I am quite stupefied by this statement. NASA and other organisations most certainly uses Classical mechanics (whether in its Newtonian, Lagrangian, or Hamiltoni

I am quite stupefied by this statement. NASA and other organisations most certainly uses Classical mechanics (whether in its Newtonian, Lagrangian, or Hamiltonian formulations does not impinge upon the central issue) when simulating celestial motions and calculating trajectories. That there exists an acknowledged ”Three Body Problem” (i.e., that the trajectories followed by more than two bodies interacting gravitationally are in general not algebraic) matters not one iota for numerical simulations such as those performed by aforementioned organisations for aforementioned purposes. Some kind of relativistic correction might be made for motions that occur within the orbit of Mercury, but again, those are numerical in nature. And as far as I know there are no exact solutions known for general-relativistic interactions between two gravitational objects, placing it at an even greater ’disadvantage’ compared to the ’Newtonian’ mechanics you erroneously deplore.