57 research outputs found
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.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, 201
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 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
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 level.Comment: Accepted for publication in Physical Review D. 12 pages, 6 figure
Platform and environment requirements of a satellite quantum test of the Weak Equivalence Principle at the level
The Space Time Explorer and QUantum Equivalence principle Space Test
(STE-QUEST) recently proposed, aims at performing a precision test of the weak
equivalence principle (WEP), a fundamental cornerstone of General Relativity.
Taking advantage of the ideal operation conditions for high-precision quantum
sensing on board of a satellite, it aims to detect possible violations of WEP
down to the level. This level of performance leads to stringent
environmental requirements on the control of the spacecraft. We assume an
operation of a dual-species atom interferometer of rubidium and potassium
isotopes in a double-diffraction configuration and derive the constraints to
achieve an E\"otv\"os parameter in statistical and systematic
uncertainties. We show that technical heritage of previous satellite missions,
such as MICROSCOPE, satisfies the platform requirements to achieve the proposed
objectives underlying the technical readiness of the STE-QUEST mission
proposal.Comment: 18 pages, 6 figure
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.Comment: 61st International Astronautical Congress (Prague, Czech Republic -
September 2010), 7 page
MICROSCOPE mission analysis, requirements and expected performance
The MICROSCOPE mission aimed to test the Weak Equivalence Principle (WEP) to
a precision of . The WEP states that two bodies fall at the same rate
on a gravitational field independently of their mass or composition. In
MICROSCOPE, two masses of different compositions (titanium and platinum alloys)
are placed on a quasi-circular trajectory around the Earth. They are the
test-masses of a double accelerometer. The measurement of their accelerations
is used to extract a potential WEP violation that would occur at a frequency
defined by the motion and attitude of the satellite around the Earth. This
paper details the major drivers of the mission leading to the specification of
the major subsystems (satellite, ground segment, instrument, orbit...).
Building upon the measurement equation, we derive the objective of the test in
statistical and systematic error allocation and provide the mission's expected
error budget.Comment: References update
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 10â15 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 ÎŽ(Ti,Pt)=[â1±9(stat)±9(syst)]Ă10â15 (1Ï statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations
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