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The possibility for Lorentz/CPT-breaking, which is motivated by unification theories, can be systematically tested within the standard-model extension framework. In the pure gravity sector, the mass dimension 5 operators produce new Lorentz and CPT-breaking terms in the 2-body equations of motion that depend on the relative velocity of the bodies. In this Letter, we report new constraints on 15 independent SME coefficients for Lorentz/CPT-violations with mass dimension 5 using lunar laser ranging. We perform a global analysis of lunar ranging data within the SME framework using more than 26,000 normal points between 1969 and 2018. We also perform a jackknife analysis in order to provide realistic estimates of the systematic uncertainties. No deviation from Lorentz/CPT symmetries is reported. In addition, when fitting simultaneously for the 15 canonical SME coefficients for Lorentz/CPT-violations, we improve up to three orders of magnitude previous post-fit constraints from radio pulsars., Comment: 8 pages, 1 figure

International audience; The standard-model extension (SME) is an effective field theory framework aiming at parametrizing any violation to the Lorentz symmetry (LS) in all sectors of physics. In this Letter, we report the first direct experimental measurement of SME coefficients performed simultaneously within two sectors of the SME framework using lunar laser ranging observations. We consider the pure gravitational sector and the classical point-mass limit in the matter sector of the minimal SME. We report no deviation from general relativity and put new realistic stringent constraints on LS violations improving up to 3 orders of magnitude previous estimations.

Lorentz symmetry violations can be parametrized by an effective field theory framework that contains both general relativity and the standard model of particle physics called the standard-model extension (SME). We present new constraints on pure gravity SME coefficients obtained by analyzing lunar laser ranging (LLR) observations. We use a new numerical lunar ephemeris computed in the SME framework and we perform a LLR data analysis using a set of 20 721 normal points covering the period of August, 1969 to December, 2013. We emphasize that linear combination of SME coefficients to which LLR data are sensitive and not the same as those fitted in previous postfit residuals analysis using LLR observations and based on theoretical grounds. We found no evidence for Lorentz violation at the level of 10^{-8} for s[over ¯]^{TX}, 10^{-12} for s[over ¯]^{XY} and s[over ¯]^{XZ}, 10^{-11} for s[over ¯]^{XX}-s[over ¯]^{YY} and s[over ¯]^{XX}+s[over ¯]^{YY}-2s[over ¯]^{ZZ}-4.5s[over ¯]^{YZ}, and 10^{-9} for s[over ¯]^{TY}+0.43s[over ¯]^{TZ}. We improve previous constraints on SME coefficient by a factor up to 5 and 800 compared to postfit residuals analysis of respectively binary pulsars and LLR observations.

Lorentz symmetry violations can be parametrized by an effective field theory framework that contains both General Relativity and the Standard Model of particle physics, called the Standard-Model Extension or SME. We consider in this work only the pure gravitational sector of the minimal SME. We present new constraints on the SME coefficients obtained from lunar laser ranging, very long baseline interferometry, and planetary motions., Comment: 4 pages, Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 2016

On the basis of the semi-analytical theory ELP, a new solution has been built that makes use of the planetary perturbations MPP01 constructed by P. Bidart. This new solution, called ELP/MPP02, is an analytical solution that contains all the perturbations to represent the lunar motion. The level of truncation for the series is the centimeter. This limit induces analytical developments of a reasonable dimension. ELP/MPP02 is compared to the JPL ephemerides DE405 and DE406. After fitting the constants and the reference frame to DE405, over a few centuries, numerical comparisons with DE405 show a significant improvement in precision, in particular for the radius vector. Over the long range of several millennia, comparisons with DE406 show an improvement in the long periodic perturbations due to planets. On the time interval of one century around J2000 we added to ELP/MPP02 numerical complements based on the differences with DE405 in such a way that ELP/MPP02+ has the precision of the numerical integration. Using this new ephemeris to analyse LLR data provided since 1970, we build the solution ELP/MPP02(LLR) fitted to LLR observations. Various approximations have been also tested on the residuals DE406 - ELP/MPP02. We first determined corrections to the secular variations of the mean longitude, longitudes of the node and perigee under a simple polynomial form; they reduce the differences between ELP/MPP02 and DE406 to less than 3 arcsec in longitude and latitude and 2 km in distance over the whole time interval of DE406 [ -3000; +3000] . Next, the differences themselves between the two solutions are approximated over 2 millennia with Poisson series in a pseudo analytical form similar to ELP/MPP02. We reduce the residuals to less than 0.03 arcsec in longitude and latitude and 30 m in distance.

An analysis of Lunar Laser Ranging (LLR) observations from January 1972 until April 2001 has been performed, and a new solution for the lunar orbital motion and librations has been constructed that has been named S2001. With respect to prior solutions, improvements in the statistical treatment of the data, new nutation and libration models and the addition of the positions of the observing stations to the list of fitted parameters have been introduced. Globally, for recent observations, our rms (root mean square error) is within 2 to 3 centimeters in the lunar distance. Special attention has been paid to the determination of the correction to the IAU76 luni-solar constant of precession, and the value of the secular acceleration of the Moon's longitude due to the tidal forces. The main results are: - correction to the constant of precession: Δp = -0.302 ′ 0.003"/cy, - tidal acceleration of the lunar longitude: Γ = -25.858 ′ 0.003"/cy 2 . The positions and velocities of the stations have also been determined. The results are consistent with the ITRF2000 determinations from SLR observations. The lunar theory ELP is referred to a dynamical system and introduces the inertial mean ecliptic of J2000.0. The positioning of the reference system of the theory with respect to ICRS is performed (and also with respect to some useful JPL numerical integrations). Finally the orientation of the celestial axes with respect to the ICRS reference system has been derived as well as the offsets of the Celestial Ephemeris Pole.

Analytical complements have been brought to Moons’ lunar libration theory concerning tidal effects, direct perturbations due to the Earth’s figure, and indirect non periodic perturbations. Comparisons to JPL numerical integrations DE245 and DE403 have been performed and the residuals treated by frequency analysis, allowing the determination of fitted free libration parameters and numerical complements.

An iterative method for the construction of planetary theories has been developed in order to determine the high order perturbations with respect to the masses. These perturbations are indeed needed to enlarge the validity span of analytical theories up to some million years. The application to the simplified Sun-Jupiter-Saturn problem gives a solution accurate over several ten million years. Throughout the study of the four outer planets we meet with convergence difficulties especially in the determination of fundamental frequencies. One of the results of this study is it shows evidence of long period terms with large amplitude in the mean longitudes: 12 000″ in Saturn longitude, 20 000″ in that of Uranus.

Analytical complements have been brought to Moons’ lunar libration theory concerning tidal effects, direct perturbations due to the Earth’s figure, and indirect non periodic perturbations. Comparisons to JPL numerical integrations DE245 and DE403 have been performed and the residuals treated by frequency analysis, allowing the determination of fitted free libration parameters and numerical complements.