Well, from what I've read, I think a good marine sextant is more accurate than you give it credit for. The pictures I've seen indicate they are calibrated to the tenth of an arc-minute, which is a tenth of a nautical mile on a great circle.
Having said that, I wasn't really thinking of taking a sextant on my next backpacking trip. But this forum isn't concerned solely with backpacking or getting lost in the woods, either - I'm also interested in surviving if I manage to get lost in bad weather in a light plane, for example. Not that I'd be likely to carry a sextant for that either <img src="/images/graemlins/wink.gif" alt="" />
The problem with traditional celestial navigation for most "survival" scenarios is that it requires several sets of printed documents (or a computer that will generate the equivalent information), none of which may be available.
Lofty Wiseman, in The SAS Survival Guide, gives a technique for finding True North using a vertical stick and the sun's shadow. I now realise that, basically, he's constructing a crude sextant and taking the Sun's Meridian Passage (I think). With a good wrist-watch and a measuring tape, and a knowledge of high-school geometry (one of the few subjects I ever scored a 100% in :nerd: ) and trigonometry, I think you should (theoretically) be able to measure your latitude and longitude. (If you can measure the tip of the sun's shadow at noon to within 1 cm - about the width of my index finger - using a yardstick 1 m high, that should give a True Altitude accurate to within +/- 5 arc-minutes - approximately.)
Does knowing your position within a radius of 5 nm help? It would probably depend on the circumstances. It might help you pinpoint your position on a map, for example (if you were hopelessly lost), or determine which side of a particular river you're on. If you were in dire circumstances (plane crash, search called off, and the only map available is a 1:500,000 VFR Sectional/VNC - or worse, a 1:1,000,000 WAC) I might well try to figure out my lat/long using any available technique - just for something to do, if nothing else.
But mostly, it's just something I would like to know how to do.
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"The mind is not a vessel to be filled but a fire to be kindled."
-Plutarch