Classical observables from the exponential representation of the gravitational S-matrix

A bstract By combining the KMOC-formalism with exponential representation of scattering matrix we show that two-body angle is given by corresponding element representation. This holds to all orders in Post-Minkowskian expansion gravity when restricted conservative sector. Once gravitational radiation taken into account new terms correcting this relationship appear starting at fourth order. systematic momentum kick provided any order, thus illustrating iterative structure partly recycles from lower expansion. We provide explicit results for computation first complete calculation order based on amplitudes.