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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Angular Distance Between Stars By Camera and Sextant
From: Marcel Tschudin
Date: 2012 Sep 21, 11:56 +0300
We are finally converging. I notice at last that my following Dref value was indeed wrong:

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 proceeded again the same way and get now a different result for Dref. I cannot reproduce my above mentioned value. May be I made a typo when copying the values in the spread sheet. Here therefore two revised results:

Using Andrés Hc values for calculating the refracted distance:

Alioth       Alkaid
28.317414    34.115333  Hc
+ 0. 030001  +  0.023934  refraction (Sæmundsson adjusted to P and T)
----------------  ----------------
28.347415    34.139267  refracted alt

With Andrés' Azimuths and using Williams' online Great Circle Calculator resulting in a refracted distance of
Dref = 10.455469°

or when transferring Dec, GHA and Hc in Bill's Excel sheet:
Dref = 10.455575°

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.

The largest difference between these 4 values is less than 0.8". Most of these differences result likely from having calculated refraction differently. Yes, one could also use Bennett's formula or George's trimmed version of it by finding the value for Hc iteratively as Andrés appears to do it, or yet some other empirical values.

Finally a note regarding Frank's approximation for the shrinking of the star-star distance due to refraction. That this approximation matched so nicely my previous wrong result appears to be purely accidental. This approximation was actually also "wrong" because it should only be used for stars above about 45° altitude whereas in this example the altitudes are well below this limit.

This exercise shows again the importance of comparing the results from different programs in order to understand to what extend a certain program or data can be used. Thank you Greg for posing the initial question on how to calculate star-star distances, and thanks to all of you who helped evaluating the means for doing it.

Marcel
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