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Henry Halboth's interesting posting [NavList 1668] Latitude by lunar
distance, has rather changed the direction of this discussion, so I
have tried renaming the thread, to correspond.

Henry must have as many sea-observations under his belt as the rest of
us put together, and I am pleased to agree with much, though not all,
of what he has said.

I fully concur, when he writes- "I am obliged to say that backyard
Lunars, taken under antiseptic conditions from a known position,
although they may be a fair exercise in the determination of sextant
accuracy/capability, do not replicate conditions of observation at
sea; if the altitudes are obtained by use of the artificial horizon,
they do replicate conditions probably faced by land explorers. To the
best of my knowledge, gleaned through both experience and research,
the best average accuracy attainable at sea by the use of Lunars
was/is in the range of fifteen arc minutes of Longitude."

I would quibble a bit with the following-

"For example: to clear a Lunar Distance normally requires (at sea at
least) observations of the respective altitudes which, with multiple
observers, does not present much of an obstacle, but with only one
observer requires additional calculation;..."

That was the case, I'm sure, in the days of lunars in the Royal Navy,
overstaffed with officers and middies under training, and making a
ceremony out of it.. However, one skilled man could do the whole job:
any additional calculation, if the job was done systematically,
involved no more than an extra bit of time-averaging. The most logical
sequence was to take a star (or Sun) altitude, then a Moon altitude,
then some lunar distances, then a Moon altitude, then a star altitude,
in a regular time-sequence like clockwork, so that the averaged times
for all three sets of measurements were the same. That was how a
lightly-officered merchant vessel would proceed, and was how Kieran
Kelly's postings described Gregory land-navigation techniques in the
Australian bush in the mid 19th century.

Henry continued-

"... yes, I know it's possible to calculate the altitudes - however,
does not that require a position/time of reasonable accuracy - some
authorities stating these calculated altitudes should be within four
arc minutes of the truth,..."

Asking for the calculated altitude to be within four arc-minutes of
the truth may be a bit over the top, but it's not entirely
unreasonable. The biggest effect would be on the parallax correction
for a high Moon at about the same azimuth as the relevant star. With
such an error, the resulting error in the parallax correction could be
no more than about 4 arc-sec.

and he goes on to ask-

" ...and does not such accuracy require a position/time accuracy
better than is ultimately determinable by the Lunar Distance. "

Here, my answer is "No, it doesn't. It's possible to proceed by a
process of iteration. Knowing latitude and local apparent time, you
can assume a trial-value for your longitude, and work out what the
apparent altitude of the Moon and star would be on that basis. It's
the Moon's altitude, and the resulting parallax, that has by far the
biggest effect on the corrections for clearing the lunar distance.
Then proceed by clearing the observed distance on that basis, and then
from the almanac tables you get Greenwich time, and from the known
local apparent time, a new value for longitude. If that is far from
your trial value, go round that loop once again, with the new value
for longitude as a trial-value. Each time you go round such a loop,
the error reduces by a factor of 30 or so, and you very quickly home
in to the correct value. Once or twice around will normally suffice.

Done by hand, this involves a lot of tedious calculation, but of
course it's just the sort of tedious calculation that a calculator can
do in a twinkling.

Nevil Maskelyne, bless his soul, included, in his "British Mariner's
Guide" of 1763, four years before the first Nautical Almanac appeared,
"A rule to compute the apparent altitude of the Moon or a star,
supposing they were not observed". However, I would not claim to
defend the details of that section.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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