On Mars, the cycle is similar (25.19° tilt) but slower (687-day year) and more eccentric (Mars's orbit is more elliptical, so its seasons have unequal durations).
The terminator has a long history as the scientifically richest place to observe surface detail. Shadows are longest there, exaggerating topography. Apollo-era lunar imagery for crater geology was almost always taken with the terminator nearby. Voyager 1 + 2's most striking outer-planet imagery (Saturn's ring structure, Neptune's Great Dark Spot) was taken near each body's terminator for the same reason: low Sun angle picks out features.
On airless bodies, the temperature swing across the terminator is brutal. Mercury's day side reaches 430 °C; its night side drops to −180 °C. The Moon swings from +127 °C to −173 °C every lunar day (29.5 Earth days). With an atmosphere, thermal inertia softens this swing dramatically — Earth's surface temperature varies maybe 15 °C between day and night at temperate latitudes, because the atmosphere holds and redistributes heat. Venus, with its dense CO₂ atmosphere, has essentially no day-night temperature variation despite its 117-day solar day — the atmosphere homogenises temperature across the planet.