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    Re: Exercise #14 Multi-Moon LOP's
    From: Brad Morris
    Date: 2009 May 1, 16:53 -0400

    Hi Jeremy
    
    The newly linked file method just worked.  Don't be so hard on yourself 
    regarding the variance in DR. S--- happens.
    
    Upon review of the data, it shows that you are indeed subject to the SMG 
    estimation and not to the DR position.  That really isn't a surprise.  As 
    each LOP is advanced or retarded by a function of velocity, the fix changes 
    as a function of each LOP.  The error in SMG contributes almost directly to 
    the error in fix.  The same applies to the course made good.
    
    The overall method works because of the least squares fit (assuming that is 
    the regression method) at the end.  This is nothing more than good old Saint 
    Hilaire.  We wouldn't try this on a plotting sheet, simply because all the 
    lines are at a relatively shallow angle.  Further, 25 LOPS with 24 advanced 
    LOPS might confuse the living heck out of me, especially when I go for the 
    "cocked hat".
    
    However, for a computer, it is an easy day to create the fix.  It cannot be 
    confused by the multiplicity of lines, nor will it make a plotting error in 
    advancement or retardation.  Yes, a human could perform all of this, albeit 
    at the risk of many minor errors as they go.
    
    For similar reasons, the Latitude by Double Altitude methods espoused by 
    Bowditch fell out of favor.  Just too easy to make a mistake, and very long 
    in computation.  This is very evident in the 4th method (variance of 
    declination permitted).  That method is twice as long as any other and 
    certainly longer than a lunar.  That makes it easy to make a mistake.  I 
    spent a very long time creating a spreadsheet to do this, simply because the 
    directions are obtuse and the cases are many.  Now that I have the method 
    programmed, it is easy to fill in the altitudes, declinations and time 
    interval.  The latitude pops out.  I would never really try this by hand, it 
    is just too cumbersome and error prone.
    
    The "rapid fire fix", at least for me, falls into that category.  Yes, a 
    computer can perform the calculation.  A human, not so much!
    
    Best Regards
    Brad
    
    
    
    
    
    
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