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Marcel Tschudin wrote:
> Instead of using Ha I used his unrefracted Hc which I expect to be related
> to the astronomical horizon (ZD=90°). Calculating first the unrefracted
> distance with Hc and Z (yes, only the difference in Z is relevant) results
> in an unrefracted distance of
> Dtrue = 10.460896°
> resulting in
> Dref =  10.457595° (using Bill's Excel sheet with GHA, Dec and Hc from
> Andrés)

I agree with your unrefracted distance within .000001°.

For refracted distance, I think a more direct solution is to use the 
refraction and Hc from Andrés' program. That gives refracted az/alt. 
Then calculate distance.

Your guess is correct - I assumed Ha included refraction only. That is 
the definition of Ha, but "Ha" from his program is something different. 
If we add his values for Hc and refraction, and compare the sum to his 
Ha, the latter is about 3" - 4" greater:

      Alioth       Alkaid
   28.317414    34.115333  Hc
+   .028946  +   .023032  refraction
-----------  -----------
   28.346360    34.138365  refracted alt
- 28.347441  - 34.139225  "Ha"
-----------  -----------
    -.001081     -.000860

The refracted altitudes are very close to my values (.000009° and 
.000017° different). The separation angle computed with the refracted 
altitudes above (not "Ha") is 10.455629° vs. my 10.455680. The 
difference is only .18". But the Excel solution is 6.9" different from 
my angle.

There is a mistake in the formula Andrés gave for Ha:

 >> Ha = Hs + IE - dip;

Index error should be subtracted, not added. E.g., if the sextant says 
+.1' when the direct and reflected images coincide, index error = +.1', 
which should be subtracted from all altitudes. It is helpful if the 
sextant is adjusted so index error is always zero or positive, never 
negative. That makes the math easier: index error, dip, and refraction 
are all subtracted from Hs to obtain Ho.

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