Re: the discussion of shooting the Sun vs Polaris to determine latitude
How will you know when it is local noon? Actually that is pretty easy to figure out but are we sure anyone on the plane can figure it out?
What is the Sun’s declination that day or are we assuming this happens on the equinox?
When fighting the Persians at Thermopylae
IT doesn’t have to be anyone, just someone. In a plane of 300 people, I would guess a fair few know how to figure this out.
Still doesn’t answer the declination problem.
If cell phones are taken, do we have access to a calculator with trig functions?
Look I know I’m not an English teacher, but I’m pretty sure in that context “anyone” means at least one and so is synonomous with “someone”.
That’s because the sun is easier to work with. Because its during the day when you are doing stuff. But you know what DAY it is AND have an astronomical almanac.
If you don’t have both of those (or a good memory) the sun isn’t that helpful in determining latitude. And its certainly less useful than using the north or south celestial pole to determine latitude with a minimal amount of information.
The reason modernish navigation uses the sun is because WHEN you have that almanac AND you know what time it is at a given reference point on earth that allows you to determine your longitude as well. But you can use the moon or stars for that instead of the sun also.
Sorry, then I misunderstood. Yes, I think it could be virtually guaranteed that there is at least one passenger on an average flight of 300 people who could grok out how to find local noon (and north or south in the process.)
Don’t need it if you are willing to accept that you will only get as much accuracy as your ability to eyeball an angle with whatever aids you can dream up. Any guide with a bunch of angles depicted on it, such as a map compass rose or somebody happening to have a simple protractor would help immensely. Without any such thing, you can construct angles of 60, 45 and 30 from right triangles with integer ratios for two of the legs. More, I suppose, if you remember a few more trig results that come out rational. You still have to eyeball a right angle, or find something with a square corner on it, which probably wouldn’t be too dificult. Comparing even that to your observed angle would help, particularly in temperate zones, where your angle is between 45 and 60 or 45 and 30 - you only wind up eyeballing where your angle falls in a 15 degree slice. If you can get down to 3 degree accuracy, you are within a tiny bit over 200 miles for a latitude reading.
We have had a similar thread about this topic a few years back.
Latitude (north south) is easy to determine if you know a bit about astronomy. Some careful eyeballing of the north or south celestial pole and you are good to go.
Longitude (east west) is the problem. Now if you know your latitude AND you REALLY know your flora/fauna/georgraphy, you can use your latitude, envision where that latitude circle on earth intersects various geographic points on earth and combine those two bits of information to figure out your longitude. But IMO that is A LOT of knowledge to have and I suspect some reference material would be required for all practical purposes.
The other way to find your longitude is to know what time it is at a specific spot on earth (typically Universal Time, which the local time in Greenich, England - longitidue 0 degrees).
You need to figure out that time to within about half an hour to get to within 500 miles longitude.
If they let you keep your watch, you are pretty much there already.
But, that seems a bit of cheat.
During the last thread, here is the solution I came up with. You need a variable star. It turns out there are a handful that are bright enough, with periods fast enough, that figuring out what time it is to within half an hour is doable. Not easy, but doable.
You would have to have a handful of star positions and brightneses memorized. And a bit of training observing variables by eyeball. And remember a few key numbers. And be able to be a bit of basic very low level algebra.
Back then at least IIRC I convinced myself I could do it. And I suspect somewhere between 1 in 10 and 1 in 100 folks could be prepped to be able to do the same depending on their natural inclinations, how much training time one allows, and how likely you want them to be able to succeed.
True, many places have at least somewhat distinctive signage that can help. If you encounter road signs that look (shape, color, layout) mostly like typical US road signs but are in Spanish, it is likely that you are in Puerto Rico.
If you see a road sign with anything marked in “miles”, you can limit that down to only a few countries.
If you see bilingual English/French road signs, Canada is a pretty good bet. If a large percentage of the signs are bilingual, you are more likely to be in a practically bilingual area (e.g. Ottawa metro area, Maritime provinces) than you are to be in BC.
That’s at the equator. Away from the equator, knowing GMT at local noon will do even better. A better way to put it is that time within half an hour equals 7.5 degrees of longitude (longitude lines converge away from the equator - latitude lines are equidistant, one nautical mile per minute of latitude). And if they left you an accurate watch, you should be able to do better than half an hour.
But, yeah, the OP’s rules preclude you having a watch.
If you have any avid birders on the plane, you can probably narrow it down to continent and very likely much closer than that. Most birders would be most familiar with their local critters, but would have at least some familiarity with exotics.
Me too, although my drug of choice is mapcrunch.
I’m pretty good at gauging from flora, fauna, geography too.
Danish road signs have red text. Latvian has lots of umlauts.
Maybe you’re thinking of something like Estonian or Hungarian? Latvian doesn’t have any umlauts. That said, it does have a distinctive cedilla under the letters g, k, l, and n, (well, over the “g” in the lowercase form) so any of those would point strongly, if not exclusively, to Latvian.
Well, if you have road signs to work with, I suspect that it makes the job easier than for the scenario the OP had in mind.
I’m reminded of a list of tips I saw somewhere for what to do if you’re lost in an urban area. For instance, if you go downhill, you’ll probably get to a body of water. Um, sure. But if you’re in a freaking urban area, there are probably easier ways to find your way around.
You’re right, I was thinking Estonian 
Let me throw in a few “Professor from Gilligan’s Island”-class methods for approximating the time (and therefore longitude).
- Sunspots. Suppose the Professor was up-to-date on the latest sunspot activity upon arrival and memorized the current data. (And assuming there’s a decent sunspot cycle going on.)
One can observe sunspots without significant equipment. E.g., a pinhole projector or even on a modestly overcast day.
By noting the motion of a major sunspot and comparing it with your memory of it’s expecting appearance, without a telescope and other gear you can get the time down to … maybe a couple days. (Drat the slow rotation of the Sun.)
Okay, okay. Forget that.
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The ISS. It orbits in a fixed plane. It is easily seen. It isn’t likely to be mistaken for another satellite. With a single, good observation, knowledge of the orbit, the date, and some Math, you could figure out the time pretty well I think.
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Occultation of stars by the Moon. You merely have to have an eidetic memory and previously looked over a suitable table. Easy, peasy.
I just tried that game. It could be addictive. I did pretty well, mostly going by signs and road markings, plus vegetation.
Except that, if they happen at all, they’ll happen at different times at different locations on the Earth’s surface. It could still in principle be done, but it’d require a heck of a lot of rather hairy math in addition to the tables.
Are/were we on a treadmill?
If so, the shape of the power plug might be of help.