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    Re: Lunars - Even Easier
    From: Andr�s Ruiz
    Date: 2008 Jul 7, 12:39 +0200

    Very interesting Frank,
    This topic and your "Latitude by Lunar Distance" must be properly published. I 
    am wondering, and I think other navlist members too, if You are planning to 
    write any paper or book about it? 
    Andr�s Ruiz
    Navigational Algorithms
    -----Mensaje original-----
    De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de frankreed@HistoricalAtlas.net
    Enviado el: viernes, 04 de julio de 2008 21:54
    Para: NavList@fer3.com
    Asunto: [NavList 5686] Re: Lunars - Even Easier
    I wrote previously:
    "But sometimes a miracle happens. Even when the objects aren't perfectly 
    aligned, the same almost trivial math applies. The math doesn't care whether 
    the objects are really aligned so long as there is an equivalent case where 
    they are in fact aligned. For example, the two objects could be separated in 
    azimuth by 170 or even 165 degrees instead of 180 degrees, and under the 
    right conditions we can "pretend" that they are separated in azimuth by 180 
    degrees, and it all works out correctly. 
    How can this be?! Some kind of crazy voodoo? No, just good old rigorous 
    math. It works because the altitude of the Moon doesn't matter much, 
    especially when the observed lunar distance is close to 90 degrees or the 
    Moon's altitude is near the zenith." 
    I thought a picture might help to see the variety of cases where this works 
    properly. In the attached graphic, we see the surprisingly large region of 
    the celestial sphere where "trig-free" clearing of a lunar distance would 
    yield near-perfect results. Note that this diagram applies when the Moon's 
    altitude is 40 degrees. At lower altitudes, the zones are a bit smaller. At 
    higher altitudes, they expand greatly. When the Moon's altitude is 80 
    degrees, they cover half the sky. 
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