arXiv subjects

Gilles Métris

Publications and source records attributed to Gilles Métris.

27 records · Page 2Linked to original sources

arXiv2017

The MICROSCOPE mission: first results of a space test of the Equivalence Principle

According to the Weak Equivalence Principle, all bodies should fall at the same rate in a gravitational field. The MICROSCOPE satellite, launched in April 2016, aims to test its validity at the $10^{-15}$ precision level, by measuring the force required to maintain two test masses (of titanium and platinum alloys) exactly in the same orbit. A non-vanishing result would correspond to a violation of the Equivalence Principle, or to the discovery of a new long-range force. Analysis of the first data gives $δ\rm{(Ti,Pt)}= [-1 \pm 9 (\mathrm{stat}) \pm 9 (\mathrm{syst})] \times 10^{-15}$ (1$σ$ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations.

astro-ph.IM↗

arXiv2017

Determination of the Equivalence Principle violation signal for the MICROSCOPE space mission: optimization of the signal processing

The MICROSCOPE space mission aims at testing the Equivalence Principle (EP) with an accuracy of $10^{-15}$. The test is based on the precise measurement delivered by a differential electrostatic accelerometer on-board a drag-free microsatellite which includes two cylindrical test masses submitted to the same gravitational field and made of different materials. The experiment consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless at a well-known frequency. This high precision experiment is compatible with only very little perturbations. However, aliasing arises from the finite time span of the measurement, and is amplified by measurement losses. These effects perturb the measurement analysis. Numerical simulations have been run to estimate the contribution of a perturbation at any frequency on the EP violation frequency and to test its compatibility with the mission specifications. Moreover, different data analysis procedures have been considered to select the one minimizing these effects taking into account the uncertainty about the frequencies of the implicated signals.

astro-ph.IM↗

arXiv2017

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 $10^{-15}$. 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.

astro-ph.IM↗

arXiv2016

Dealing with missing data in the MICROSCOPE space mission: An adaptation of inpainting to handle colored-noise data

The MICROSCOPE space mission, launched on April 25, 2016, aims to test the weak equivalence principle (WEP) with a 10^-15 precision. To reach this performance requires an accurate and robust data analysis method, especially since the possible WEP violation signal will be dominated by a strongly colored noise. An important complication is brought by the fact that some values will be missing -therefore, the measured time series will not be strictly regularly sampled. Those missing values induce a spectral leakage that significantly increases the noise in Fourier space, where the WEP violation signal is looked for, thereby complicating scientific returns. Recently, we developed an inpainting algorithm to correct the MICROSCOPE data for missing values. This code has been integrated in the official MICROSCOPE data processing pipeline because it enables us to significantly measure an equivalence principle violation (EPV) signal in a model-independent way, in the inertial satellite configuration. In this work, we present several improvements to the method that may allow us now to reach the MICROSCOPE requirements for both inertial and spin satellite configurations. The main improvement has been obtained using a prior on the power spectrum of the colored-noise that can be directly derived from the incomplete data. We show that after reconstructing missing values with this new algorithm, a least-squares fit may allow us to significantly measure an EPV signal with a 0.96x10^-15 precision in the inertial mode and 1.2x10^-15 precision in the spin mode. Although, the inpainting method presented in this paper has been optimized to the MICROSCOPE data, it remains sufficiently general to be used in the general context of missing data in time series dominated by an unknown colored-noise. The improved inpainting software, called ICON, is freely available at http://www.cosmostat.org/software/icon.

astro-ph.IM↗

arXiv2016

Gaussian regression and power spectral density estimation with missing data: The MICROSCOPE space mission as a case study

We present a Gaussian regression method for time series with missing data and stationary residuals of unknown power spectral density (PSD). The missing data are efficiently estimated by their conditional expectation as in universal Kriging, based on the circulant approximation of the complete data covariance. After initialization with an autoregessive fit of the noise, a few iterations of estimation/reconstruction steps are performed until convergence of the regression and PSD estimates, in a way similar to the expectation-conditional-maximization algorithm. The estimation can be performed for an arbitrary PSD provided that it is sufficiently smooth. The algorithm is developed in the framework of the MICROSCOPE space mission whose goal is to test the weak equivalence principle (WEP) with a precision of $10^{-15}$. We show by numerical simulations that the developed method allows us to meet three major requirements: to maintain the targeted precision of the WEP test in spite of the loss of data, to calculate a reliable estimate of this precision and of the noise level, and finally to provide consistent and faithful reconstructed data to the scientific community.

gr-qc↗

arXiv2016

Analytical theory for highly elliptical orbits including time-dependent perturbations

Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited to quasi-circular orbits. On the other hand, the time-dependency due to the motion of the third body (e.g. Moon and Sun) is almost always neglected. We propose several tools to overcome these limitations. Firstly, we have expanded the third-body disturbing function into a finite polynomial using Fourier series in multiple of the satellite's eccentric anomaly (instead of the mean anomaly) and involving Hansen-like coefficients. Next, by combining the classical Brouwer-von Zeipel procedure and the time-dependent Lie-Deprit transforms, we have performed a normalization of the expanded Hamiltonian in order to eliminate all the periodic terms. One of the benefits is that the original Brouwer solution for J2 is not modified. The main difficulty lies in the fact that the generating functions of the transformation must be computed by solving a partial differential equation, involving derivatives with respect to the mean anomaly, which appears implicitly in the perturbation. We present a method to solve this equation by means of an iterative process. Finally we have obtained an analytical tool useful for the mission analysis, allowing to propagate the osculating motion of objects on highly elliptical orbits (e>0.6) over long periods efficiently with very high accuracy, or to determine initial elements or mean elements. Comparisons between the complete solution and the numerical simulations will be presented.

astro-ph.EP↗

arXiv2016

Towards an analytical theory of the third-body problem for highly elliptical orbits

When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon as the altitude of the satellite becomes high, which is the case around the apocentre of this type of orbit. For several reasons, the traditional tools of celestial mechanics are not well adapted to the particular dynamic of highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and therefore limited to quasi-circular orbits [17, 25]. On the other hand, the time-dependency due to the motion of the third-body is often neglected. We propose several tools to overcome these limitations. Firstly, we have expanded the disturbing function into a finite polynomial using Fourier expansions of elliptic motion functions in multiple of the satellite's eccentric anomaly (instead of the mean anomaly) and involving Hansen-like coefficients. Next, we show how to perform a normalization of the expanded Hamiltonian by means of a time-dependent Lie transformation which aims to eliminate periodic terms. The difficulty lies in the fact that the generator of the transformation must be computed by solving a partial differential equation involving variables which are linear with time and the eccentric anomaly which is not time linear. We propose to solve this equation by means of an iterative process.

astro-ph.EP↗

arXiv2015

Dealing with missing data: An inpainting application to the MICROSCOPE space mission

Missing data are a common problem in experimental and observational physics. They can be caused by various sources, either an instrument's saturation, or a contamination from an external event, or a data loss. In particular, they can have a disastrous effect when one is seeking to characterize a colored-noise-dominated signal in Fourier space, since they create a spectral leakage that can artificially increase the noise. It is therefore important to either take them into account or to correct for them prior to e.g. a Least-Square fit of the signal to be characterized. In this paper, we present an application of the {\it inpainting} algorithm to mock MICROSCOPE data; {\it inpainting} is based on a sparsity assumption, and has already been used in various astrophysical contexts; MICROSCOPE is a French Space Agency mission, whose launch is expected in 2016, that aims to test the Weak Equivalence Principle down to the $10^{-15}$ level. We then explore the {\it inpainting} dependence on the number of gaps and the total fraction of missing values. We show that, in a worst-case scenario, after reconstructing missing values with {\it inpainting}, a Least-Square fit may allow us to significantly measure a $1.1\times10^{-15}$ Equivalence Principle violation signal, which is sufficiently close to the MICROSCOPE requirements to implement {\it inpainting} in the official MICROSCOPE data processing and analysis pipeline. Together with the previously published KARMA method, {\it inpainting} will then allow us to independently characterize and cross-check an Equivalence Principle violation signal detection down to the $10^{-15}$ level.

astro-ph.IM↗

arXiv2011

Odyssey 2 : A mission toward Neptune and Triton to test General Relativity

Odyssey 2 will be proposed in December 2010 for the next call of M3 missions for Cosmic Vision 2015-2025. This mission, under a Phase 0 study performed by CNES, will aim at Neptune and Triton. Two sets of objectives will be pursued. The first one is to perform a set of gravitation experiments at the Solar System scale. Experimental tests of gravitation have always shown good agreement with General Relativity. There are however drivers to continue testing General Relativity, and to do so at the largest possible scales. From a theoretical point of view, Einstein's theory of gravitation shows inconsistencies with a quantum description of Nature and unified theories predict deviations from General Relativity. From an observational point of view, as long as dark matter and dark energy are not observed through other means than their gravitational effects, they can be considered as a manifestation of a modification of General Relativity at cosmic scales. The scientific objectives are to: (i) test the gravitation law at the Solar System scale; (ii) measure the Eddington parameter; and (iii) investigate the navigation anomalies during fly-bys. To fulfil these objectives, the following components are to be on board the spacecraft: (i) the Gravity Advanced Package (GAP), which is an electrostatic accelerometer to which a rotating stage is added; (ii) radio-science; (iii) laser ranging, to improve significantly the measure of the Eddington parameter. The second set of objectives is to enhance our knowledge of Neptune and Triton. Several instruments dedicated to planetology are foreseen: camera, spectrometer, dust and particle detectors, and magnetometer. Depending on the ones kept, the mission could provide information on the gravity field, the atmosphere and the magnetosphere of the two bodies as well as on the surface geology of Triton and on the nature of the planetary rings around Neptune.

gr-qc↗