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    Re: Frank's formulas, was: Lunars: altitude accuracy
    From: Frank Reed CT
    Date: 2004 Nov 4, 21:52 EST
    George H wrote:
    "What has surprised me (and intrigued Frank) is that the above expression
    continues to give a value for D in circumstances that are QUITE IMPOSSIBLE,
    in that the lunar distance is such that there's no value of azimuth
    (between 0 and 180) between Sun and Moon that can accomodate such a lunar
    distance. In those circumstances, although any attempt to deduce that
    azimuth would fail, the expression for D still seems to work, and gives
    some sort of result."

    Not only "some sort" of result, but the correct result. That's the fun thing.

    And wrote:
    "When the numbers input to the equation correspond to azimuths in range 0 to
    180, then the result D has a simple physical meaning, the true lunar
    distance D. In other situations, is there any physical meaning we can
    attach to D?"

    I think it's fine to say that D is still the cleared lunar distance. But the intermediary Z, which should be a difference in azimuth, has left the real number line in a case like this, and there's no way to "draw it" in a simple diagram or interpret it as an azimuth. It's just a meaningless intermediate quantity. Here's something to ponder: imagine what the reputation of lunars would have been if navigators 200 years ago had learned that the difference in azimuth might occasionally be partly an imaginary number but, not to worry, this is normal, and it's a good thing! Maybe that's why this issue is not discussed in the usual sources. They were afraid it might drive mariners mad...  :-)

    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
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