  We review the description of classical gravitational scatterings of two
compact objects by means of the eikonal framework. This encodes via scattering
amplitudes both the motion of the bodies and the gravitational-wave signals
that such systems produce. As an application, we combine the next-to-leading
post-Minkowskian (PM) waveform derived in the post-Newtonian (PN) limit with
the 4PM static loss due to the linear memory effect to reproduce known results
for the total angular mometum loss in the center-of-mass frame up to $\mathcal
O(G^4)$ and 2.5PN order. We also provide similar expressions for the change in
the system's mass dipole, discussing the subtleties related to its sensitivity
to the Coulombic components of the field and to the nonlinear memory effect.
