Theoretical alignment accuracy

Following the amazing performance of the refreshed AZ-EQ6 mount a few nights back, I started to wonder what the theoretical limits of polar alignment might be, given the practicalities of turning the mount’s adjustment knobs in the field.  I had managed a six-minute shot of Vega – see my last post – with no trailing, and no external guiding.  That’s just the mount doing what it’s supposed to do, and doing it rather well.

All other things being equal – and with the caveat that in the real world this is never the case – we can consider that there are two variables in the system:  the inaccuracy of the polar alignment and the length of the exposure.  The more the error in aligning the mount, the greater the difference between the axis of rotation of the camera and the axis of rotation of the Earth.  This difference will show as trailed stars, and the length of the trail will increase with the duration of the exposure.

Given my setup of the Nikon D90 on the Altair Wave 115/805, the sensor resolves the image to 1.41 arc seconds per pixel.  My calculations* are very encouraging, as they suggest that if the mount is aligned to within a very achievable half a degree of the celestial pole, the drift will not show as a complete pixel for 10 minutes.  Even an exposure of 4 minutes will only drift a tenth of a pixel.

_DSC0001

More practice, experimentation and experience will show just how far the real world parameters are from this ideal.

*Many thanks to Abhijit Pendse for his most generous assistance and guidance on the maths of this problem, through the Facebook page for Astrophotography/ Amateur Astronomy Enthusiasts.

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