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The Newtonian regime of a recent nonlocal extension of general relativity (GR) is investigated. Nonlocality is introduced via a scalar "constitutive" kernel in a special case of the translational gauge theory of gravitation, namely, the teleparallel equivalent of GR. In this theory, the nonlocal aspect of gravity simulates dark matter. A nonlocal and nonlinear generalization of Poisson's equation of Newtonian gravitation is presented. The implications of nonlocality for the gravitational physics in the solar system are briefly studied.

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Based upon a simple cosmological model with no expansion, we find that the rotational terms appearing in the Gödel universe are too small to explain the Pioneer anomaly. Following a brief summary of the anomaly, cosmological effects on the dynamics of local systems are addressedincluding a derivation of the equations of motion for an accelerated Pioneer-type observer in a rotating universe. The rotation or vorticity present in such a cosmological model is then subjected to astrophysical limits set by observations of the cosmic microwave background radiation. Although it contributes, universal rotation is not the cause of the Pioneer effect. In view of the related fly-by anomalies, frame-dragging is also discussed. The virial theorem is used to demonstrate the nonconservation of energy during transfers from bound to hyperbolic trajectories.

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