The sky turns at the sidereal rate; the Moon and Sun drift slower
Earth turns once relative to the stars every 23 hours 56 minutes, so the sky moves 15.04 arcseconds per second of time at the celestial equator, less toward the poles. A mount tracking at this sidereal rate holds stars still. The Moon moves eastward against the stars by about half a degree an hour, so mounts offer a slower lunar rate; the Sun drifts by about 1 degree a day, hence a solar rate for solar observing.
Without tracking, stars trail in seconds at telescope focal lengths
The table gives the longest exposure before a star at the celestial equator drifts 2 pixels on a camera with 3.76-micron pixels, a common size in current astronomy cameras and mirrorless bodies. Wide lenses can photograph the Milky Way on a fixed tripod; anything longer needs tracking.
| Focal length | Pixel scale (″ per pixel) | Untracked exposure (s) | Drift allowed (″) |
|---|---|---|---|
| 14 mm lens | 55.4 | 7.4 | 111 |
| 24 mm lens | 32.3 | 4.3 | 65 |
| 50 mm lens | 15.5 | 2.1 | 31 |
| 135 mm lens | 5.7 | 0.8 | 11 |
| 250 mm, small refractor | 3.1 | 0.4 | 6.2 |
| 500 mm | 1.6 | 0.2 | 3.1 |
| 1,000 mm | 0.8 | 0.1 | 1.6 |
| 2,000 mm SCT | 0.4 | 0.1 | 0.8 |
Periodic error repeats with every turn of the worm, so it can be trained out
No gear is perfect. In a worm-gear mount, small flaws in the worm make the tracking run fast and slow in a cycle that repeats with each turn of the worm, usually every 8 to 10 minutes. This periodic error is typically 5 to 15 arcseconds either way on mounts like the Sky-Watcher EQ6-R Pro and Celestron CGEM II. Because it repeats, periodic error correction (PEC) can record it once and play back the opposite.
Strain-wave drives such as the ZWO AM5N and Sky-Watcher Wave 150i have a larger error, often 20 arcseconds or more, and it changes faster, so PEC helps less. Their makers assume you will guide. Mounts with high-resolution encoders on the axes, such as the Sky-Watcher EQ8-Rh Pro and the encoder versions of the iOptron HEM27, measure their own position and correct most of it without a guide camera.
An autoguider watches a star and corrects the mount every second or two
An autoguider is a small camera on a guide scope or an off-axis guider. Software, usually the free PHD2 or the guiding built into ZWO's ASIAIR, measures a star's position every 1 to 3 seconds and nudges the mount back. A good mount on a good night guides to about 1 arcsecond, and the exposure length is then set by the sky, not the gears. Guiding also corrects polar alignment error and flexure that PEC cannot.
Smart telescopes such as the ZWO Seestar and Dwarflab Dwarf take the opposite approach: many 10-second exposures on an alt-az mount, stacked with the trailed and rotated frames thrown out. See telescope mounts for the mounts themselves.