NavList:

Shoot a bright star for longitude. Then Polaris for latitude. Get a fix --fast. Note that this scenario is partially set up as a practice problem for some of the navigators in my Advanced Celestial Navigation workshop, but I encourage any and all of you to give it a try. Brute-force or clever methods, variations welcome... where are you?

The scenario:
I'm approaching Bermuda from the northwest. It's June 25, 2023 (local date). I have a nice new Astra IIIB sextant with a 7x scope (*). I shoot Venus in early twilight. Height of eye is 25 feet. Sextant index correction is -1'. My estimated position a few minutes before taking sights is 35.00° N, 67.15° W. I'm sailing on course 150°T at 6 knots.

At 00:24:55 UT (so the Greenwich date has rolled over to June 26), I shoot Venus, nearly due West. I get Hs 23°28.5'.
Can't see Polaris quite yet in my sextant, though it's visible naked-eye...

Darker and darker...
At 00:35:00 UT I shoot Polaris. The raw sextant altitude, Hs, is 34°28'.

At 00:45:08 UT I decide to shoot Venus again. I get Hs 19°18'.

So what is my 0035 fix? What approaches can you take to working this puzzle? Do you need to do a running fix? Is there any way to avoid it (yes **)? Can you do it by the intercept method with plotting? What sight reduction method would be efficient? Can you do it without plotting? Can you do it without using the intercept method? Assuming the sights are accurate to the nearest minute of arc, can we trust the result to a similar level? Consider two levels of accuracy for doing the work: what's a solution at +/-0.5' accuracy in the altitude corrections and clearing math? and what's a solution at +/-0.1' in the work? Any and all variations welcome!

Frank Reed

*  7x scope? Why relevant? It's a detail to consider for fans of small corrections. What can you see? What would you shoot? :)
** Yes. Avoid a running fix by averaging the times and altitudes of the two Venus sights. How valid is this procedure? What would reduce its accuracy and by how much?