Reference frames, gauge transformations and gravitomagnetism in the postNewtonian theory of the lunar motion
Abstract
We construct a set of reference frames for description of the orbital and rotational motion of the Moon. We use a scalartensor theory of gravity depending on two parameters of the parametrized postNewtonian (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 spacetime is asymptotically flat. The primary reference frame has the origin at the solarsystem 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 EarthMoon 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 freefalling 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 retroreflector on the Moon to the observable quantities which are the proper time and the laserranging distance. We solve the gravity field equations and find the metric tensor and the scalar field in all frames. We also derive the postNewtonian 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.
 Publication:

Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis
 Pub Date:
 January 2010
 DOI:
 10.1017/S1743921309990123
 Bibcode:
 2010IAUS..261...40X
 Keywords:

 gravitation;
 relativity;
 astrometry;
 reference systems