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    Example sights very near the North Pole
    From: Frank Reed
    Date: 2017 Jun 1, 13:51 -0700

    Sights get weird when you get near the pole. Imagine going there today. The altitude of the Sun barely changes during the course of a few hours. But that doesn't matter in terms of the accuracy of a position fix. You take a sight at some known instant of UT, and the result is a line of position. And if the measured altitude has an uncertainty of, let's say, +/-1 minute of arc, then the line of position has an uncertainty of +/-1 nautical mile. This doesn't change. That's always true. It's not worse near the pole. The only problem near the pole is the coordinate singularity, and that can be dealt with in a number of ways (including "grid coordinates" [...]). There is no pole-specific problem of sight accuracy. 

    If you try to think about this in 19th-century terms, where a navigator needs to determine local time to compare against a chronometer, there is the illusion that accuracy fails near the pole since altitudes change very slowly (and thus a determination of local time becomes more difficult). But this is completely and exactly cancelled out by the convergence of longitude lines near the pole. It might seem troubling at 89 degrees latitude to have a longitude uncertainty of a whole degree... until you realize that this is only one nautical mile in the position. You can avoid all of this just confusion by sticking to the fundamental concept that one minute of arc in the altitude corresponds to one nautical mile in the location of the line of position on the ground... everywhere on the globe.

    Try an example. Go to a point within a few dozen miles of the north pole today, May 31, 2017. For example I measure the Sun's altitude at 15:00:00 UT and get 22°08' (that's Ho, after corrections). Then measure it again at 18:00:00 and get 22°09'. What is my position fix? What is the uncertainty of my fix, assuming +/-1' observational uncertainty?

    To find your fix from these observations, you have to deal with the coordinate singularity. One slick way to do this is to use the pole itself as the assumed position. If you attempt to plot intercepts, you'll realize that the Hc is always identical to the Dec (which is nice!), but the Zn is, of course, indeterminate at the coordinate singularity. The solution is simple: use GHA for plotting direction instead of Zn! You'll see. It works beautifully, and there is no problem with sight accuracy or careful timing --no more so than anywhere else on the globe. What do you get for a fix? What uncertainty does it have? It just works.

    Frank Reed
    PS: For anyone in the area, this weekend is Advanced Modern Celestial Navigation at Mystic Seaport, and this is one of the topics I'll be covering. Still plenty of time to sign up!

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