Recent progress in analytical modeling of the relativistic effects in the lunar motion

Lunar motion serves for a number of important tests of the relativity theory. Although the final quantitative results come out from the direct numerical treatment of the lunar laser ranging data, the analytical solutions yield important keys for understanding sensitivity of the lunar motion on diverse effects. In the last few years, important relativistic phenomena, notably the equivalence principle violation and the preferred direction effects, have been reexamined using detailed Hill-Brown type theories. Surprising amplification of the former effect, indicated also from the numerical tests, has been explained by intricate coupling with the tidal deformation of the lunar orbit. Similar treatment proved that the lunar motion hides potentially a high-quality test of the preferred frame effects. In both cases, fundamental resonances of the problem cause singular amplification of the effects for particular lunar-like orbits.