We construct a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of the Moon and Earth by means of lunar laser ranging (LLR) with the precision of one millimeter. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom, which is used for removing spurious post-Newtonian effects from the equations of motion of the solar system bodies.
We present new constraints on Lorentz symmetry (LS) violations with lunar laser ranging (LLR). Those constraints are derived in the standard-model extension (SME) framework aiming at parameterizing any LS deviations in all sectors of physics. We restrict ourself to two sectors namely the pure gravitational sector of the minimal SME and the gravity-matter coupling. We describe the adopted method and compare our results to previous analysis based on theoretical grounds. This work constitutes the first direct experimental determination of the SME coefficients using LLR measurements.
Lunar Laser Ranging Science: Gravitational Physics and Lunar Interior and Geodesy
激光脉冲发射在月球上的后向反射器提供了非常精确的范围。分析产生关于地球、月球和轨道的信息。高度精确的后向反射器位置的不确定性小于一米。月球上的潮汐表现出强烈的耗散，一个月的Q=33 \pm 4，对周期的依赖性很弱。月球的自转取决于其内部的性质;流体核心的半径约为月球半径的20%。相对论重力测试验证了\pm 1.4 x 10^{-13}的等效原理，限制了与爱因斯坦广义相对论的偏差，并表明引力常量$\dot{G}/G$没有速率，不确定度为9 x 10^{-13} 1/年。
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 …
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 26,00…
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 20721 normal points covering the period of August, 1969 to December, 2013. We emphasize that linear combination of SME coefficients to which LLR dat…
The Earth-Moon-Sun system has traditionally provided the best laboratory for testing the strong equivalence principle. For a decade, the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has been producing the world's best lunar laser ranging data. At present, a single observing session of about an hour yields a distance measurement with uncertainty of about 2~mm, an order of magnitude advance over the best pre-APOLLO lunar laser ranging data. However, these superb data have not yet yielded scientific results commensurate with their accuracy, number, and temporal distribution. Th…
We derive approximate analytical solutions to the environment-dependent dilaton field theory equations in the presence of a one or two mirror system or a sphere. The one-dimensional equations of motion are integrated for each system. The solutions obtained herein can be applied to \textit{q}BOUNCE experiments, neutron interferometry and for the calculation of the dilaton field induced "Casimir force" in the \textsc{Cannex} experiment as well as for Lunar Laser Ranging. They are typical of the Damour-Polyakov screening mechanism whereby deviations from General Relativity are suppressed by a van…
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.
We study the impact of the limit on $|\dot{G}|/G$ from Lunar Laser Ranging on "nonlocal gravity", i.e. on models of the quantum effective action of gravity that include nonlocal terms relevant in the infrared, such as the "RR" and "RT" models proposed by our group, and the Deser-Woodard (DW) model. We elaborate on the analysis of Barreira et al. [1] and we confirm their findings that (under plausible assumptions such as the absence of strong backreaction from non-linear structures), the RR model is ruled out. We also show that the mechanism of "perfect screening for free" suggested for the DW …
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。
The Lunar Laser Ranging (LLR) experiment has accumulated 50 years of range data of improving accuracy from ground stations to the laser retroreflector arrays (LRAs) on the lunar surface. The upcoming decade offers several opportunities to break new ground in data precision through the deployment of the next generation of single corner-cube lunar retroreflectors and active laser transponders. This is likely to expand the LLR station network. Lunar dynamical models and analysis tools have the potential to improve and fully exploit the long temporal baseline and precision allowed by millimetric L…
Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model
Istituto per le Applicazioni del Calcolo, CNR（意大利国家研究委员会计算应用研究所）；INFN - Laboratori Nazionali di Frascati (LNF)（意大利国家核物理研究所弗拉斯卡蒂国家实验室）；Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto（波尔图大学理学院物理与天文系）；Centro de Física das Universidades do Minho e do Porto（米尼奥大学和波尔图大学物理中心）；Universitá di Camerino（卡梅里诺大学）；Al-Farabi Kazakh National University（阿里-法拉比哈萨克国立大学）；ICRANet（国际相对论天体物理中心网络）
The validity of General Relativity, after 100 years, is supported by solid experimental evidence. However, there is a lot of interest in pushing the limits of precision by other experiments. Here we focus our attention on the equivalence principle, in particular the strong form. The results of ground experiments and lunar laser ranging have provided the best upper limit on the Nordtvedt parameter η that models deviations from the strong equivalence principle. Its uncertainty is currently σ[η] =4.4 $\times$ $10^{-4}$. In the first part of this paper we will describe the experiment, to measure η…
The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) began millimeter-precision ranging to the Moon in 2006. Until now, a comprehensive validation of APOLLO system range accuracy has not been possible because of centimeter-scale deficiencies in computational models of the Earth-Moon range, and because APOLLO lacked an internal timing calibration system. Here, we report on the development of a system that enables in-situ calibration of the timing response of the APOLLO apparatus, simultaneous with lunar range measurements. The system was installed in August 2016. Preliminary resu…
Lunar laser ranging (LLR) to the Apollo retro-reflectors, which features the most long-lasting experiment in testing General Relativity theories, has remained operational over the past four decades. To date, with significant improvement of ground observatory conditions, the bottleneck of LLR accuracy lies in the retro-reflectors. A new generation of large aperture retro-reflectors with intended dihedral angle offsets have been suggested and implemented based on NASA's recent lunar projects to reduce its ranging uncertainty to be less than 1.0 mm. The technique relies on the retro-reflector's a…
In dark energy models where a scalar field $ϕ$ is coupled to the Ricci scalar $R$ of the form $e^{-2Q (ϕ-ϕ_0)/M_{\rm pl}}R$, where $Q$ is a coupling constant, $ϕ_0$ is today's value of $ϕ$, and $M_{\rm pl}$ is the reduced Planck mass, we study how the recent Lunar Laser Ranging (LLR) experiment places constraints on the nonminimal coupling from the time variation of gravitational coupling. Besides a potential of the light scalar responsible for cosmic acceleration, we take a cubic Galileon term into account to suppress fifth forces in over-density regions of the Universe. Even if the scalar-ma…
In 1859, Le Verrier discovered the Mercury perihelion advance anomaly. This anomaly turned out to be the first relativistic-gravity effect observed. During the 157 years to 2016, the precisions and accuracies of laboratory and space experiments, and of astrophysical and cosmological observations on relativistic gravity have been improved by 3-4 orders of magnitude. The improvements have been mainly from optical observations at first followed by radio observations. The achievements for the past 50 years are from radio Doppler tracking and radio ranging together with lunar laser ranging. At the …
Lunar laser ranging provides a number of leading experimental tests of gravitation -- important in our quest to unify General Relativity and the Standard Model of physics. The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has for years achieved median range precision at the ~2 mm level. Yet residuals in model-measurement comparisons are an order-of-magnitude larger, raising the question of whether the ranging data are not nearly as accurate as they are precise, or if the models are incomplete or ill-conditioned. This paper describes a new absolute calibration system (ACS) int…
