  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.
