Testing for gravitationally preferred directions using the lunar orbit

TL;DR

This paper investigates the potential of lunar laser ranging to detect preferred directions in gravity, constraining parameters that indicate deviations from General Relativity, with a focus on the parameter alpha_1.

Contribution

It provides a detailed Hill-Brown analysis showing lunar laser ranging can constrain preferred-frame effects at the 10^{-4} level, extending previous work.

Findings

Lunar laser ranging can constrain alpha_1 at the 10^{-4} level.

Certain retrograde orbits are highly sensitive to fixed spatial directions.

No significant solar tide enhancement observed in lunar orbit.

Abstract

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.