Equatorial Mount Tracking Calculator
Enter your imaging setup and how well your mount is polar aligned to see how long each sub can be before stars drift by more than you allow.
Mount tracking and drift
How long you can expose before polar alignment error or Earth's rotation blurs the stars.
Orion Nebula -5°, Andromeda Galaxy +41°.
Polar scope about 5 to 15′, plate-solved routines under 1′.
1 px is strict. Up to 2 px is hard to see once the image is scaled down.
Longest tracked exposure
59.09 s
Worst case declination drift from polar alignment error, with perfect tracking in right ascension.
- Pixel scale
- 1.29″/px
- Allowed drift
- 1.29″
- Declination drift
- 1.31″/min (1.02 px/min)
- Star motion, mount off
- 13.03″/s (10.08 px/s)
- Longest untracked exposure
- 99.2 ms
- Alignment needed for 5 min subs
- 0.985′
Tracking rates
| Rate | ″/s | Star drift |
|---|---|---|
| SiderealStars, nebulae and galaxies | 15.0410 | 0 px/min |
| KingStars, corrected for refraction | 15.0369 | 0.16 px/min |
| SolarThe Sun | 15.0000 | 1.65 px/min |
| LunarThe Moon (average) | 14.6850 | 14.31 px/min |
Star drift is how fast stars move on the sensor if you track at that rate.
Real drift also depends on hour angle, periodic error and balance, so test with a few subs. Autoguiding removes most of it.
How this is calculated
- 1
Pixel scale and tolerance
Pixel scale is 206.265 × pixel size (µm) / focal length (mm). A 600 mm telescope with 3.76 µm pixels gives 1.29″ per pixel, so a 1 pixel tolerance is 1.29″ of drift.
- 2
Drift without tracking
With the mount off, stars move at 15.041″/s × cos(declination). At +30° that is 13.0″/s, so the tolerance is used up in about a tenth of a second.
- 3
Drift from polar alignment error
A polar axis that is E arcseconds off drifts in declination by up to E × 2π / 86,164 arcseconds per second, about 0.26″ per minute for each arcminute of error. A 5′ error gives 1.31″ per minute.
- 4
Longest exposure
Dividing the tolerance by the drift rate gives the longest sub. Here 1.29″ / 0.0219″/s is about 59 s with tracking.
Frequently asked questions
How accurate does polar alignment need to be?
It depends on focal length and exposure. For 5 minute subs at 600 mm with 3.76 µm pixels you need about 1′. A 135 mm lens with the same camera can tolerate about 4′ for the same subs.
What is the difference between sidereal, solar and lunar tracking?
Sidereal rate, 15.041″ per second, follows the stars. Solar rate, 15.000″/s, follows the Sun, which moves slowly east against the stars. Lunar rate, about 14.685″/s, follows the Moon, which moves east much faster.
What is the King tracking rate?
The King rate, about 15.0369″/s, is slightly slower than sidereal. It allows for atmospheric refraction, which lifts objects more near the horizon, so tracked stars stay put a little better.
Why do my stars trail even with tracking?
Common causes are polar alignment error, periodic error in the gears, poor balance, flexure between the guide scope and main scope, and wind. This calculator covers the first of these. Autoguiding corrects most of the rest.