We construct a set of reference frames for description of the orbital and rotational motion of the Moon. We use a scalar-tensor theory of gravity depending on two parameters of the parametrized post-Newtonian (PPN) formalism and utilize the concepts of the relativistic resolutions on reference frames adopted by the International Astronomical Union in 2000. We assume that the solar system is isolated and space-time is asymptotically flat. The primary reference frame has the origin at the solar-system barycenter (SSB) and spatial axes are going to infinity. The SSB frame is not rotating with respect to distant quasars. The secondary reference frame has the origin at the Earth-Moon barycenter (EMB). The EMB frame is local with its spatial axes spreading out to the orbits of Venus and Mars and not rotating dynamically in the sense that both the Coriolis and centripetal forces acting on a free-falling test particle, moving with respect to the EMB frame, are excluded. Two other local frames, the geocentric (GRF) and the selenocentric (SRF) frames, have the origin at the center of mass of the Earth and Moon respectively. They are both introduced in order to connect the coordinate description of the lunar motion, observer on the Earth, and a retro-reflector on the Moon to the observable quantities which are the proper time and the laser-ranging distance. We solve the gravity field equations and find the metric tensor and the scalar field in all frames. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom of the solutions of the field equations. We discuss the gravitomagnetic effects in the barycentric equations of the motion of the Moon and argue that they are beyond the current accuracy of lunar laser ranging (LLR) observations.
Testing for gravitationally preferred directions using the lunar orbit
由于引力是一种长程力，{ \it a priori}可以想象，宇宙的全球物质分布为局部引力物理学选择了一个优选的静止坐标系。在后牛顿近似下，偏好框架效应的现象学由两个参数描述，$α_1$和$α_2$，其中第二个参数已经受到非常严格的约束。重申以前的建议，我们通过一个详细的Hill-Brown型计算的扰动月球轨道，月球激光测距数据有可能约束$α_1$在$10^{-4}$水平。据发现，某些逆行平面轨道表现出共振敏感性的外部扰动链接到一个固定的方向在空间中。月球轨道离这样的共振很远，由于太阳潮汐，月球轨道没有明显的增强。我们的希尔-布朗分析扩展到与可能的差分加速度向银河系中心的扰动。然而，有人认为，有很强的{ \it先验}的理论约束，这种效果的可想象的大小。
