Twilight is the between-light after sunset or before sunrise, graded civil, nautical and astronomical by how far the Sun sits below the horizon. For satellite spotting it is prime time: your sky is dark while satellites overhead still catch full sunlight.
Understanding Twilight
The geometry of a visible pass
Three conditions stack: the satellite above your horizon, the Sun 6–18° below yours, and the satellite outside Earth's shadow cone. The shadow is a cylinder-cum-cone stretching away from the Sun; at 550 km altitude a satellite exits it only when its ground position is within ~20–25° of the terminator. Overlay those constraints and the classic result appears: visibility windows hugging dusk and dawn, longer for higher orbits, all-night in polar summer.
Twilight as an observing economy
Astronomers budget twilight: observatories time flat-fields and bright-target work to it, and deep exposures wait for astronomical dark. Satellite constellations complicated the ledger — twilight is exactly when trains and flares photobomb wide-field surveys, since that is when spacecraft gleam. The same geometry that delights spotters costs survey pixels, and mitigation scheduling is now part of telescope operations.