  We obtain a conservative Hamiltonian describing the interactions of two
charged bodies in Yang-Mills through $\mathcal{O}(\alpha^2)$ and to all orders
in velocity. Our calculation extends a recently-introduced framework based on
scattering amplitudes and effective field theory (EFT) to consider
color-charged objects. These results are checked against the direct integration
of the observables in the Kosower-Maybee-O'Connell (KMOC) formalism. At the
order we consider we find that the linear and color impulses in a scattering
event can be concisely described in terms of the eikonal phase, thus extending
the domain of applicability of a formula originally proposed in the context of
spinning particles.
