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Author
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Topic: Longitude by LAN
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Paul
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posted May 05, 2007 04:49 PM
While reading section 11.17 of David's very excellent book, I wondered about the following:
Suppose I was in Fiji, at about the International Date Line, dead in the water to avoid change of lattitude complications, and I went through the full longitude by LAN procedure on December 18, 2007. If I did everything perfectly, wouldn't my computed longitude still be off by about 4' because the tabulated time of LAN at my location would be off by about 15 seconds?
My thinking is that tabulated LAN changes by 30 seconds from 12/18 to 12/19 and I'm half way around the world, so my actual LAN is off by 15 seconds from the tabulated value which amounts to 15'/4 or about 4'.
From: Muncie
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David Burch
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posted May 06, 2007 01:37 PM
I do not exactly follow the argument, but my reaction would be that being near the dateline, one side or the other should not matter at all.
To find your longitude at noon by these methods, you somehow decide when the sun was at its peak height. Then at this time you look up the GHA of the sun and that is your longitude.
The relative location of the dateline or any other unique meridian like Greenwich does not enter into it.
The key point comes back to the issue of time keeping. You have a watch with a known watch error and known zone description—and that zone description "of your watch" has nothing to do with where you are, you could be on New York City time. You take the watch time of observed LAN, apply the WE, apply the ZD, which gives you GMT, and then look up the GHA of the sun.
Does that make sense, or am i missing the point you are making? --david
Put another way, the main problem with this procedure is not the principle, nor that it requires any special knowlege of your DR. The problem is it requires finding the time of peak height of the sun to a good accuracy... ie better than we might do with a simple running fix from AM to PM. The very thing that makes Lat from LAN easy (ie it is not sensitive to time) makes longitude more difficult.
From: Starpath, Seattle, WA
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Paul
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posted May 06, 2007 06:28 PM
David:
OK. I'm an idiot. Mea Culpa. Ph.D., MIT, Dunce.
Once again I assumed I knew what I was talking about, and I didn't. I had recently read the Sumner book where the time of LAN figured prominently in the determination of longitude, and I assumed (incorrectly, I guess) that it would also figure in this case.
But isn't it true that longitude by the old methods (which include the use of the equation of time) could be off a bit for the reasons I stated in my previous message?
From: Muncie
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David Burch
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posted May 06, 2007 11:25 PM
Sumner's book is online at http://quod.lib.umich.edu/cgi/t/text/text-idx?c=moa;idno=AAN0447.0001.001
His description of the discovery is something like:
Having sailed from Charleston, SC, November 25th, 1837, bound for Greenock, a series of heavy gales from the westward promised a quick passage; after passing the Azores the wind prevailed from the southward, with thick weather; after passing longitude 21 W. no observation was had until near the land, but soundings were had not far, as was supposed from the bank.
The weather was now more boisterous and very thick, and the wind still southerly; arriving about midnight, December 17th within 40 miles, by reckoning, of Tuskar light (52° 10' N, 06° 12' W), the wind hauled SE. true, making the Irish coast a lee shore; the ship was then kept close to the wind and several tacks made to preserve her position as nearly as possible until daylight, when, nothing being in sight, she was kept on ENE. under short sail with heavy gales.
At about 10 a. m. an altitude of the sun was observed and the chronometer time noted; but, having run so far without observation, it was plain the latitude by dead reckoning was liable to error and could not be entirely relied upon.
The longitude by chronometer was determined, using this uncertain latitude, and it was found to be 15' E. of the position by reckoning; a second latitude was then assumed 10' north of that by dead reckoning, and toward the danger, giving a position 27 miles ENE. of the former position; a third latitude was assumed 10' farther north, and still toward the danger, giving a third position ENE. of the second 27 miles. Upon plotting these three positions on the chart, they were seen to be in a straight line, and this line passed through Smalls light (51° 43' N, 05° 40' W).
It then at once appeared that the observed altitude must have happened at all of the three points and at Smalls light and at the ship at the same instant.
Then followed the conclusion that, although the absolute position of the ship was uncertain, she must be somewhere on that line. The ship was kept on the course ENE. and in less than an hour Smalls light was made, bearing ENE. 1/2E. and close abord.
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i have added italics to see the key point. they used a method then called "longitude by chronometer." This technique as done in those days is described in this 1878 bok by Galton
http://books.google.com/books?q=intitle:hints+to+travellers+date:1875-1885
among other places.
this method done by modern methods does not care about the date line as i outlined, but in those days the time keeping was different. we will have an article on old-style time keeping by Bruce Stark (an expert on the subject) in the Navigator's Newsletter coming up in issue after next. www.navigationfoundation.org.
How the dateline concept might affect this old method has to be investigated...there is in passing an article on the interesting history of the date line in maritime affairs at http://www.phys.uu.nl/~vgent/idl/idl.htm
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a very long way to say, i do not know!
From: Starpath, Seattle, WA
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Paul
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posted May 07, 2007 09:04 AM
David:
Thanks again for you prompt and thoughtful reply. I'm very new to celestial navigation, and I don't yet quite know how to talk the talk, which is part of the problem here. And I think that I probably muddied the waters by choosing the International Date Line as the focus of my comments. Any location other than the Prime Meridian would fit my argument, I just wanted a spot far away from Greenwich.
What I was trying to get at is the following: Suppose you use the method Sumner used, longitude by chronometer, which I guess they called taking a time sight, and you employ the tabulated equation of time to correct your apparent time at the ship to mean time at the ship. If you're far from Greenwich, the value for the equation of time will have changed from the tabulated value and your calculated longitude will be off.
Maybe the real question here is how did a navigator get a value for the equation of time in 1837? Did they have a nautical almanac with two daily values like we have? Maybe they interpolated. Maybe they had hour-by-hour tabulations of the equation of time. Looking in the second reference you gave might possibly shed some light; I'll get right on it.
In messing around with this I see that SP-89 and the Starpath Perpetual Almanac give significantly different values for the equation of time on December 17, 1837. It could be a reflection of just the issue I've talking about: they could give it for different times of the day.
Thanks for noodling with me on this.
From: Muncie
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David Burch
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posted May 07, 2007 10:11 PM
In the online course in cel nav or maybe here earlier we have had other questions come up on the history of navigation. These are best answered by those who know such things and everyone has access to these experts in the Navigator's Newsletter. I hate to pass the buck, but for anyone with interest in the history of cel nav, this Navigation Foundation is a tremendous resource. Many members know all about this and could answer thoroughly and quickly. Please see www.navigationfoundation.org. it is $35 per year, but with the savings you get at many outlets you more than make that up very quickly.
From: Starpath, Seattle, WA
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David Burch
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posted May 07, 2007 10:36 PM
another thought... as i see it and use the convept in the course, the equation of time is not related to the location of any observer. We think of it as the difference between 12:00:00 GMT and the GMT of LAN at greenwich on any particular day. Certainly the time of LAN will vary around the world, but not the equation of time listed in the almanac (they actually give two values for each day).
as i recall, the old method used to relate all times to the time of LAN. So they were actually measuring the chronomter time of LAN and then comparing that to the chronometer time of the sight. I think this is called using apparent time, but i am not up to speed on these older methods.
we may have some old almanacs in the office, and i will look this up if i can. I think we have some in the old books we produce in the elibra catalog section called Mariner's Antique Library.
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just noted from an online search that the British almanac switched from apparent time to mean time in 1834... also saw reference to EqT as difference between apparent and mean time, which is the official definition, in which case it would be changing throughout the day, but if they were using mean time in 1837 then it is basically the same as discussed above as modern methods... i still do not know how this is handled in the old methods.
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the official definition from Bowditch:
EqT is The difference at any instant between apparent time and local mean time. It is a measure of the difference of the hour angles of the apparent (true) sun and the mean (fictitious) sun. The curve drawn for the equation of time during a year has two maxima: February 12 (+14.3m) and July 27 (+6.3m) and two minima: May 15 (-3.7m) and November 4 (-16.4m).
The curve crosses the zero line on April 15, June 14, September 1, and December 24. The equation of
time is tabulated in the Nautical Almanac, without sign, for 00h and 12h GMT on each day. To obtain apparent time, apply the equation of time to mean time with a positive sign when GHA sun at 00h GMT exceeds 180°, or at 12h exceeds 0°, corresponding to a meridian passage of the sun before 12h GMT; otherwise apply with a negative sign.
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So we are back to the point you make... in the old system, how did they apply this to convert measurments in apparent time to get Lon... though it seems Sumner's almanac may have been in mean time.
From: Starpath, Seattle, WA
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Paul
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posted May 08, 2007 06:08 PM
I guess I'm still an idiot. As a precaution, I've put the dunce hat back on.
To answer your question, my calculator gives the time of LAN as 11:56:26. Unless I'm confused, I note that SPA (as shown by your screen shot) gives 11:56:40, which does in fact disagree with the JPL data you quoted.
I still don't get it that the EqT is not related to the geographical position of the observer. Doesn't the EqT tell me the relationship between LAN and mean time? And doesn't that change from meridian to meridian, with the passage of time, as the earth continues in its orbit and has to, according to Kepler, spin more (or less) to align me with the sun? The data I mentioned previously about a 30s difference in LAN at Greenwich from 12/18/07 to 12/19/07 would seem to indicate that on 12/18 LAN occurs at 11:56:26 GMT at Greenwich, 11:56:36 at 120 W, 11:56:46 at 120 E and 11:56:56 back at Greenwich the next day. And the EqT accordingly changes continuously along the way by longitude from 3:34 to 3:04.
From: Muncie
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David Burch
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posted May 08, 2007 09:26 PM
Well... i can only hope there are enough caps to go around! i mixed up the pictures. and you are right the only one that is correct is the StarPilot PC. So I am looking into this now. As it turns out, SPA and SPPC use the same almanac, and so i copied the SPPC almanac function into the SPA and ran it, and sure enough i still get the same 40s for SPA and 25 (correct) for SPPC.
So this will be more work...
maybe they are not reporting them at the same time, we will have to look into the code.
also my next step is to rewrite the note above to take into account your correction and label the pictures. thanks for pointing that out.
Pls let me comeback to more discussion of the mean sun and apparent sun. i have to digest what you are asking compared to how we use this concept in practical navigation today.
From: Starpath, Seattle, WA
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Paul
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posted July 05, 2007 08:49 AM
What I was incoherently trying to get at in the above is embodied on p. xxxii of the Nautical Almanac. If you want a correct value at your longitude for an astronomical event (sunrise, moonrise, etc.), you need to correct the tabulated value (Greenwich) for the event by doing a linear interpolation between longitude and today's time for the event and an adjacent day's time.
So in the olden days when they needed a highly accurate value for LAN (equation of time) at their location because they were doing a time sight to determine their longitude, shouldn't they have interpolated for longitude?
I see no indication in Sumner's book that they took such things into account.
Now there's a conundrum. You're trying to determine your longitude, and you need your longitude to determine it. Sounds like an iterative process is looming. But not really, since your DR longitude should be close enough to let you estimate the interpolated value of LAN to within a second or so. And of course the whole calculation is impacted by uncertainties in the value you used for latitude in your calculation.
Maybe the ones who made it to the end of the trip had the good fortune of having the chronometer, lattitude, and equation of time errors (which seem independent to me) tend to cancel.
From: Muncie
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