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Something I would love - would be if someone really mathematically gifted looked at the detailed formulea, to find a way of confirming polar misalignment of both axes whilst tracking a star at almost any elevation or compass point.
I understand why we do two stars in specific locations, but we have powerful computers at our beck and call. I always wondered if the results of solving just one axis at a time might be too simplistic. I would be reassured if the algorithms used take into account elevation and assumed refraction and simultenously modelled polar misalignment in both axes.
I know the model would find it easier and a higher confidence interval if a star 20 degree above the east and one almost straight up (from originally pointing East) are used. But I would be only too delighted to see the software calculating polar misalingment in both axes simultaneously!
Stasticians are used to dealing with this sort of challenge (where two variables interfere with each other to differening degrees - colinearity).
I would have expected the best approach would be measure at Star due East elevated at 20 degrees above the horizon for 5-10 minutes, then raise elevation 10 degrees and repeat again for 5-10 minutes and so forth all the way to 90 degrees, or back from 90 all the way to due west 20 degrees above the horizon. This should give the best curve to fit points to. Then go to a star 45 degrees above the horizon facing die East and show on the screen exactly where that star should be so folk could manually adjust their mounts alignment bolts.
The check high, check low and repeat just feels ... 1900s sort of mathematical prowess. If a PC today can (pardon the foreign financial jargon) caluclate a complex long look forwad kick back derevitative for a advanced synthetic in multiple curriences on several exchanges in a few milli-seconds, surely fiting data to a hyperbolic path with multiple points to determine its offset deltas in two dimensions isn't harder?
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