Star trail rotation calculator
Plot one star’s changing sky direction during an exposure. Latitude places the celestial pole; declination sets the star’s distance from that pole.
A 120-minute exposure rotates the star’s hour angle by 30.082°. At declination 70°, the trail covers 10.289° along its small circle. Both locations describe the same time interval; their longitude difference changes the starting hour angle. Only A’s above-horizon path is drawn.
| Latitude | Visible celestial pole | Start altitude / azimuth | End altitude / azimuth | Visibility in this interval |
|---|---|---|---|---|
| 51.5° | North celestial pole · 51.5° | 62.37° / 31.432° | 70.245° / 15.1° | Above horizon throughout |
| -33.9° | South celestial pole · 33.9° | -37.107° / 335.68° | -46.826° / 339.79° | Below horizon throughout |
Read this calculation
Hour-angle change = 360° × exposure / one sidereal day
The top-view plot has north at the top and east on the right. Solid portions are above the geometric horizon; points below it are left out. A star at the celestial pole remains still while the surrounding field turns.
The rotation angle is the change in hour angle. The path length on the sky also depends on cos(declination), so a near-pole trail is shorter than an equatorial trail in the same exposure.
Sirius has catalogue declination −16° 42′ 58.0171″ (ICRS, epoch J2000), or −16.7161159°. Polaris is near +89.2641°. The presets use these measured coordinates with the entered common starting hour angle, rather than claiming an exact apparent coordinate for today.
For simultaneous observations, B’s hour angle is A’s hour angle plus longitude B minus longitude A. The comparison reports geometric visibility, local celestial pole and altitude/azimuth at each end. Different latitude changes visibility and pole elevation; longitude changes the phase of the same rotating sky. Atmospheric bending and precession are separate corrections.