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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Rocky Mountain Lunar Distance
From: Arthur Pearson
Date: 2002 Dec 16, 21:57 -0500
From: Arthur Pearson
Date: 2002 Dec 16, 21:57 -0500
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@LISTSERV.WEBKAHUNA.COM] On Behalf Of George Huxtable Sent: Monday, December 16, 2002 2:32 PM To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM 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@huxtable.u-net.com George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. Tel. 01865 820222 or (int.) +44 1865 820222. ------------------------------