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    Re: Sun Moon Lunars to 155 degrees
    From: George Huxtable
    Date: 2010 Apr 6, 17:09 +0100

    Frank wrote-
    
    Why?? Well, remember that "lunars miracle" that I've discussed with you 
    several times in the past few years?? The altitude of the Moon matters LESS 
    than the altitude of the other body, and when the lunar distance is close 
    to 90 degrees, the altitude of the Moon can be wrong even by several 
    degrees with no significant effect on the lunars clearing process. You're 
    still thinking of the altitude as an index to get into the altitude 
    correction table. That's only part of it. The altitudes also affect the 
    geometric factors determining what portion of the altitude corrections act 
    along the lunar arc. Those factors or "corner cosines" change when the 
    altitudes change. By a lucky accident, the change in the corner cosine 
    cancels out the change in the Moon's altitude correction as the distance 
    approaches 90 degrees. Also notice that if you move the Sun up or down, you 
    can significantly change the geometry at the other side of the standard 
    lunar triangle. So even though the Sun's altitude correction may be very 
    small, it will still impact the lunar clearing process. In other words, 
    even if there were no refraction AT ALL, you would still need to get the 
    Sun's altitude correct to better than 6' (actually 6'*sin(LD)/cos(h)) if 
    you want to clear a lunar correctly. Try it yourself with a few simple 
    cases.
    
    ===============
    
    Very well. Let's consider a simple case, leaving out any "miracles".
    
    Here is a simple case, with lunar distance at 90 degrees. The Sun is at the 
    zenith, the Moon is on the horizon. How sensitive is the cleared distance 
    to the altitude of the Moon? And that of the Sun?
    
    Now put the Moon at the zenith, the Sun on the horizon. How sensitive is 
    the cleared distance to the altitude of the Sun? And the Moon?
    
    Just to avoid ambiguities of definition, instead of the high object being 
    actually at the zenith, I'm content for it to be put at say 88º altitude, 
    on the same azimuth as the lower object.
    
    I'm yet to be convinced...
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 
    
    
    
    

       
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