Planetarium Star Dome (2D)

Observer

Latitude 50° N

Time of night 00:00

Date 21 Jun

Animate time (fast night)

Show constellation lines

Live Readout

Local sidereal time

0.0 h

Sun altitude

0°

Stars above horizon

0 / 0

Circumpolar stars

How it works

Every star has a fixed position on the celestial sphere given by right ascension (RA, its "sky longitude") and declination (Dec, its "sky latitude"). What you actually see depends on where and when you look, so the engine converts RA/Dec to local altitude and azimuth with the standard equatorial→horizontal transform:

H   = LST − RA                 (hour angle, °)
alt = asin( sin(dec)·sin(lat) + cos(dec)·cos(lat)·cos(H) )
cosA = ( sin(dec) − sin(alt)·sin(lat) ) / ( cos(alt)·cos(lat) )
sinA = −cos(dec)·sin(H) / cos(alt)
az  = atan2(sinA, cosA)          (from North, clockwise)

Local Sidereal Time (LST) is derived from the Sun's ecliptic longitude on the chosen date (λ = 280.46° + 0.9856474°·day-of-year) converted to right ascension through the 23.44° axial tilt, plus the clock offset from local midnight. That single number is why the same star rises about 4 minutes earlier each night — a real sidereal-vs-solar-day effect, not a decoration.

Latitude — moves the north/south celestial pole to the top/bottom of the dome; push it toward ±90° and whole constellations stop rising or setting at all.
Circumpolar — a star never sets when |dec + lat| > 90°, and never rises when |dec − lat| > 90° (exact culmination-altitude conditions, not an approximation).
Sun altitude — computed with the same transform for the Sun's own RA/Dec; above ~−6° the sky is still twilight-bright, exactly as outdoors.

Star (size ~ brightness) Sun Constellation line