In massive gravity, galileon, and braneworld explanations of cosmic acceleration, force modifications are screened by nonlinear derivative self-interactions of the scalar field mediating that force. Interactions between the field of a central body (“A”) and an orbiting body (“B”) imply that body B does not move as a test body in the field of body A if the orbit is smaller than the Vainshtein radius of body B. We find through numerical solutions of the joint field at the position of B that the A-field Laplacian is nearly perfectly screened by the B self-field, whereas first derivative or net forces are reduced in a manner that scales with the mass ratio of the bodies as (M_B/M_A)^(3/5). The latter causes mass-dependent reductions in the universal perihelion precession rate due to the fifth force, with deviations for the Earth-Moon system at the ∼4% level. In spite of universal coupling, which preserves the microscopic equivalence principle, the motion of macroscopic screened bodies depends on their mass providing in principle a means for testing the Vainshtein mechanism.