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I've relabelled the threadname to better reflect the topic being discussed.

Frank Reed wrote-

"If the goal is to preserve as much as possible of the simplicity and
familiarity in the clearing process that comes from this longitude by lunar
altitudes system, and I think we all agree that this is appealing to
navigators raised on standard late-20th-century LOP navigation..."

Why on Earth would we all agree about that? I, for one,  disagree strongly.

Why is longitude-by-lunars being taught, I ask? Not, these days, to obtain a
qualification. Nor, presumably, as an emergency backup, nowadays, when
everyone in a lifeboat is likely to have a sufficiently precise timepiece
strapped to his wrist. Nor for those who just want to measure lunar distance
to test-out their prowess with a sextant, but live too far inland from a sea
horizon; for them, Frank's lunar distance website will suffice.

The only reason for learning, and for teaching, the lunar-distance technique
is because of its historical significance. It's a historical subject, and a
fascinating one, but it belongs entirely to the past. If anyone wishes to
repeat such observations today, it's entirely because in doing so, he is
following the path of his forebears, who had no alternative, until they were
rich enough to possess a chronometer (or three).

So why, if a student is to learn about measuring lunar distance, should he
be taught a method that, because of its inferior performance, no mariner
ever used? If he leaves the class, having learned that lunar distances were
measured by observing altitudes above the horizon, and not angles across the
sky, he will have learned an untruth. Navigators of that era knew what they
were doing. Their accepted way of doing the job squeezed all the possible
accuracy out of it, and that accuracy was all-important, because imprecision
is the bugbear of lunar distance. And lunar-distance could be applied most,
though not all, of the time; as long as the Moon, with Sun or star, could be
seen in the sky; not just occasionally in special circumstances and from
special places. Pretending that it was done otherwise, to minimise its
calculational problems, is lazy teaching, short-changing any serious student
who seeks to know how it was done. It's an attempt to rewrite the history.

Frank seems to be aiming towards teaching celestial-navigation without trig.
And that's not possible. If the trig is stripped out of it, it isn't
celestial navigation any more; it's some sort of "pretend" game instead. A
method that works only within a narrow range of low latitudes,
close-azimuths, similar altitudes, and near twilight, is hardly a
navigational technique at all. For use by navigators, it's wanted when it's
needed, not when all the omens are right. Already, any celestial navigation
method is limited enough, requiring clear skies. Any lunar technique is
further limited, being ruled out near New Moon. Further restrictions are
unwanted.

========================

In a posting on 5 Jan, in the thread "Longitude by lunar altitudes", I
wrote-

"The deficiencies in the method, resurrected by Frank, are all concerned
with the problems of using the horizon for precise measurement. Those
problems are what the tradititional measurement of lunar distance avoids.
Being an angle between two bodies, up in the sky, the horizon plays no part
in lunar distance (except in an auxiliary measurement which calls for no
great accuracy). So a precise observation can be made, which depends only on
the skill of an observer and the precision of his sextant.

Altitude measurements from the horizon, on the other hand, are always
bedevilled by the inherent inaccuracies involved. There is systematic error
of inconstant and unknown dip, refraction, index error. The random errors
caused by horizon haze, problems of seeing the horizon when observing stars
at night, the waves that make up the horizon's profile from a small vessel,
the unknown height-of-eye resulting from the vessel's heave, the general
rock-and-roll of a ship's motion, produce a scatter in altitude, which
affects altitude observations of both moon and star. In contrast, a lunar
distance is affected only by index error, differential refraction, and the
vessel's motion."

Initially, the only weakness Frank recognised in the altitude method was in
the angle-of-rise of the bodies, about which he judged, referring to the
line between the Moon's horns- "within 45 degrees of horizontal is good,
within 30 is excellent". Hardly "good", if both bodies are shifting at 45º,
which on its own will double the error compared to a conventional lunar
distance. Now, he has come to recognise the contribution of dip, which then
limits him to a close pair of azimuth directions, in which case dip can
cancel.. But he neglects all the other problems that bedevil the horizon,
that I have listed above, and which do not enter into a lunar-distance.
Instead, what does he concentrate on? Just read this-

"Of these two approaches, the latter has all the advantages of a true lunar
distance observation, and it works regardless of the orientation of the
Moon. On the other hand, it requires an exact measurement of the sextant's
index correction. If that's uncertain then the method by altitudes is
better."

It is, indeed, true that a good knowledge of index error is needed to
measure a lunar distance, and also true that where two bodies are observed
at nearly-similar azimuths, any effect of index error will cancel. That's
the one-and-only aspect in which the lunar altitude method, used in that
way, can possibly be described as "better". But is there any problem of
uncertainty in the knowledge of index error? Not ever! If a navigator is
uncertain about index error, its simply because he hasn't bothered to check
it; the work of a moment. So that claim, that the method by altitudes can be
"better" for that reason, is a spurious one.

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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