AZ PA with AT

[Demonperformer]

When doing AZ polar alignment with Astrotortilla, I cannot get at the celestial equator on the eastern horizon, because that is ~alt 0.  I basically have two options, both of which will presumably produce less than optimal results because I am using a position away from the optimal one, but I do not have sufficient understanding of the math involved to know which is best, or if there is any difference.

(1) I can stay on the eastern horizon (az 90) and just raise the scope in alt.  This puts me on a declination about 10N, rather than the equator, but I am still pointing East.

(2) I can stay on decl 0, and slew W by about an hour, which raises me above the horizon to a point where I have access to the sky, so I am no longer pointing E, but I am on the celestial equator.

Is there anyone here who understands the math involved enough to be able to give a definitive answer as to which option is best?

Thanks.

[Demonperformer]

Is there anyone here who understands the math involved enough to be able to give a definitive answer as to which option is best?

Seems not.

So, based on my 'by-gsoh-and-by-golly' thinking ... I think I will go with the 10 degrees above Az90, rather than moving along the equator away from Az90.

Two reasons for this:

(1) I suspect that the error introduced will be proportional to the cos of the declination, which is .985, so only 1.5% - I have no idea what the error introduced by moving away from Az90 will be, although as it is moving in the direction that gives you the AZ error, I suspect that the result will be a combination of AZ and ALT making the whole thing more complicated.

(2) This is about the amount that I have to use at Az180 for measuring the AZ error, as I cannot get down to the equator in the south over the house, so this will have the same 1.5% error (maybe).  There is a sort of symmetry about using the same offset for both readings that quite appeals to me. (IIRC it was Russell Crowe who said something like 'you know you are getting close to the truth when the equations start looking beautiful')