  We employ scattering amplitudes in curved space to model the dynamics of a
light probe particle with mass $m$ orbiting in the background spacetime induced
by a heavy gravitational source with mass $M$. Observables are organized as an
expansion in $m/M$ to all orders in $G$ -- the gravitational self-force
expansion. An essential component of our analysis is the backreaction of the
heavy source which we capture by including the associated light degrees of
freedom. As illustration we consider a Schwarzschild background and verify
geodesic motion as well as the first-order self-force correction to two-body
scattering through ${\cal O}(G^3)$. Amplitudes in curved space offer several
advantages, and further developments along these lines may advance the
computation of gravitational-wave signals for extreme-mass-ratio inspirals.
