  We revisit the old problem of the self-force on a particle moving in a
weak-field spacetime in the context of renewed interest in two-body
gravitational scattering. We analytically calculate the scalar,
electromagnetic, and gravitational self-force on a particle moving on a
straight-line trajectory at a large distance from a Newtonian star, and use
these results to find the associated correction to its motion. In the
gravitational case we must also include the matter-mediated force, which acts
at the same perturbative order as the gravitational self-force. We further
augment the gravitational results with geodesic calculations at second order in
the central body mass to determine the full, explicit solution to the two-body
gravitational scattering problem at second post-Minkowskian order (2PM). We
calculate the momentum transfer (which reproduces Westpfahl's old result), the
change in mechanical angular momentum (which matches the radiative flux
recently computed by Damour), and the change in mechanical mass moment (the
time-space components of the angular momentum tensor), which has not previously
appeared. Besides the new 2PM results of explicit trajectories and all
conserved quantities, this work clarifies the role of gravitational self-force
in PM scattering theory and provides a foundation for higher-order
calculations.
