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This didn't take long.

1) Skyscout Right Ascension values are defective by small, but significant amounts
2) Skyscout Declination values are defective by small, but significant 
amounts.  For example, Sirius is given as -16.7175 (S16d 43.1m), while the 
USNO provides S16d 44.0m
3) My spreadsheet calculates GHA Aries.  I had a defective hourly rate for 
Aries, yielding GHA Aries which was incorrect by a small, but significant 
result.
It is apparent to me that I will have to get the exact values for the Objects 
and Aries from the Nautical Almanac day page and not rely upon my Skyscout.

I bypassed these three defects, by inserting the correct GHA & Dec for Sirius 
and Alphard from the USNO into the spreadsheet, instead of computing them.

My altitudes are now
        Sirius     31d 56.8     USNO 31d 56.8
        Alphard 31d 51.6        USNO 31d 51.6
Perfect.

My altitude corrections are
        Sirius     1.591m               USNO -1.6m (sign convention, not a problem)
        Alphard 1.596m          USNO -1.6m
Perfect.

Apparent distance should then be
        using Corner Cosines, I get an apparent distance of    40d 21m 24.68s
        Using Young's formula, I get an apparent distance of 40d 24m 22.05s
This yields a difference of 0d 2m 57.37s.

Back to my original inquiry, which one provides the more accurate answer?  Is 
it Young's or is it the Corner Cosine method.

Best Regards
Brad




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