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After posting my answer to the cave puzzle, I realised that I hadn’t allowed for dip and refraction.  I amended he spreadsheet accordingly, and it took me 6nm further towards the cave, but I was still a long way from it.

Having put the spreadsheet together, I thought I ought to try it locally with some reliable altitudes.  I planned to use Vega-Alpheratz-Vega, the Astrovan being on the west side of my house.  However, by 20.00 there was so much haze, light pollution, and Moon glow to the SW that Alpheratz kept disappearing, so with some reluctance, I observed the Moon instead.  To my surprise, the technique placed me at 53degrees 11minutes N only 0.8nm north of my actual position.  Having always considered the Moon my ‘bete noir’, I think I ought to use it more often.

I encountered two problems.  Firstly, unlike the stars, the moon is constantly moving.  All I could do was take the Moon’s declination from the Air Almanac and calculate an instantaneous SHA by subtracting GHA Aries from GHA Moon and adding 360.  This required accurate Greenwich time, so it rather defeated the object of the exercise.

The spreadsheet also showed the undesirability of using the cosine rule to solve a side, side, side spherical triangle, because above 54N the spreadsheet crashed.  Somehow the formula was managing to come up with cosA values greater than unity.  Fortunately I was at 53.10N.

My resolutions for 2018 are, try this again with two stars, learn how to plot graphs in Excel, and re-familiarise myself with the half angle formula. DaveP