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    NavList 9435] Re: Multi-Moon line exercise in 2 parts
    From: George Huxtable
    Date: 2009 Aug 10, 15:00 +0100

    Jeremy's "moonlines" provide useful real-life material for us to learn from.
    
    I've taken his two sets of moonline data, just the raw data without
    correcting for anything in terms of North-South speed. All I've done to his
    data is to exclude the one errant observation in his "away from LAM" set,
    the second one.
    
    Then I've reorganised the numbers into decimal hours and decimal degrees,
    and persuaded Excel to plot them and to fit a quadratic polynomial
    "trendline", as shown..
    
    Just for interest, in the third sheet, labelled "plots.", those plots are
    placed side by side. Note the big differences in the vertical scale.
    
    The deduced scatter, of one standard deviation about the fitted trendline, I
    now make to be 0.53 arc-min in the case of the "Moon near LAM" set, and 0.38
    arc-min in the case of the "Moon away from LAM" data set. That's no better,
    and no worse, than one would expect from observations at sea from a large
    vessel.
    
    That scatter differs enormously from my assessment in [9412], which read as
    follows- "A least-squares fit to the non-culminating series arrives at a rms
    scatter of little more that 0.1 arc-minute, and of the series around
    culmination of about 0.15 arc-min". That was quite wrong, suffering from a
    bit of Excel finger-trouble on my part. The reassessed scatter now seems
    much more reasonable.
    
    For the maximum value of the peak near LAM, Excel 's deduced fit corresponds
    to an uncorrected maximum altitude at 9.8598 hours, or 9h 51m 35.3 sec., at
    which the observed altitude was 55.4446 degrees, or 55º 26.7.
    
    From a bit of simulation, I reckon that with the observed scatter of 0.53
    arc-min, the peak of the curve can be timed with a precision (one standard
    deviation) of 15 seconds of time, which would in itself contribute an
    uncertainty in deduced longitude of  3.7'  (again, one standard deviation).
    
    If anyone agrees with (or even more so, if they differ from) these numbers,
    I would be interested to learn.
    
    Note that if instead of taking so many closely-spaced observations near the
    maximum, just two observations, of objects 90 degrees apart in azimuth, or
    of a single body after it's moved through 90 degrees in azimuth, would fix
    latitude and longitude to about half an arc- minute (one SD). This
    "rapid-fire" procedure appears to be a way of combining large numbers of
    first-rate observations to produce a second-rate result.
    
    George.
    
    contact George Huxtable, at  george@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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    File: 109459.moonlines-063009.xls
       
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