  Making use of the recently-derived, all-spin, opposite-helicity Compton
amplitude, we calculate the classical gravitational scattering amplitude for
one spinning and one spinless object at $\mathcal{O}(G^{2})$ and all orders in
spin. By construction, this amplitude exhibits the spin structure that has been
conjectured to describe Kerr black holes. This spin structure alone is not
enough to fix all deformations of the Compton amplitude by contact terms, but
when combined with considerations of the ultrarelativistic limit we can
uniquely assign values to the parameters remaining in the even-in-spin sector.
Once these parameters are determined, much of the spin dependence of the
amplitude resums into hypergeometric functions. Finally, we derive the eikonal
phase for aligned-spin scattering.
