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Even Bowditch is confused about the effect of refraction on apparent
separation angle of stars. The 1984 edition of Vol. 1 has this to say
about the use of such angles to determine sextant error, if known
horizontal angles measured with a theodolite are not available:

"An alternative method is to measure angles between the lines of sight
to stars, comparing the measured angles with computed values. To
minimize refraction errors, one should select stars at about the same
altitude, and avoid stars near the horizon."

As my previous posting showed, for stars at the same altitude
refraction causes a significant decrease of the apparent separation
angle, and it's practically unaffected by the altitude of the stars.

In fact, I'd say you're better off watching for opportunities to shoot
stars positioned one above the other. The refraction effect is then
simply the differential refraction between the two altitudes, and can
be mentally computed by inspection of the table in the Almanac,
perhaps with corrections applied. These can be significant: at 2400
feet above sea level and 25 C (typical summer evening where I live)
the corrected refraction is 87% of the book value.

I have a hunch that minor non-vertical alignment of the stars affects
the differential refraction according to the cosine of the departure
from the vertical. E.g., 20 degrees out of vertical means refraction
correction should be .94 of the book value. Have not backed that up
by calculation, though.

   

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