Seeing the Sun rising in the “wrong” place is not exclusive to Concorde, as is shown by compressor stall’s nice picture. I enjoyed it a number of times way back when flying from Europe to Alaska. You can also see it on some other routes in a subsonic aircraft, provided you fly at high enough latitude.
With the good old B707, we used to take off around 10 am and, in February or November sunset occurred behind us as we passed in the area of Jan Mayen Island. Since we arrived at ANC a little before noon, local time, there was a sunrise to the south sometime later over the Beaufort Sea.
We were INS equipped already but still had the HO-249 tables and the periscopic sextant on board. We could use them to check the grid heading of the excellent “Polar Path” gyroscopic compass should our INS system become unreliable.
Not necessary for navigation but more as a challenging diversion, we used to predict sunset and sunrise times by drawing what we called “the absolute trajectory of the airplane” on the polar stereographic chart. The trick was first to draw a line representing separation between day and night at a time when the position was known. The tables gave the GHA and declination of the Sun and the necessary corrections. The line was a quasi-straight line on this type of projection. Then, you had to rotate counterclockwise each downstream waypoint around the North Pole by an angle depending on the time difference between its ETO and the time over the starting waypoint using a rate of 15 deg per hour. Joining these new points gave a nice curve, the “absolute trajectory”, and its intersections with the day/night separation line corresponded to sunset and sunrise.
DJ.