Validation of the in-flight calibration procedures for the MICROSCOPE space mission

The MICROSCOPE space mission aims to test the Equivalence Principle with an accuracy of 10^-15${10}^{-15}$. The drag-free micro-satellite will orbit around the Earth and embark a differential electrostatic accelerometer including two cylindrical test masses submitted to the same gravitational field and made of different materials. The experience consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless. The accuracy of the measurements exploited for the test of the Equivalence Principle is limited by our a priori knowledge of several physical parameters of the instrument. These parameters are partially estimated on-ground, but with an insufficient accuracy, and an in-orbit calibration is therefore required to correct the measurements. The calibration procedures have been defined and their analytical performances have been evaluated. In addition, a simulator software including the dynamics model of the instrument, the satellite drag-free system and the perturbing environment has been developed to numerically validate the analytical results. After an overall presentation of the MICROSCOPE mission, this paper will describe the calibration procedures and focus on the simulator. Such an in-flight calibration is mandatory for similar space missions taking advantage of a drag-free system.     

Free fall tests of the accelerometers of the MICROSCOPE mission

The MICROSCOPE mission is fully dedicated to the in-orbit test of the Universality of free fall, the so-called Weak Equivalence Principle (WEP), with an expected accuracy better than 10⁻¹⁵. The test principle consists in comparing the accelerations of two proof masses of different composition in the Earth gravitational field. The payload embarks two pairs of test-masses made of Platinum Rhodium and Titanium alloys at the core of two dedicated coaxial electrostatic accelerometers. These instruments are under qualification for a launch in 2016.     

The Science Case for STEP

The Satellite Test of the Equivalence Principle (STEP) will advance experimental limits on violations of Einstein’s Equivalence Principle (EP) from their present sensitivity of 2 parts in 10¹³${10}^{13}$ to 1 part in 10¹⁸${10}^{18}$ through multiple comparison of the motions of four pairs of test masses of different compositions in an earth-orbiting drag-free satellite. Dimensional arguments suggest that violations, if they exist, should be found in this range, and they are also suggested by leading attempts at unified theories of fundamental interactions (e.g., string theory) and cosmological theories involving dynamical dark energy. Discovery of a violation would constitute the discovery of a new force of nature and provide a critical signpost toward unification. A null result would be just as profound, because it would close off any possibility of a natural-strength coupling between standard-model fields and the new light degrees of freedom that such theories generically predict (e.g., dilatons, moduli, quintessence). STEP should thus be seen as the intermediate-scale component of an integrated strategy for fundamental physics experiments that already includes particle accelerators (at the smallest scales) and supernova probes (at the largest). The former may find indirect evidence for new fields via their missing-energy signatures, and the latter may produce direct evidence through changes in cosmological equation of state—but only a gravitational experiment like STEP can go further and reveal how or whether such a field couples to the rest of the standard model. It is at once complementary to the other two kinds of tests, and a uniquely powerful probe of fundamental physics in its own right.     

Studies of strong gravitational fields near super-massive black hole horizons with space missions

General relativity (GR) can be probed by several tests in the weak gravitational field limit. On the contrary, very poor information exists about GR tests in strong gravitational fields. Here, we focus on the interaction of light rays with the strong gravitational field of a massive black hole and show that relativistic images may form. Hence, we calculate the shapes of shadows (mirages) forming just near BH horizons and discuss the possibility to estimate the black hole parameters (mass, spin and charge) by future astrometric missions. In 2007, the Radioastron space telescope will be launched and it will allow to evaluate those parameters for the black hole hosted at the center of our Galaxy.     

Numerical modeling of a Global Navigation Satellite System in a general relativistic framework

In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space–time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are obtained analytically, describing respectively trajectories of satellites and electromagnetic signals. We implement an algorithm to calculate Schwarzschild coordinates of a GNSS user who receives proper times sent by four satellites, knowing their orbital parameters; the inverse procedure is implemented to check for consistency. The constellation of satellites therefore realizes a geocentric inertial reference system with no a priori realization of a terrestrial reference frame. We perform a simulation of position determination and show that the determination of the four coordinates with a 25–32 digit accuracy takes only around 60 ms. Effects of non-gravitational perturbations on positioning errors are assessed, and methods to reduce them are sketched. In particular, inter-links between satellites could greatly enhance stability and accuracy of the positioning system. Effects of gravitational perturbations are omitted in this paper in order to make a clearer comparison between the relativistic and non-relativistic scheme, but they will be included in subsequent work. We believe that the final algorithm will be a serious alternative to the usual post-Newtonian scheme.     

面外轴向检测MEMS加速度计研究现状

面外轴向检测微机电系统（MEMS）加速度计（Z轴MEMS加速度计）是MEMS惯性系统中用于提供面外加速度信号的重要器件。文章首先介绍了Z轴加速度计的两种典型结构,列举了国内外科研机构近年来的研究成果,概述其在结构设计、工艺制造等方面的特点,以及在性能指标、三轴单片集成等方面的进展。最后,结合Z轴MEMS加速度计的研究现状,对其在结构优化、性能提升、工艺制造、单片三轴集成等方向的发展进行了展望。     

The LAGEOS satellites orbit and Yukawa-like interactions

LAGEOS II general relativity pericenter precession has been analysed in terms of the errors produced by the mismodelling of both the gravitational and non-gravitational perturbations acting on the satellite orbit. The accuracy in the pericenter determination may be considered as an upper-bound value for the estimate of the strength α of a possible new-long-range-interaction described by a Yukawa-like potential. In the present work we have focused on the constraints in α that can be obtained with the current best multi-satellites gravity field model EGM96 (α < 2.6 × 10⁻¹⁰) and also with the first promising models from the CHAMP (α < 1.8 × 10⁻¹⁰) and GRACE (α < 1.2 × 10⁻¹⁰) gravimetric missions. These results represent, potentially, an improvement of two or three orders-of-magnitude with respect to the best constraints obtained in the past with Earth–LAGEOS and Lunar–LAGEOS data (|α| < 10⁻⁵–10⁻⁸). The impact of the non-gravitational perturbations mismodelling in the final error budget has been determined together with the improvements obtainable in the constraint of the strength α with the proposed LARES satellite.     

X-ray timing beyond the Rossi X-ray Timing Explorer

With its ability to look at bright galactic X-ray sources with sub-millisecond time resolution, the Rossi X-ray Timing Explorer (RXTE) discovered that the X-ray emission from accreting compact stars shows quasi-periodic oscillations on the dynamical timescales of the strong field region. RXTE showed also that waveform fitting of the oscillations resulting from hot spots at the surface of rapidly rotating neutron stars constrain their masses and radii. These two breakthroughs suddenly opened up a new window on fundamental physics, by providing new insights on strong gravity and dense matter. Building upon the RXTE legacy, in the Cosmic Vision exercise, testing General Relativity in the strong field limit and constraining the equation of state of dense matter were recognized recently as key goals to be pursued in the ESA science program for the years 2015–2025. This in turn identified the need for a large (10 m² class) aperture X-ray observatory. In recognition of this need, the XEUS mission concept which has evolved into a single launch L2 formation flying mission will have a fast timing instrument in the focal plane. In this paper, I will outline the unique science that will be addressed with fast X-ray timing on XEUS.     

Gamma astrometric measurement experiment (GAME) – Science case

We report here on the science case of a concept for a satellite orbiting at 1 AU from the Sun and using a baffled Fizeau interferometer to look as close as possible to its limb. This configuration, and the need for looking nearby the Sun, is required for the main scientific driver of the mission, namely the measure of the γ parameter of the Parameterized Post-Newtonian formulation to the 10⁻⁶–10⁻⁷ level at least. This would lead to an accurate test of the General Theory of Relativity against other alternative theories of gravity, and set stringent constraints on some of the most significant issues of Astrophysics like those involving exotic forms of dark matter and dark energy. Exploiting the possibilities offered by the observation strategy, it is also possible to target other interesting scientific goals. One is, again, in the realm of General Relativity and aims at measuring the light deflection nearby the Giant Planets to detect asymmetric effects induced by their quadrupoles, predicted by GR but never measured so far. Others can be found in the observation of selected extrasolar systems where, e.g., the astrometric and photometric capabilities of GAME will help to improve on the knowledge of the brown-dwarf regime and on the search for exo-planets with the transit method, respectively.     

Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging

Lunar laser ranging (LLR) measurements are crucial for advanced exploration of the laws of fundamental gravitational physics and geophysics as well as for future human and robotic missions to the Moon. The corner-cube reflectors (CCR) currently on the Moon require no power and still work perfectly since their installation during the project Apollo era. Current LLR technology allows us to measure distances to the Moon with a precision approaching 1 mm. As NASA pursues the vision of taking humans back to the Moon, new, more precise laser ranging applications will be demanded, including continuous tracking from more sites on Earth, placing new CCR arrays on the Moon, and possibly installing other devices such as transponders, etc. for multiple scientific and technical purposes. Since this effort involves humans in space, then in all situations the accuracy, fidelity, and robustness of the measurements, their adequate interpretation, and any products based on them, are of utmost importance. Successful achievement of this goal strongly demands further significant improvement of the theoretical model of the orbital and rotational dynamics of the Earth–Moon system. This model should inevitably be based on the theory of general relativity, fully incorporate the relevant geophysical processes, lunar librations, tides, and should rely upon the most recent standards and recommendations of the IAU for data analysis. This paper discusses methods and problems in developing such a mathematical model. The model will take into account all the classical and relativistic effects in the orbital and rotational motion of the Moon and Earth at the sub-centimeter level. The model is supposed to be implemented as a part of the computer code underlying NASA Goddard’s orbital analysis and geophysical parameter estimation package GEODYN and the ephemeris package PMOE 2003 of the Purple Mountain Observatory. The new model will allow us to navigate a spacecraft precisely to a location on the Moon. It will also greatly improve our understanding of the structure of the lunar interior and the nature of the physical interaction at the core–mantle interface layer. The new theory and upcoming millimeter LLR will give us the means to perform one of the most precise fundamental tests of general relativity in the solar system.     

空间引力红移实验的原理与精度

通过对文献[4,5]关于空间引力红移实验原理与精度的分析,根据爱因斯坦惯性力与引力等效的原理,提出在航天器内部,重力的大部分被惯性力抵消,因而其中的微重力比轨道重力小很多（失重）.因此,应当把星载原子钟的重力势取为与微重力相当的有效重力势,而不能简单地将星载钟的重力势取为轨道重力势.另外,检验相对论红移需要将理论值与实验值进行对比,这两种数值均具有误差,而检验精度取决于误差较大者.因此,如果不提高地球重力模型（例如EGM2008）精度而只提高测量精度则不能提高检验精度.     

The fundamental physics explorer: An ESA technology reference study

ESA technology reference studies are used as a process to identify key technologies and technical challenges of potential future missions not yet in the science programme. This paper reports on the study of the Fundamental Physics Explorer (FPE), a re-usable platform targeted to small missions testing fundamental laws of physics in space. The study addresses three specific areas of interest: special and general relativity tests based on atomic clocks, experiments on the Weak Equivalence Principle (WEP), and studies of Bose–Einstein condensates under microgravity conditions. Starting from preliminary science objectives and payload requirements, three reference missions in the small/medium class range are discussed, based on a re-adaptation of the LISA Pathfinder spacecraft. A 700/3600 km elliptic orbit has been selected to conduct clock tests of special and general relativity, a 700 km circular orbit to perform experiments on the Weak Equivalence Principle and to study Bose–Einstein condensates, each mission being based on a three-axis stabilised spacecraft. It was determined that adaptation of LISA Pathfinder would be required in order to meet the demands of the FPE missions. Moreover it was established that specific payload and spacecraft technology development would be required to realise such a programme.     

智能传感器—微机在惯性器件中的运用

本文论述了采用我校研制的SCE-48单片机开发装置,开发MCS-48系列单片机,使之与加速度计相结合,并研究提高微重力加速度计性能的具体方法。对加速度计的数学误差模型进行了测定,试验分析表明,加速度计与单片机组合后,其精度、零偏和非线性等均有明显改善。本文的研究方法也可推广到陀螺仪和其它传感器。     

基于Fabry-Perot干涉仪的闭环微光机电加速度计

设计了一种闭环反馈差动式双FP腔的微光机电(MOEMS)加速度计,介绍了其工作原理及系统构成.利用惯性敏感单元将对载体加速度的测量转变为对载体位移的测量,利用光纤自聚焦透镜的端面与质量块组成的FP腔测量载体位移.为了提高系统的测量灵敏度和抑制温度等环境因素的影响,设计了一种差动式双FP腔测量机构.为提高微加速度计的输出线性度和动态测量范围,提出了采用静电力平衡技术构成闭环加速度计.建立了其数学模型,对所设计的加速度计重要参数指标——灵敏度、敏感头受载、固有频率等一一进行了详细计算和分析.在此基础上完成了设计背景要求下加速度计参数的优化设计,结果表明:该系统精度可以达到5×10-6g以上.      

原子重力仪动态测量系统中加速度计的现场标定

加速度计可用于原子重力仪的振动校正,抑制振动噪声的干扰,提高原子重力仪的动态测量精度,是测量系统中不可缺少的一部分。为了获得更高的器件精度,在使用前需对加速度计误差进行标定。本文结合原子重力仪动态测量系统,基于加速度计重力矢量模不变原则,将加速度计置于稳定平台多个姿态下测量,对比原子重力仪高精度重力输出,建立代价函数。为了避免迭代方法耗时长、对初始值依赖较大等问题,对代价函数进行简化,推导了线性模型,采用最小二乘方法计算零偏、标度因数和非正交系数等标定参数。开展仿真试验,探究加速度计噪声水平,加速度计姿态数量以及参数初始值对各标定方法的影响,初步证明了本文方法的有效性和精度优势。进一步开展码头系泊条件下的实测试验,结果表明,标定后加速度计输出矢量模的平均值从1.0035 下降到1.0001 ,更接近重力加速度参考值 ,且标准差下降了70.5%。     

静电悬浮加速度计伺服控制分析

根据广义相对论原理选定的坐标系参照物为理想情况下在轨道上自由飘浮的卫星, 据此讨论静电悬浮加速度计检验质量块的运动和电极笼的运动, 得到检验质量在电极内运动的动力学方程, 证明以往相关文献提供的公式存在明显缺陷; 在此基础上分析了伺服控制电路, 给出了电阻尼系数、闭环自然谐振的角频率(或称为加速度计的基础角频率)、受静电负刚度等非受控刚度制约的角频率、来自于静电悬浮的加速度、检验质量的相对位移等一系列表达式, 从而提出必须有足够的增益以提供适度的闭环自然谐振角频率. 给出了位置噪声引起的加速度噪声表达式, 证明当伺服回路的增益足够大时, 在悬浮频带内检验质量的相对位移几乎为零.     

基于数据融合的MEMS阵列加速度传感器实现方法

针对单MEMS加速度计性能有限无法满足实际工程中日益复杂且严苛的检测需求的问题,提出了一种基于数据融合的MEMS阵列加速度传感器实现方法。首先,设计了MEMS阵列加速度传感器的系统架构,并分析了对数据融合算法的技术需求;然后,针对已有的数据融合技术无法满足MEMS阵列加速度传感器的精度与实时性要求的问题,提出了基于离散对数映射的自整定加权融合算法,在此基础上,设计了MEMS阵列加速度传感器的仿真验证方案。仿真实验结果表明,提出的方法通过三个不同范围MEMS加速度计的阵列集成提高了信号检测能力,相比于最优拼接法其平均损失降低了6.1%,且融合数据精度优于各个加速度传感器的原始仿真数据,是高性能MEMS阵列加速度传感器的有效实现方案。