Periodic error and Polar alignment error model

Using linear algebra, a model for calculating the trails that stars produce when making astrophotos from an equatorial mount was created.

An ideal mount that is perfectly parallel to earth rotation axis results in photo’s with pinpoint stars.
In the real world, the stars will always produce trails. Main causes are

- imperfect polar alignment
- periodic error of the (worm) drive
- RA drive rate that is different for siderial rate

Download Star Trails (2004) here.

All of these parameters can be played with in this model.

What I learned from the simulations:

For DEC=0 and a small polar alignment errors, the stars will describe a vertical line over 24h:

24h DEC 0

For DEC>0 and a small polar alignment errors, the stars will describe an ellipse, over 24h. The ellipse will be wider for larger DEC:

24h DEC 30

The periodic error will always add a wiggle in RA to the curve:

24h DEC 30 plus PE

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