  In this work we propose to use leading singularities to obtain the classical
pieces of amplitudes of two massive particles whose only interaction is
gravitational. Leading singularities are generalizations of unitarity cuts. At
one-loop we find that leading singularities obtained by multiple
discontinuities in the t-channel contain all the classical information. As the
main example, we show how to obtain a compact formula for the fully
relativistic classical one-loop contribution to the scattering of two particles
with different masses. The non-relativistic limit of the leading singularity
agrees with known results in the post-Newtonian expansion. We also compute a
variety of higher loop leading singularities including some all-loop families
and study some of their properties.
