NavList:

A few minutes ago, I wrote:
"Unlike the tangent function, which diverges at the pole, the sine, of course tops out at a value of unity. So the error in east/west position, dx here, is only 3.8 nautical miles for high latitudes. "

Here's another way to think about this. Stan noted that the difference between culmination and meridian passage is about half an hour at 89.5° latitude. Half an hour sounds like a big error in longitude. Every hour error in estimating the local time yields an error of 15° in the longitude. But up there so close to the pole, the circle of latitude we're talking about is quite small. Its radius is 30 nautical miles. That gives a circumference of 188 nautical miles. If I incorrectly estimate the time by half an hour, that's one part in 48. And 188 divided by 48 is only 3.9 nautical miles. If I drive around that circle of latitude at 89° 30', for every nautical mile that I travel, my longitude changes by about two degrees.

Frank Reed