  We compute the total radiated momentum carried by gravitational waves during
the scattering of two spinless black holes at the lowest order in Newton's
constant, $\mathcal O(G^3)$, and all orders in velocity. By analytic
continuation into the bound state regime, we obtain the ${\cal O}(G^3)$ energy
loss in elliptic orbits. This provides an essential step towards the complete
understanding of the third-post-Minkowskian binary dynamics. We employ the
formalism of Kosower, Maybee, and O'Connell (KMOC) which relates classical
observables to quantum scattering amplitudes and derive the relevant integrands
using generalized unitarity. The subsequent phase-space integrations are
performed via the reverse unitarity method familiar from collider physics,
using differential equations to obtain the exact velocity dependence from
near-static boundary conditions.
