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Frank Reed has re-opened this question of whether it's profitable, or
possible, to detemine longitudes by means of moon altitude observations made
at sea.

This has been dealt with in Navlist, in some detail before, and can be found
in the archives, but if Frank wishes to retread old ground, I will go along.
Indeed, since those days, we have many newcomers who may add fresh views of
their own.

A modern proponent of the lunar altitude method is John S Letcher, jr, in
"Self-Contained Celestial Navigation with H O 208" (1977), in chapter 17,
who considered it "slightly inferior to lunar distance in accuracy".

A more recent view is by John Karl, "Celestial Navigation in the GPS Age",
my edition being 2007., pages 73-77, though readers should beware of some
wildly wrong numbers on page 77 (in my edition).  He ends- "A more direct
method of obtaining UT is discussed in chapter 8 on lunar distances, which
is less sensitive to the vagaries of altitude observations, such as
refraction corrections".

As Frank has pointed out, this proposed method has been discussed in papers
by Francis Chichester and others, and in his book "Along the Clipper Way".
Letcher points out that Chichester has failed to recognise some of the
defects, and mentions that in "Commonsense Celestial Navigation" (1975),
Hewitt Schlereth gave an incorrect explanation of why and when it works.
Comments from Hew would be welcome.

Don Sadler, then in charge of the UK Hydrographic Office, wrote an article
in the Journal of Navigation, 1978, issue 2, page 144, "Lunar methods for
'Longitude without Time'", which I attach. It gives an authoritative
critique of the proposal, which is worth reading. I find his diagram
somewhat inscrutable, though. He quotes Raper's dismissive views, and
provides many references.

It was described, in earlier times, by Chauvenet, who dismissed it as of
little use at sea. Brad Morris  mentioned a book reference, clearly
Chauvenet, to which Frank's response was-

"Don't worry. If it's Chauvenet, as I suspect, PLEASE don't bother scanning
and posting. Several editions of his treatise are available online.


Here's the reference, from Chauvenet's "Spherical and Practical Astronomy",
of 1863. The relevant paragraph is in Volume 1, on page 423, in the chapter
headed "Longitude at sea". It reads as follows-

"261. By the moon's altitude. -
This method, as given in Art. 243, may be used at sea in low latitudes; but,
on account of the unavoidable inaccuracy of an altitude observed from the
sea horizon, it is even less accurate than the method of the preceding
article, and always far inferior to the method of lunar distances, although
on shore it is one which admits of a high degree of precision when carried
out as in Art. 245."

The "preceding article" referred to finding longitudes by the eclipses of
Jupiter's satellites. Art 243 and 245 involve measuring Moon altitude from
on land, with a precise astronomical instrument including a level, or by
doubled altitudes using a Mercury artificial horizon. These call for either
absolute measurements of Moon altitude, or differential observations using a
nearby star. But neither uses the sea horizon.

Chauvenet, as usual, gets it absolutely right. Frank does his bit to dismiss
Chauvenet, in these words, which we've heard before-
"Bear in mind that Chauvenet has very little connection with practical
navigation. Chauvenet was a land-bound nautical astronomer and one of the
most prominent mathematicians in the USA in his era.".
Wikipedia provides a rather more balanced view-
"In 1841 he was appointed a professor of mathematics in the United States
Navy, and for a while served on Mississippi. A year later, he was appointed
to the chair of mathematics at the naval asylum in Philadelphia,
Pennsylvania. He was instrumental in the founding of the United States Naval
Academy at Annapolis, Maryland".
Does that sound like "a land-bound nautical astronomer"?

All commentators, then, acknowledge that the method is inferior in precision
to that of lunar distance, but there's some disagreement about how inferior
it is.

The big problem, with any sort of lunar observation for longitude, is to
achieve sufficient accuracy to make it worthwhile. Anything that worsens the
precision of a lunar observation is detrimental. Frank acknowledges just one
such defect in the lunar altitude, that it measures only the vertical
component of the Moon's speed, so it's applicable only when the Moon's
motion is nearly vertical (that is, only at low latitudes). Frank sets a
lower limit to the angle of rise or fall as 45 degrees, by which point only
50% of the accuracy of a lunar distance is retained (if the altitude of the
relevant star is changing at a similar angle).

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.

Frank, in his first posting, acknowledged the contribution of refraction,
claiming that if the Moon and star are at roughly the same altitude, then
any differences in refraction will mostly cancel out. Not so, unless the
azimuths of the two bodies are also close together (a condition which he did
not specify). In the worst case, when the two bodies are 180 degrees apart
in azimuth, or nearly so, such as a rising star measured to the eastward
being compared with a falling Moon to the westward, or vice versa, any such
systematic errors are doubled, not cancelled. As for the scatter, that's
increased because two such altitude observations are combined, both
requiring high accuracy.

Very high precision of relative timing of the two altitude observations is
called for. Both bodies are rising  or falling at a rate approaching 15
degrees per hour, but the difference between their altitudes is wanted to a
fraction of an arc-minute, to get a worthwhile result. So both observations
need to be timed to the second, or thereabouts.

Frank wrote, on 4 Jan- "The night before last, I saw the Moon rising in
northwest LA (the other "LA" --Louisiana) with Castor and Pollux above it.
Though it was just past full, it was clear that it was rising in a good
orientation and there were plenty of stars to choose from."

Maybe, but if he had chosen Castor or Pollux, there would have been 25
degrees or so difference from the Moon altitude, so no "cancellation" of
refraction in that case. Nearby Mars, in conjunction with the Moon, might
have made a better choice. But how would Frank have seen a horizon, to
measure altitude above it?The Sun was by then long set, and there would be
only moonlight to see the horizon by; we know how deceptive that can be.

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

There's something familiar about all this, and listmembers may recognise a
pattern. Frank Reed proposes some technique, but avoids mentioning its
drawbacks. It's left to others (usually me, it seems) to point those out.
It's a role I'm prepared to play, but wouldn't it be better if the presenter
of such a notion offered a balanced view, warts and all, himself?

Frank's first posting ended-

"But this method never made it in. Why was that? Just navigational
tradition? Actually, I think there's a bigger issue, something practical.
Have a look at the data for the Moon available in any 19th century Nautical
Almanac. What is included? What is missing, as compared with a modern
Nautical Almanac? What sort of problems would this create for a navigator
hoping to experiment with longitude (GMT) by lunar altitudes back in that
period?"

Well, I think we can see why it never made it; because it was so inferior,
in so many ways, to the lunar distance. But Frank's words puzzled me, and
sent me to my 1864 copy of the (British) "Nautical Almanac and Astronomical
Ephemeris". I could find no defect there that would hamper analysis of such
a lunar altitude.

Now, in his latest posting Frank writes-

"But there really is a considerable problem with that method if you're using
an almanac from that era. At what intervals are the Moon's RA and Dec
published in the almanac? At what intervals are the lunar distances
published? Why is there a difference?"

In my 1864 almanac, lunar distances are provided, as usual, at 3-hour
intervals. But Moon's Right Ascension and Declination are printed for every
hour of every day. So where is the "considerable problem": the "bigger
issue" that Frank refers to?

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.

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


----- Original Message -----
From: 
To: 
Sent: Tuesday, January 05, 2010 8:15 AM
Subject: [NavList] Re: Longitude by lunar altitudes


Brad, you wrote:
"I have a two issues of the same navigational text book (one issued about
1856 and the other issued about 1900) which explicitly discusses longitude
by Moon's altitude. "

Sorry if I was misleading in my previous message. I did not mean to suggest
that the method was unknown. It was widely known to the serious experts in
nautical astronomy, but almost unknown to practicing navigators. It has come
up again and again over the past 250 years in articles and books where
authors somewhere in the middle ground between experts and practitioners
would discover it independently. But it never made it into the standard,
widely-used navigational manuals. It certainly never made it into common
practice among sea-going navigators. There have been a number of people even
in the past fifty years who "re-discovered" the method of finding longitude
(really, GMT) by lunar altitudes. Chichester did. John Letcher did, and his
comments on how it would be so much easier for navigators to learn since
navigators are comfortable with taking altitudes echoes similar comments
from 150 years earlier.

I suspect that the book you're referring to is Chauvenet's. It would roughly
fit the time span you mentioned, and I do believe he had a section on it,
though I haven't double-checked. Bear in mind that Chauvenet has very little
connection with practical navigation. Chauvenet was a land-bound nautical
astronomer and one of the most prominent mathematicians in the USA in his
era. His book included everything that he could squeeze in for every
possible user from the common sailor to the professional astronomer in the
best observatories of the day. He did write about longitude by lunar
altitudes (somewhere, if not in his most famous textbook) and recommended it
as a method that might be most useful to astronomers and surveyors on land,
but not at sea.

So WHY was longitude by lunar altitudes impractical for sea-going
navigational use? Some of us, me included for a while, have much too
cavalierly dismissed it on grounds that really don't matter that much in
actual practice so long as you make reasonable rules on when it can be used.
But there really is a considerable problem with that method if you're using
an almanac from that era. At what intervals are the Moon's RA and Dec
published in the almanac? At what intervals are the lunar distances
published? Why is there a difference? If there's a lot more calculational
work, the method ceases to be a practical replacement for the standard
method of lunar distances.

You concluded:
"Being overwhelmingly busy right now at work, I can't scan it in and post
the method.  I will try to get this to the list when I can."

Don't worry. If it's Chauvenet, as I suspect, PLEASE don't bother scanning
and posting. Several editions of his treatise are available online.

-FER

=========================
Frank's first posting on this topic was on 4 Jan-
You can get GMT and then longitude by lunar distances, as most NavList
followers know, but as many navigators have discovered, both theoretically
and practically, it's also possible to get GMT by meausuring the altitude of
the Moon along with the altitude of one other body at about the same time
and roughly the same altitude (since then any differences in refraction will
mostly cancel out). Then if you plot LOPs (for a modern navigator), they
will be consistent only if the GMT is correct. Or for a historical
navigator, if you calculate local time from the star and then from the
Moon's altitude, they will agree only if you started with the right GMT for
the Moon. If they don't agree, you adjust until they do.

This "lunar altitude" method only works if the Moon's altitude is changing
measurably as a result of the Moon's motion along its orbit. That means that
the path of the Moon along the celestial sphere should be more or less
vertical from the observer's point of view when the sights are taken.
Observationally, this implies that the poles or "horns" of the Moon should
be roughly horizontal at the time of observation. Acceptably horizontal is
within 45 degrees of horizontal if we go by the same standards of acceptable
rates of change implied by the lunar distance tables. Except in high
latitudes, this happens more often than you might expect. The night before
last, I saw the Moon rising in northwest LA (the other "LA" --Louisiana)
with Castor and Pollux above it. Though it was just past full, it was clear
that it was rising in a good orientation and there were plenty of stars to
choose from.

Now back in the 19th century navigation manuals included lots of special
methods that would only work sometimes, only when conditions were "just
right" as with the longitude by lunar altitude conditions above. But this
method never made it in. Why was that? Just navigational tradition?
Actually, I think there's a bigger issue, something practical. Have a look
at the data for the Moon available in any 19th century Nautical Almanac.
What is included? What is missing, as compared with a modern Nautical
Almanac? What sort of problems would this create for a navigator hoping to
experiment with longitude (GMT) by lunar altitudes back in that period?

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