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Subject: Re: Rocky Mountain Lunar Distance
From: George Huxtable (george@XXX.XXX)
Date: Mon Dec 16 2002 - 14:31:53 EST
Well done, Arthur Pearson!
Instead of sitting in an armchair arguing it out (I plead guilty to that),
you have gone out and tried it. And given a good coherent account of it for
the rest of us to follow. Thank you, Arthur.
It's left me with a few assorted questions and comments.
1.I've never used a "bubble horizon" with a sextant, and wonder what
performance can be expected from it on land. Is Arthur's experience of the
bubble horizon being "a real challenge" a common one, and does an error of
7 minutes strike other users as the sort of accuracy (or inaccuracy) one
has to expect? For measuring such on-land altitudes, would an aircraft
bubble-sextant have done better?
2. If the afternoon Sun altitude had been measured halfway through the
set-of-four lunar distances, then this could have been treated as an
observed altitude (which it was) rather than an altitude to be calculated.
Did Arthur also observe a Moon altitude at or near that time? I appreciate
that he was demonstrating the art of calculated altitudes, rather than
mmeasured ones (and has done it well). It would be interesting to see any
figures.
3. On returning to civilisation, did Arthur check his wristwatch against
Zone time, to retrospectively confirm the time-accuracy of his afternoon
sun observation? Just for cross-checking. It depends, of course, on how
reliable was the timekeeping of his wristwatch, over that interval.
4. I hope Arthur doesn't mind too much if I quibble somewhat about the way
he treated his four lunar-distance observations. His rejection of the first
two (because although more than a minute apart they gave identical values)
would not find favour in a science lab. The lunar distance changes only by
about half-a-degree in an hour, or in a minute of time by about 0.5
arc-minutes (maybe somewhat less if parallactic retardation is
significant). Even if the error of each observation was as little as 0.25
arc-minutes, it would be quite unsurprising to find two observations, 1
minute of time apart, giving exactly the same lunar distance. Arthur
should, I suggest, plot out all four observations against time, and draw a
best-line between them by eye, with a slope that he can work out in
advance. That line will probably steer a path roughly midway between those
first two observations. It would be easier for us to check on this if all
the raw data was provided.
If this plot was made, and all four observations taken account of in this
way, my guess is that the resulting longitude would come within 45 minutes
or so of the true value, which wouldn't be a bad value for a lunar,
especially at first attempt. Captain Cook would have been pleased with
him...
5. Arthur quotes the expression for LHA Moon as-
(LHA Sun +/- difference between GHA Sun and GHA Moon)
but the ambiguities in this could cause trouble and it should be expressed
more exactly as-
LHA Moon =LHA Sun + GHA Moon - GHA Sun (adding or taking off 360° where
necessary).
GHA values have been provided the nautical almanac since 1952. Earlier
almanacs gave Right Ascensions (RA) instead, which were in terms of time
rather than angle, and measured Eastwards rather than Westwards, from a
different base. Because of that, LHA Moon was derived from-
LHA Moon = LHA Sun + 15*( RA Sun - RA Moon) where the 15 is to convert time
in hours to degrees, and the subtraction is the other way round.
6. Arthur says-
>David Thompson explored western Canada and his navigational procedures
>are documented by J. Gottfred at
>http://www.northwestjournal.ca/dtnav.html. Thompson’s use of calculated
>altitudes is elaborately reconstructed by Gottfried who provides a
>comprehensive set of diagrams and trigonometric formulas in explanation
>of the technique. It is interesting to note that Thompson worked his
>own sights to a full solution in the field.
Well, I have read Jeff Gottfred's account, and it that he quotes no
longitudes obtained by Thompson. Thompson may indeed have calculated
longitudes in the field, but I can't find that in Gottfred's paper. I may
have missed something, though.
I agree with Arthur's conclusions about insensitivity to errors, but point
out that he has demonstrated this just for one particular configuration of
Moon and Sun, and it will not be true to quite the same extent with
differing geometries.
I do hope that Arthur enjoyed the skiing part of his trip, and that he will
take his observing gear with him next time too, though it can't be much fun
lugging a sextant about on skis.
George Huxtable.
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george@XXX.XXX
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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