[Wavytone]

Originally Posted by peter_4059

I've got a polar alignment question I was hoping someone here might be able to help me with it.

I would like to know if it is feasible to determine polar alignment error by taking a series of plate solved images, two near the horizon maybe 15-30 minutes of arc apart and then two near the meridian with similar spacing.

It is feasible... the polar alignment error is a constant offset in altitude and an offset in azimuth. Mathematically the offsets can be computed from ONE short image taken near the east/west horizon and ONE short image near the zenith, provided you accurately know

a) the time the images were taken, and

b) the precise pointing of the telescope for each axis when each image was taken, ie from encoders or at worst, setting circles.

c) it assumes the mechanical axes of rotation of the mount and the optical axis of the scope are precisely orthogonal. They never are.

Notes:

1. the accuracy is fundamentally limited by the accuracy of the measurements of the telescope position in each axis. For example, if you used setting circles with 1-degree resolution the best accuracy you might achieve is +/- 0.5 degree. With encoders you can do significantly better, but there's another limitation...

2. orthogonality of the mount and optical axis - if the RA and dec axis aren't exactly perpendicular, nor the optical axis perpendicular to the dec axis, these introduce more errors in the calculation. Errors up to 1 degree or even more are not uncommon in commercial budget-grade mounts for the amateur market.

There are ways to measure these errors and correct them - this is fundamental to the precision of theodolites used in surveying - where accuracy of 1 arc second is considered common.

3. two images are not required.

The maths is also known as the "surveyors equation" as this is also the same as the method used for a 2-star astrometric fix to determine latitude and longitude in absolute coordinates using a theodolite. It is also the same maths in the heart of GOTO mounts to determine how to calibrate the mount using 2 stars, and to do the GOTO calculations.

My hypothesis is there would be constant dec in each of the plate solves

Incorrect, study the spherical trig in say Smart's book. The the polar alignment error is a constant offset in altitude and an offset in azimuth, and is not a constant error in dec. Atmospheric refraction can be approximated using some formulae that take into account your site position, site altitude, air pressure and humidity but its not perfect, there are other variables in play (eg weather systems).

if ... the polar alignment is perfect

but it cant be perfect. It never is, because...

atmospheric effects can shift the apparent location of the star

Yup, atmospheric refraction produces a vertical shift (ie in the apparent altitude) of a star - it appears higher in altitude than it really is. This produces an offset in its hour angle (ie RA) AND its declination - and worse, these offsets vary as the star moves across the sky.

So wherever you aim your polar axis, its really only an approximation and you DO need to guide in RA and dec to account for the changing offsets as the stars altitude changes.

If my first hypothesis holds true

Don't hypothesize - do the maths. It's describe in Smart's book "Spherical Trigonometry" and it isn't trivial - it is a significant challenge for someone with good highschool year 12 trig and calculus. I did all this 35 years ago to produce a program for determining position from 2-star alignments using a HP41CX... but don't ask me now.

Cheers, indeed.

Wavy.