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    Re: Low Alt Refraction
    From: Paul Hirose
    Date: 2013 Apr 28, 16:49 -0700

    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
    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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