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George H, you wrote:
"I am sorry not to be attending."

I'm sorry you can't attend, too. As I said, when I invited you, it would be
a pleasure to meet you after several years of chatting online.

And you asked:
"ask how a navigator at sea, without internet access, would obtain
sufficiently accurate predictions of the Moon's position, other than by
using the Nautical Almanac."

First, I presume here that you are talking about predicted lunar distances
of sufficient accuracy, right? Well, our hypothetical navigator could easily
PRINT THEM OUT from any of a number of sources. Isn't that just obvious? I
mean really, REALLY obvious?? He could print them from my web site [and on
my site, he could choose to get them in degrees, minutes, and seconds, or
degrees,minutes, and tenths of minutes, or decimal degrees. on my web site,
he could also choose to get those distances in GAT instead of GMT]. He could
print them from Ken Muldrew's software. I can't recall right now all the
people who have made tables like these available, but there are many. That
makes sense, doesn't it, George?

Or, if we relax the rules a bit and permit the use of a computing device
on-board, the navigator might use some stand-alone (non-Internet) software.
I've got something like that nearly ready. It may be ready by Sunday in some
form... or maybe not... --we'll see how much time I spend entertaining in
the next few days (Geoffrey should be landing in Boston right this second).
One could argue that using software isn't playing fair by the rules of the
game, but different folks play the celestial "game" with different rules.
For example, in ocean sailing races, e.g. from Newport to Bermuda, you can
get a few percentage points in your favor if you do all your navigating with
a sextant. But they don't care one bit how you reduce your sights, and it's
quite legitimate to use navigational software on a computer on-board.
Similarly, we've seen many people on this list who get pleasure from taking
sights who don't feel like they're cheating at all when they work the sights
in software. So that problem is no problem.

The Moon's position has been calculated to a level far beyond the needs of
celestial navigation, once and for all. The positions of the Sun, Moon, and
the navigational planets at one-arc-second accuracy for 300 years occupy
only 11 megabytes in my software, and that's with minimal effort at saving
space. I can hide that in a "dusty corner" of a 2 gigabyte flash drive that
fits on my key chain.

And you asked:
"Also to ask for a complete error-budget, to include numerical estimates of
the the following errors and how they combine-
Systematic errors such as; sextant calibration, sextant adjustment, index
check, observer irradiation correction and/or personal bias, celestial
position prediction, any abnormal atmospheric refraction.
Random errors (and therefore reducible by averaging many observations):
Observer's scatter between readings."

Wow, George, with all those errors, it's a wonder that ANYONE even
considered using lunar distances!! I can see now that Dava Sobel was
correct: lunars must be just about impossible, and Nevil Maskelyne must have
been an idiot for proposing their use at sea. I'm kidding, of course, but
when you go to such lengths to exaggerate the possibility of error, it's
hard to resist...

Now, of course, some people have lousy sextants. You had nothing but a
plastic sextant for most of the time I've known you in this group. For a
while, I had a sextant with 1.5' of arc error in some ranges (that's
correctable once it's measured, but not before). Some people have sextants
that are poorly calibrated. Others use low-power telescopes when they've
been told they need a high-power telescope. Do we take these people who are
fundamentally "doing it wrong", and say that they represent the real limits
of lunar distances?? I sure as hell wouldn't. I've already described a bunch
of things that have to be done right if you're going to do lunars. If we get
lazy and ignore some of them, that's not a problem with the sight (though
one could fairly complain that it makes lunars more trouble than they're
"worth" --whatever that means).

As for errors in "celestial position prediction" and "abnormal refraction"
they are completely insignificant. The only exception I can think of would
be if an observer chose to take sights when the Sun or the Moon was below
three degrees in altitude. Nearly everyone I know who has even considered
taking lunars is aware that low altitudes are to be avoided. In fact, most
avoid lunars when either object is below ten degrees, though that's not
really necessary.

So how shall we ever determine the remaining error?? Uh, how about we shoot
some trial sights at a known locations? That's obvious, right? And then
whatever standard deviation you get, that's what you should apply. I should
add that some navigators need a little practice before they get the hang of
it, so that s.d. can improve dramatically after the first dozen or so
trials.

But while you're laying out this long chain of terrible sources of errors
weighing heavily upon the observer, let me ask you this: what do YOU think
an observer should expect for the standard deviation of errors in individual
lunar distance observations?? And for four sights in a row averaged? If you
decide to do that, pleas let me know how many lunar distances you've taken
to reach your conclusions.

And you wrote:
"These were all questions asked of Frank on that earlier thread, some by me,
some by others. All were evaded."

That is yet another mis-representaion, George. This is getting to be quite a
habit with you. If you mis-understood my answers, then you should ask for
help. I am always interested in making my points as clearly as possible.

And you wrote:
"It would also be useful to be clear whether any accuracy claims that are
made will be in terms of maximum expected error,  standard deviation
(one-sigma), or some other multiple of sigma."

When I quote errors, I am referring to one standard deviation. I believe I
have been abundantly clear on that, but I'm sorry you missed it. I will
remind you often, if you need me to do so.

 -FER



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