NavList:

Gary you wrote - Dip from 40,000 feet is 3 04' so, in theory, it might be possible to measure a celestial altitude of three degrees below horizontal from a B-52 on its way to the Soviet Union. Of course, due to extinction, the only body that can be observed below horizontal is the sun. To support this

military mission, HO 249 shows computed altitudes as low as minus 8° 16' at lat 71°, dec 6 °contrary, LHA 98°! You'd have to be flying at 261,000 feet to measure an altitude that low, (bombing from the Space Shuttle?)

Such low values would be usable with the RAF Mk2T Periscopic Sextant.  T was for twilight facility.  This sextant incorporated a polarization analyser to assist in polar navigation.  The 2T used the fact that when the Sun is at low altitude or just below the horizon, sky light from the zenith is largely plane polarized.  You couldn’t get a celestial position line, but you could get a bearing.  It was claimed that under practical conditions azimuth bearings accurate to about 1.75° were possible when the Sun’s altitude was between 20° above and 6° below the horizon even when the Sun was obscured by cloud, provided there was a clear sky in the zenith region. I never used the 2T, but I’d rather like to have one.  I’m not sure if the analyser was inside the sextant or an add-on to the eyepiece.  Neither am I sure if the sextant could also be used normally.  The interesting thing is you didn’t set the sextant to the altitude of the Sun; you set it to about 70°. A facsimile of the AP for the RAF Mks 2, 2A, 2B, and 2T periscopic sextants is available from Paul Brewer on ebay for a few $s.  DaveP