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Jeremy, on averaging a set of lunars, you asked:
"What is the traditional means of averaging?  Do you average the time
and then the LDs and just do one reduction?"

Yes, exactly. If you shoot the altitudes, you can usually do them by
averaging, too. A good sequence is: body altitude, Moon altitude, four lunar
distances, Moon altitude, body altitude. When you average the bracketing
altitudes, you often find that their average time falls very close to the
average time of the observed lunar distances. If they're not quite right,
it's very easy to adjust them a little to bring them to the correct time. If
you don't shoot the altitudes (which is the way almost everyone uses my
online clearing tool), you just average the times, average the LDs, and
clear them as if it's a single sight. With a set of four, this typically
doubles the accuracy. The rule is that random error is reduced in proportion
to the square root of the number of sights. So you cut the error in half
with four sights. To cut it in half again, you need a total of 16 sights
(this applies to random observational error, not systematic error).

And regarding getting an LOP from a lunar you wrote:
"I would like to try this, but am not sure how you do it."

It's remarkably easy (again we're assuming GMT is known here, as it always
is for a modern navigator). Try this: take that set of Moon-Jupiter lunars
you posted. Go ahead and average the times and the distances. Now go to my
online calculator and try different DR points scattered about your known
position. You will discover that the "error" in the sight goes to zero along
a narrow path. That's your LOP. If you want to be a little more systematic,
pick four points around your DR in a square, each offset by one degree in
latitude and longitude. Suppose we determine the error in the lunar at each
corner of the square. For some example numbers, suppose the error at the
northwest corner is 0.5', at the northeast 1.0', at the southwest, -1.0', at
the southeast -0.5'. I'm sure you can see that there must be a line across
the middle of this square where the error is zero. It should run across the
square from a point approximately one-third of the way down the west side to
a point apprximately two-thirds of the way down the east side ("down" here
is north biased). Anywhere along that line, our lunar observation would be
'true', so that's the line of position.

And again, if the horizon is lost in thick haze, you can often still see the
Moon clearly. If you take two lunars separated by a few hours, you can cross
those "lunar LOPs" and get a fix. This is a rough fix. An error of 0.1
minutes of arc in the LD yields a 6 n.m. error in the LOP. If you have a
bubble sextant (which also requires no visible horizon) you could get this
sort of accuracy without even trying very hard. Then again, I could just
turn on the GPS and be done with it. :-)

 -FER



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