Testing for gravitationally preferred directions using the lunar orbit

As gravity is a long-range force, it is a priori conceivable that the Universe’s global matter distribution selects a preferred rest frame for local gravitational physics. At the post-Newtonian approximation, the phenomenology of preferred-frame effects is described by two parameters ${\mathrm{\alpha }}_1$ and ${\mathrm{\alpha }}_2$, 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 ${\mathrm{\alpha }}_1$ at the ${10}^{\mathrm{-}4}$ 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 a priori theoretical constraints on the conceivable magnitude of such an effect. © 1996 The American Physical Society.