A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2020 Jun 3, 14:17 -0700
Polaris is a unique case because it is near a "coordinate singularity". But is it an actual difference? A big difference? The longitude lines converge at the pole. So how much difference is there between SHA=328° and SHA=316° right near the celestial pole?
The polar distance of Polaris is about two-thirds of a degree right now. Draw it on the ground at the pole. Stop the rotation, and drop a couple of flares on the ice (if any), at two spots: one is 40 miles from the pole on longitude 10° (any arbitrary initial longitude) and the other is 40 miles from the pole at a longitude pf 22° (12° different, like the two SHA values). How far apart are those two points? It's not hard to work out. Those twelve degrees amount to one thirtieth of a complete circle around the pole. The complete circle would have a circumference of 2pi times the radius which is around 250 nautical miles, and a thirtieth of that amounts to about 8 miles on the ground, or on the chart. Equivalently, take the difference in longitude, 12°, and multiply by cos(lat), in this case that's cos(89.33°). The result is a distance in degrees. Multiply by 60 to get miles. The result is the same: about 8.
Though other stars on that chart may have shifted their positions by a similar order of magnitude in the years since the chart was drawn, it's not visible on the plot. Eight miles (minutes of arc) is below the resolution of the chart everywhere except near the poles.
How old is the chart? Your discovery is excellent evidence. The SHA of Polaris was near 328° in 1975. This does not, in fact, prove that it was drawn in 1975. It might have been drawn a decade earlier or a decade later using astronomical data for 1975, but I would suspect sometime in that window.
It makes no difference for a finder chart, of course.