How this screen works
For each local calendar day, Astronomy Engine searches for the morning instant when the geometric center of the Sun rises through the selected altitude: −6° (civil twilight), −12° (nautical twilight), or −18° (astronomical twilight). It then calculates the selected star’s geometric altitude and azimuth at that instant. The reported date is the first morning in the selected year after a previous morning below the chosen star-altitude threshold, provided the star is on the eastern half of the sky.
These cutoffs are an inspectable geometry test, not a visual-detection model. The result can shift when the thresholds change. It omits atmospheric extinction, twilight sky brightness in the star’s direction, observer eyesight, weather, horizon obstruction, Moon glare, local elevation, and individual stellar proper motion. It is deliberately bounded to modern years 1900–2100 and 20 selected IAU-named stars. At high latitudes some twilight crossings do not occur; the screen reports those missing days and does not bridge the gap as though it were a measured reappearance.
The US Naval Observatory defines the twilight solar altitudes and explains why actual visibility varies with atmospheric and horizon conditions. Schaefer’s research on heliacal rise phenomena addresses the much richer visibility problem. The star names and J2000 directions come from the International Astronomical Union table, while local positions use the open-source Astronomy Engine API.