  We compute classical gravitational observables for the scattering of two
spinless black holes in general relativity and $\mathcal N {=} 8$ supergravity
in the formalism of Kosower, Maybee, and O'Connell (KMOC). We focus on the
gravitational impulse with radiation reaction and the radiated momentum in
black hole scattering at $\mathcal O(G^3)$ to all orders in the velocity. These
classical observables require the construction and evaluation of certain
loop-level quantities which are greatly simplified by harnessing recent
advances from scattering amplitudes and collider physics. In particular, we
make use of generalized unitarity to construct the relevant loop integrands,
employ reverse unitarity, the method of regions, integration-by-parts (IBP),
and (canonical) differential equations to simplify and evaluate all loop and
phase-space integrals to obtain the classical gravitational observables of
interest to two-loop order. The KMOC formalism naturally incorporates radiation
effects which enables us to explore these classical quantities beyond the
conservative two-body dynamics. From the impulse and the radiated momentum, we
extract the scattering angle and the radiated energy. Finally, we discuss
universality of the impulse in the high-energy limit and the relation to the
eikonal phase.
