I hope this article is not a copy of something written by a naval officer, but as it seem to be, by a guy who knows nothing about celestial navigation. If the US Navy is the first in the world to give up on celestial navigation then sigh, sigh and sigh, not that I am surprised at all.
But first of all a sextant is totally worthless without the exact time, (as mentioned), the original first problem in fact. But lets assume there is somebody with a not hacked iphone or something. Then you need the nautical almanac and why not a dead wood one if you feel the computer is hacked. A very nice book and very useful for people with insomnia who have given up on counting sheep, reading it makes wonders. Some of you will also know how that book relates to "computing" history.
Next you won't get a position at all, what you get is a line, much like what you get from GPS with only one satellite, just ask Fry, or perhaps not.
Apart from the sun and stars there are also planets and the moon.
And it's even possible to do without a sextant just by timing objects when they hit the horizon (hard to get anything very exact that way though).
However, what annoys me are "and a serious amount of math work to get your position" and "by a computer, which is a blessing for anyone who's ever had to do the work by hand".
That is complete rubbish, it takes less than a minute, paper and pencil, with mathematics kids learn when 6 to 7 years old (like + and - ). Oh dear.
Coat without the sextant I gave away.