|
|
|
|
|||||
|
||||||
Subject: Re: Rocky Mountain Lunar Distance
From: Arthur Pearson (arthurpearson@XXX.XXX)
Date: Mon Dec 16 2002 - 21:57:38 EST
As usual, George has good comments and questions. Here are my responses:
1) The bubble horizon I have is the practice model sold by Celestaire.
It is a simple plastic tube with no magnification. There is a reference
line in the view, and the trick is to bring the body down to the
reference line while bringing the reference line into the center of a
bubble. I wouldn't doubt that mounted on a tripod or locked in place
somehow, the instrument has accuracy within 2' per David's comment.
However, held in the hand I find it is a real challenge to bring all the
elements together at the same instant. I followed the instructions
Celestaire provides once and found an installed error of -2.3', but you
need a true horizon to find the error, so it is not something that can
be checked when you really need it. That said, it is inexpensive and
completely satisfactory for a quick experiment like this. If one wants a
greater accuracy, I would think a reflecting horizon would be the best
alternative, but I have never tried one.
2) I measured the sun's altitude once about 2 minutes after the last
lunar. I did not measure the moon's altitude. All my sights and times
are recorded below if anyone wants to work with them.
3) I never checked the wrist watch against accurate zone time, so I
can't assess the accuracy of the time sight. One of the virtues of this
method is the watch only had to keep accurate time over the period
during which one takes the lunars and the time sight, about 10 minutes
in this case. I think you could do this with a stop watch if you wanted
to (I hope I will hear it if I am wrong in this).
4) George is quite right about my casual selection of which sights to
favor. When I take a simple average of the longitudes derived from the 4
sights, I get 105° 14'W which is about 45' too far east.
5) George's expression for LHA moon is more exact (LHA Moon =LHA Sun +
GHA Moon - GHA Sun adding or taking off 360° where necessary). It is
worth noting that while this was the easiest way for me to understand
the calculation of LHA moon, the examples provided by Patterson to Lewis
in his "Astronomical Notebook" take a different path to the same result.
I found it easier to construct calculations by Patterson's method.
Recall that by assuming longitude we have established a correction
between local time (LT) and Greenwich Time (GT), and by our time sight,
we find a correction from watch time (WT) to LT. With WT of the lunar,
we correct to estimated GT and take GHA and Dec of moon and sun from the
almanac (in my case, I interpolated within the hour for GHA, and within
the 12 hour period for Dec). LHA of either body is simply (GHA ~
Longitude). I puzzled quite a while before accepting that this arrives
at the same value as George's expression. The elegance of the method is
in the linkage of assumed longitude and assumed GT. Preston provides a
wonderful word picture of this in Note 23 on page 190 (page # refers to
the page of the journal, not the length of the article!).
6) On review, I can't find a longitude calculation by Thompson in the
Gottfred article. I got the impression that he worked out longitude in
the field because Gottfred transcribes field notes in which Thompson
calculates altitudes, applies reverse parallax and refraction, and
clears the distance. That is the hard part! It is easy to get to
longitude from there (look in the tables, interpolate for GT, find the
time difference from LT, convert to degrees of longitude). But
Gottfred's language on this point is ambiguous:
"Thompson also computed longitudes from his knowledge of Greenwich and
Local Apparent Times, set his watches to local apparent time by
observing the sun or other stars, and computed the magnetic variation at
his locale.
To demonstrate how these values were determined, I will use a
hypothetical case (since Thompson leaves us no calculations) using the
data from November 3, 1810."
Did he or didn't he? I can't tell.
Lastly, I did have a great time on the ski trip but prefer to stay
closer to sea level in slightly warmer surroundings. In early January,
my sextant and I are headed for a long anticipated cruise through the
Grenadines, and as the moon will be "in distance", I hope to make the
best of the opportunity. This time I'll leave the bubble horizon at
home.
Regard,
Arthur
RAW DATA FROM DEC. 8, 2002, NEAR BRECKENRIDGE, COLORADO (106°W, 39°
30'N)
NOON SIGHT (IC = -3.0')
Hs Approx ZT 11:55:00
27° 29.0' 11:55:00
LUNAR DISTANCES (IC = -3.0')
Ds Watch Time
58° 9.4' 14:30:40
58° 9.4 14:31:55
58° 12.6' 14:34:18
58° 13.9' 14:36:23
SUN SIGHT FOR TIME (IC = -3.0')
Hs Watch Time
16° 21.2' 14:39:44
-----Original Message-----
From: Navigation Mailing List
[mailto:NAVIGATION-L@XXX.XXX] On Behalf Of George
Huxtable
Sent: Monday, December 16, 2002 2:32 PM
To: NAVIGATION-L@XXX.XXX
Subject: Re: Rocky Mountain Lunar Distance
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.
------------------------------
george@XXX.XXX
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
------------------------------
|