NavList:

Dave Walden you wrote:  If at 1000UT on 15 May 2020, you observe the azimuth of Vega to be 36.009 and the azimuth of Peacock to be 144.941, where are you?

That sounds a great brain cranking exercise for the 'lock-down', which I'm sure is solvable with a PC.  In practise, how are you going to measure the azimuth of a star to 1/1000^th of a degree, especially from a moving platform? Just wondering! 
The nearest I ever got was 0.1° using a Vernier scale stuck against the heading datum of a Smiths periscopic sextant mount to air-swing the GM compass in a Dominie.  Even then, you needed a good imagination, and the result was probably of dubious value, because I don’t recall having a similar Vernier stuck against the azimuth datum on the sextant.  On top of that, we were heavily dependent upon the value of magnetic variation at the exact time and position of the swing supplied by the Admiralty Compass Observatory, because there is a diurnal swing as well as an annual drift in magnetic variation.

Using my very suspect 'back of a fag packet' maths, the I in 60 rule, and a complete disregard for statistics, if the altitudes were 45°, the sub-stellar points would be 2700nm away.  Measuring azimuth to one degree would put you in a box 90nmx90nm.  O.1° accuracy would put you in a box 9x9nm.  0.01° accuracy would place you in a box 0.9x0.9nm.  0.001° accuracy would place you in box 180x180m, which would be good, if only you could measure azimuth to that level of accuracy. DaveP