Celestial reference frames and the gauge freedom in the post-Newtonian mechanics of the Earth-Moon system
We introduce the Jacobi coordinates adopted to the advanced theoretical analysis of the relativistic Celestial Mechanics of the Earth-Moon system. Theoretical derivation utilizes the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. The resolutions assume that the Solar System is isolated and space-time is asymptotically flat at infinity and the primary reference frame covers the entire space-time, has its origin at the Solar System barycenter (SSB) with spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are assumed to be at rest on the sky forming the International Celestial Reference Frame (ICRF). The second reference frame has its origin at the Earth-Moon barycenter (EMB). The EMB frame is locally inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames—geocentric and selenocentric—have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description of the metric tensor and relative equations of motion of the Moon with respect to Earth. Each local frame can be converted to kinematically non-rotating one after alignment with the axes of ICRF by applying the matrix of the relativistic precession as recommended by the IAU resolutions. The set of one global and three local frames is introduced in order to decouple physical effects of gravity from the gauge-dependent effects in the equations of relative motion of the Moon with respect to Earth.