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We introduce five post-Newtonian tracking formulae that would allow increasing the accuracy of the shooting systems on board autonomous LEO laser trackers. These formulae should be used when the current formulae cannot provide instants close enough to the optimal instants at which the trackers could safely shoot down unwished LEO middle-distant targets. In fact, they allow the trackers to produce not only the safest shooting actions, but also the most efficient ablations that might make the targets fall into the atmosphere for them to burn. The fact of the matter is in the falsifiability procedure introduced below, which allows to simulate sequences of unharming shooting actions with very narrow laser beams leading to identify the optimal pointing directions to previously selected debris objects whose size and composition are representative of these targets.
earth post-newtonian framework; middle size leo debris objects; space-based pointing and shooting laser systems; very narrow laser beams