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Telescope Mount Tracking and Webcam Autoguiding - Introduction

In an ideal world we would all have perfect telescope mounts. They would enable our telescopes to track the sky to sub arc second accuracy night after night, allowing us all take very long exposures with long focal length optics. Sadly, as we all know, this does not happen. No mount on the planet tracks perfectly. Most amateur mounts, such as the Meade LXD55, Meade LXD75, GP-DX, Meade LX200, Celestron etc have far from perfect tracking. Most mounts are either equatorial or Alt-Az. This page discusses equatorial tracking systems and gathers together some of my ideas and experiences with this troublesome topic.

First of all, why is it so difficult? To track well, the telescope mount has to follow the rotation of the sky to within a few arc seconds. To illustrate why this is so difficult, let us consider the average telescope mount. This usually has worm gear turning a big worm wheel. This wheel varies in size from 3 inch (76mm) to perhaps 20 inches (500mm) on very large mounts. Let us pretend we have a 6 inch (150mm) wheel. The wheel has to be turned through one revolution per day at a constant rate. Going too fast or too slow results in tracking errors. What if we make an error of 1mm when turning this wheel? The circumference of our 150mm diameter wheel is about 470mm. The wheel turns 360 degrees per day, so 1mm on the edge of the wheel corresponds to about 45 arc minutes - more than the diameter of the moon - very bad tracking!

The following table summarises the resulting tracking error caused by different sized movements on different sized worm wheels. Worm size along the top (mm) and error down the side (mm). The error is in arc seconds.

Tracking error
0 50 100 200 400 800 1000
5 41253 20626.5 10313.2 5156.6 2578.3 2062.6
2 16501.2 8250.6 4125.3 2062.6 1031.3 825.1
1 8250.6 4125.3 2062.6 1031.3 515.7 412.5
0.25 2062.6 1031.3 515.7 257.8 128.9 103.1
0.1 825.1 412.5 206.3 103.1 51.6 41.3
0.01 82.5 41.3 20.6 10.3 5.2 4.1
0.001 8.3 4.1 2.1 1 0.5 0.4

It is interesting to note that a reasonable standard of engineering tolerance is 1/1000th of an inch. Or 0.025mm in modern parlance. Errors of this size do appear to approximately correspond to typical amounts of periodic error. Believe you me, I understand what this kind of work mean after my ATM Lathe experiments using a mini lathe.

Telescope Mount Tracking - Why?

Why must we have good tracking? Good telescope tracking is vital for long exposure imaging. If you have good tracking, the stars will appear as nice dots. Poor tracking gives smudges, streaks and blurs - a mess. You are not going to make astronomy picture of the day without good tracking.

There is a tradeoff you need to be aware of: If you REDUCE the focal length (and therefore image scale) of your imaging train, the dependence on tracking reduces. As does the resolution of your image. Sky glow also becomes more of a factor. However, if you really can't fix your mount or afford a better one, think about imaging at a reduced focal length - perhaps with an SLR lens.

There is also a more subtle effect: If a star is focused on one pixel of the ccd chip for the whole exposure, it will appear brighter than if the star is spread out over a number of pixels. Even if your tracking appears adequate, improving the tracking makes your images deeper and sharper.

Telescope Mount Tracking - The Problems

The above table clearly illustrates the mechanical problems in building our hypothetical perfect mount. A number of factors conspire to insert gremlins into our tracking, broadly these can be summarised as follows:

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