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Antoine Couëtte wrote:
> Please find here-after various Values for Refraction published for 0° 
Apparent Height. The applicable environmental conditions are also given 
whenever available.
>
> * Explanatory Supplement Sep. 1977 (unspecified conditions) -34'
>
> * Explanatory Supplement 1992 : same as E.S. 1997

That is a standard value for rise and set computations. When you combine
it with the standard 16′ for Sun semidiameter, the sum is the nice round
number 50′. I.e., the almanac tables assume sunrise/set occurs when the
center is at -50′ unrefracted altitude.

To compute refraction (degrees) below 15°, the Explanatory Supplement
suggests this formula:

P / (273 + T) * (.1594 + (.0196 + .00002 * H) * H)
/ (1 + (.505 + .0845 * H) * H)

at pressure P millibars, temperature T Celsius, and refracted altitude H
degrees. (In the book the formula is not exactly in that format; I have
factored the polynomials as they would be written in a program.)

At zero altitude the formula reduces to P / (273 + T) * .1594, or 34.13′
at 1010 mb / 10 C, and 33.98′ at 1023.25 mb / 15 C. Both values are very
close to the standard horizontal refraction for rise/set computations.

At slightly higher altitude the formula also agrees pretty well with the
Nautical Almanac. For example, see Chauvenet's lunar distance example
with Fomalhaut in the 1855 American Ephemeris and Nautical Almanac

http://books.google.com/books?id=_yUOAAAAQAAJ&pg=RA1-PA21

After correcting for dip and semidiameter, the Moon apparent altitude is
6°38′29″. Temperature is 20 F and barometer 31 inches (-6.7 C and 1050 mb).

Per the modern Almanac, the basic refraction is 7.7′, plus 1.0′ from the
"Additional Corrections" table, for 8.7′ total. The low altitude formula
says 8.5′, and Chauvenet himself says 8.6′. I suspect any of those
numbers could be correct, depending on the temperature profile of the
atmosphere at the time.

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