Presets
Playback
Alignment and exposure
The motor turns at 15.041 arcsec per second. If the polar axis misses the celestial pole by epsilon, the pointing and the star separate as the two rotations diverge.
Model checks
The science
What is modelled
The star turns about the true celestial pole once per sidereal day, while the mount turns the telescope about its own, slightly wrong, axis at the same rate. The separation of the two rotated directions is the tracking error, computed with exact Rodrigues rotations in the horizon frame.
Equations
- Sidereal rate
360 x 3600 / 86164.09 = 15.041 arcsec/s. - Rotation
R(a, th) s = s cos th + (a x s) sin th + a (a . s)(1 - cos th). - Half-turn error for a star on the equator
2 |eps . s|; first-order drift from the error vector eps.
Checks run in the page
- The sidereal rate and the sidereal-to-solar ratio.
- Perfect alignment gives zero error.
- Half-turn error against its closed form.
- A first-order expansion against the exact rotation.
Honest simplifications
Rigid geometry only: no atmospheric refraction, flexure, periodic gear error, cone error or autoguiding. Real drift-alignment methods give the same sign conventions but need these effects handled.
What to try
- Press Well aligned, then Poor, long exposure and compare the star path.
- Press Near the pole: drift shrinks for targets close to the pole.
- Raise the pixel scale to see how undersampling hides the trailing.