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  • 1
    Language: English
    In: Advances in Space Research, 01 April 2015, Vol.55(7), pp.1855-1867
    Description: In the last decades the important increase of the number of positioning satellite constellations (GNSS, Global Navigation Satellite System), such as GPS, GLONASS, BeiDou and Galileo, has motivated a growing interest in the dynamics of the Medium Earth Orbits (MEOs). Numerical experiments show that resonances can affect the stability of MEOs; these resonances are due to a third body (the Moon or the Sun) perturbation that becomes significant for medium and high altitudes. In this work we investigate the effect of the solar perturbation and of the resulting resonances, on the stability of high MEOs (semi-major axis greater than 20000 km). We build an Hamiltonian model suitable for a large class of resonances and use it to study analytically and numerically the stability around one particular resonance, affecting orbits close to the operational Galileo orbits. We focus in particular on the evolution of the eccentricity which is of fundamental importance to ensure that orbit crossings do not occur. An important conclusion is that for some initial conditions, the eccentricity can experience very large excursions (up to 0.8 for the considered resonance) making orbit crossings possible.
    Keywords: Medium Earth Orbits ; Resonances ; (Long Term) Stability ; Solar Perturbation ; Increasing Eccentricity ; Engineering ; Astronomy & Astrophysics ; Physics
    ISSN: 0273-1177
    E-ISSN: 1879-1948
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  • 2
    Language: English
    In: Applied Mathematics, 2012-02-01, 3卷2期 (Vol.3, Issue 2), pp.113-120
    Description: For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit can't be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits to negate the separation over time due to the potential of the Earth and the third body effect. The expressions for the second order conditions that guarantee that the drift rates of two neighboring orbits are equal on the average are derived. To this end, the Hamiltonian was developed. The expressions for the non-vanishing time rate of change of canonical elements are obtained.
    Keywords: Invariant Relative Orbits ; Third-Body Perturbation ; Hamiltonian
    ISSN: 2152-7385
    E-ISSN: 21527393
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  • 3
    Language: English
    In: Physical review letters, 08 December 2017, Vol.119(23), pp.231101
    Description: 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 nonvanishing 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(Ti,Pt)=[-1±9(stat)±9(syst)]×10^{-15} (1σ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations.
    Keywords: Astrophysics - Instrumentation And Methods For Astrophysics ; Astrophysics - Cosmology And Nongalactic Astrophysics ; General Relativity And Quantum Cosmology;
    ISSN: 00319007
    E-ISSN: 1079-7114
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  • 4
    Language: English
    In: Space Science Reviews, 15 October 2013, pp.177-191
    Description: 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...
    Keywords: Sciences of the Universe ; Earth Sciences
    ISSN: 00386308
    E-ISSN: 15729672
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  • 5
    Language: English
    In: Advances in Space Research, Nov 1, 2013, Vol.52(9), p.1634(13)
    Description: To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.asr.2013.07.042 Byline: Emilie Hardy, Agnes Levy, Manuel Rodrigues, Pierre Touboul, Gilles Metris Abstract: acents An in-orbit calibration of the MICROSCOPE instrument is necessary for the Equivalence Principle test. acents Calibration procedures enabling the estimation of each limiting parameters have been determined. acents A software simulator including a model of the instrument, the satellite and its environment has been developed. acents The calibration procedures have been validated numerically thanks to the simulator. Article History: Received 13 December 2012; Revised 8 July 2013; Accepted 19 July 2013
    Keywords: Microscope ; Test of the Equivalence Principle ; Space Accelerometer ; In-Flight Calibration ; Drag-Free Satellite;
    ISSN: 0273-1177
    E-ISSN: 18791948
    Source: Cengage Learning, Inc.
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  • 6
    In: Applied Mathematics, 2012, Vol.03(02), pp.113-120
    ISSN: 2152-7385
    E-ISSN: 2152-7393
    Source: CrossRef
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  • 7
    Language: English
    In: Applied Mathematics, February 2012, Vol.3, pp.113-120
    Description: For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit can't be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node and the sum of the argu-ment of perigee and mean anomaly are set equal...
    Keywords: Sciences of the Universe ; Earth Sciences ; Mathematics
    ISSN: 2152-7385
    E-ISSN: 2152-7393
    Source: Hyper Article en Ligne (CCSd)
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  • 8
    Description: 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. Comment: To be submitted soon. Comments are welcome !
    Keywords: Astrophysics - Earth And Planetary Astrophysics ; Mathematical Physics ; Physics - Space Physics
    Source: Cornell University
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  • 9
    Language: English
    In: Physical Review D, March 2015, Vol.91(6)
    Description: The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of $10^{-15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement. Comment: 12 pages, 4 figures, to be published in Phys. Rev. D
    Keywords: Physics ; Astrophysics ; Physics ; General Relativity and Quantum Cosmology ; Physics
    ISSN: 1550-7998
    E-ISSN: 1550-2368
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  • 10
    Description: 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. Comment: Proceedings of the International Symposium on Orbit Propagation and Determination - Challenges for Orbit Determination and the Dynamics of Artificial Celestial Bodies and Space Debris, Lille, France, 2011
    Keywords: Astrophysics - Earth And Planetary Astrophysics ; Mathematical Physics ; Physics - Space Physics
    Source: Cornell University
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