# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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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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