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    Re: Refraction:Which formula for Heights below 15°
    From: Paul Hirose
    Date: 2022 May 18, 11:13 -0700

    On 5/17/2022 7:30 AM, David Iwancio wrote:
    > I'm pretty sure the model of "A * cot[Ha + B/(Ha+C)]" was the brainchild
    > of the author G. G. Bennett in a paper, published by the Royal Institute
    > of Navigation, titled "The Calculation of Astronomical Refraction in
    > Marine Navigation."  It was one of two or three models he introduced, of
    > various complexities, and analyzed them (and others) against the
    > then-standard refraction model developed by B. Garfinkel, published in
    > the Astronomical Journal.
    
    Meeus says the Bennett paper is in vol. 35 p. 255 (1982). I think only
    members can download it from the RIN archive. However, the full text of
    the 1944 Garfinkel article in online at ADS:
    
    https://ui.adsabs.harvard.edu/abs/1944AJ.....50..169G/abstract
    
    > Some authors
    > suggest using different formulas for different ranges of altitudes, to
    > avoid things like having a non-zero refraction at altitude 90° (which is
    > a sin committed by Bennett's model).
    
    Meeus gives a slightly modified constant to avoid nonzero refraction at
    the zenith in the Bennett formula.
    
    My Lunar program uses one refraction model for high altitude, another
    for low. One pitfall is the discontinuity where the program "shifts
    gears". This can be fatal when the refraction model is part of an
    iterative solution, so I have a zone of a few degrees where there's a
    linear transition between models.
    
    --
    Paul Hirose
    sofajpl.com
    

       
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