NavList:

I got intrigued by this and I wondered how unlucky you can get. I wrote a small script calculating what's the largest circle that does not contain any navigation star. The idea is that you're unlucky when the centre of that circle is at your zenith.

It was a fun exercise in spherical trigonometry and I also included a magnitude threshold to see how the answer changes by light pollution and similar circumstances. (On the other hand, if you're affected by light pollution, you're probably not lost at sea.)

In any case, this plot shows that the radius of the unlucky circle goes from 30° (no magnitude threshold) to about 120° at magnitude threshold of 0, and it also gives the three border stars between which the empty circle lies.

With magnitude threshold below -0.04, only Canopus and Sirius are visible (36.2° apart), and thus the largest empty circle has radius 161.9°. Below -0.72, the radius is 180°, as there's at most one navigation star visible. My program does not deal with these cases so they are not plotted.

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