The 3D version scatters random points and connects nearby ones for a generic "constellation" look. This 2D companion instead plots real stars: each has its actual J2000 right ascension (RA) and declination (Dec) — fixed celestial coordinates, like longitude/latitude on the sky — and its true apparent visual magnitude. The chart converts each star to your local altitude/azimuth with the standard spherical-astronomy formulas:
HA = LST − RA (hour angle, degrees)
sin(alt) = sin(δ)sin(φ) + cos(δ)cos(φ)cos(HA)
cos(Az) = [sin(δ) − sin(alt)sin(φ)] / [cos(alt)cos(φ)]
Az = 360° − acos(cos Az) when sin(HA) > 0
δ = declination, φ = observer latitude
Zenith sits at the chart's centre and the horizon is the outer ring, exactly like a planisphere: a star's radius from centre is proportional to (90° − altitude), and its angle around the circle is its azimuth (0° = North at top, clockwise through East). Anything below the horizon (negative altitude) is not drawn.
- Local sidereal time drives the hour angle — as it advances, every star's azimuth sweeps west across the sky, the true diurnal rotation caused by Earth spinning under a fixed star field.
- Latitude sets which declinations are ever visible: at your latitude φ, stars with δ > 90°−φ never set (circumpolar), and stars with δ < φ−90° never rise. That is why Cassiopeia and the Big Dipper circle the pole from northern latitudes while the Southern Cross only clears the horizon from the tropics or further south.
- Naked-eye limit hides stars fainter than the chosen magnitude, mimicking how city glow or a moonlit sky raises the faintest magnitude a human eye can pick out (a pristine dark sky reaches roughly magnitude 6.5).
The six constellation patterns use each star's real relative position and brightness (larger, brighter dot = lower magnitude number), so their shapes and proportions on screen match the real night sky, not an invented pattern.