  We provide universal expressions for the classical piece of the amplitude
given by the graviton/photon exchange between massive particles of arbitrary
spin, at both tree and one loop level. In the gravitational case this leads to
higher order terms in the post-Newtonian expansion, which have been previously
used in the binary inspiral problem. The expressions are obtained in terms of a
contour integral that computes the Leading Singularity, which was recently
shown to encode the relevant information up to one loop. The classical limit is
performed along a holomorphic trajectory in the space of kinematics, such that
the leading order is enough to extract arbitrarily high multipole corrections.
These multipole interactions are given in terms of a recently proposed
representation for massive particles of any spin by Arkani-Hamed et al. This
explicitly shows universality of the multipole interactions in the effective
potential with respect to the spin of the scattered particles. We perform the
explicit match to standard EFT operators for $S=\frac{1}{2}$ and $S=1$. As a
natural byproduct we obtain the classical pieces up to one loop for the bending
of light.
