As gravity is a long-range force, it is {\it a priori} conceivable
that the Universe's global matter distribution select a preferred rest
frame for local gravitational physics. At the post-Newtonian
approximation, the phenomenology of preferred-frame effects is
described by two parameters, $\alpha_1$ and $\alpha_2$, the second of
which is already very tightly constrained. Confirming previous
suggestions, we show through a detailed Hill-Brown type calculation
of a perturbed lunar orbit that lunar laser ranging data have the
potential of constraining $\alpha_1$ at the $10^{-4}$ level. It is
found that certain retrograde planar orbits exhibit a resonant
sensitivity to external perturbations linked to a fixed direction in
space. The lunar orbit being quite far from such a resonance
exhibits no significant enhancement due to solar tides. Our Hill-Brown
analysis is extended to the perturbation linked to a possible
differential acceleration toward the galactic center. It is, however,
argued that there are strong {\it a priori} theoretical constraints
on the conceivable magnitude of such an effect.
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