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    Re: Using any star for a lunar
    From: Bill B
    Date: 2005 Apr 7, 00:18 -0500

    > Mark three points around the equator. Point A is at 0deg West, point B is
    > at 120deg West, point C is at 240deg West. Join A to B, B to C, and C to A
    > again, with great circles, going Westerly each time. Then you have three
    > vertexes, each subtending a 180deg angle. The resulting triangle divides
    > the circle into two equal halves
    >
    > You might object that with such a 180deg angle, then each vertex has become
    > a straight line, not a corner. That's true, because it's a limiting case.
    > Think about it, if you prefer, when the angle at A, B, and C is not quite
    > (but as near as dammit) equal to 180, so there's a VERY obtuse angle at
    > each corner. Then increase these angles, very slightly.
    
    George,
    
    See your point(s).  Had not considered that case, C to A as the smallest
    GCD; but rather joined my three arbitrary points (C to A) with the greater
    GCD.
    >
    > This business of the "spherical excess" is quite new to me, but it seems to
    > work. If we add the three "angles", each 180, we get 540 deg. The spherical
    > excess over a tiny triangle, in which the angles always sum to 180deg, is
    > therefore 360 deg, or 2pi radians. Multiply this by r squared, and we get 2
    > pi r-squared, which is indeed the area of the half-sphere that the
    > "triangle" embraces. Today, I've learned something new...
    
    Ain't life grand?  Been doing dumb human tricks with spherical trig today.
    Once I got got the bigger picture, it occurred to me if swap out AP Lat and
    GP Lat (declination) and vise versa in the Z formula(s) I could obtain the
    AP, GP, pole angle.  Add those up (-180d, pi radians) and I can calculate
    area in the triangle.  I am dumbfounded as to how to use the area inside the
    triangle--other than to impress sailing friends whose eyes glaze over when I
    mention cel nav with the number of square miles of water included in the
    triangle--but betting one the list mentors has a practical application.
    
    Bill
    
    
    

       
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