This is an image a friend took of a Comet (C/2025 R3 PANSTARRS) that is visiting the night skies currently. It is a 30 second exposure and the Nikon camera had a bad internal clock so it was timestamped at an uncertain time. The exact spot was known. The challenge: can we reconstruct the same image , with the stars in the same place, identify the exact time it was taken and will everything match up? This sounds straight forward but when you consider the chain of maths and coordinate systems that has to work correctly, it still boggles my mind that it works. First, the camera location, from GPS, has to be correct. The GPS location is a lat long, and altitude. But not on a perfect sphere, it is on an oblate spheroid. It is no good putting the camera at 6371000 meters from earth center! Next, the satellites in the picture have been pinpointed at a random moment in time up to 24 hours before the picture was taken and during the intervening time they have orbited the earth dozens of times.…