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We describe a general framework for analyzing orbits of systems containingcompact objects (neutron stars or black holes) in a class of Lagrangian-basedalternative theories of gravity that also admit a global preferred referenceframe. The framework is based on a modified Einstein-Infeld-Hoffmann (EIH)formalism developed by Eardley and by Will, generalized to include thepossibility of Lorentz-violating, preferred-frame effects. It uses apost-Newtonian $N$-body Lagrangian with arbitrary parameters that depend on thetheory of gravity and on "sensitivities" that encode the effects of the bodies'internal structure on their motion. We determine the modified EIH parametersfor the Einstein-{\AE}ther and Khronometric vector-tensor theories of gravity.We find the effects of motion relative to a preferred universal frame on theorbital parameters of binary systems containing neutron stars, such as a classof ultra-circular pulsar-white dwarf binaries, the amplitudes of the effectsdepend upon "strong-field" preferred-frame parameters $\hat{\,\,\alpha}_1$ and${\hat{\,\,\alpha}}_2$, which we relate to the fundamental modified EIHparameters. We also determine the amplitude of the "Nordtvedt effect" in atriple system containing the pulsar J0337+1715 in terms of the modified EIHparameters.

Testing general relativity with compact-body orbits: A modified Einstein-Infeld-Hoffmann framework