158 research outputs found
Frequency shift up to the 2-PM approximation
A lot of fundamental tests of gravitational theories rely on highly precise
measurements of the travel time and/or the frequency shift of electromagnetic
signals propagating through the gravitational field of the Solar System. In
practically all of the previous studies, the explicit expressions of such
travel times and frequency shifts as predicted by various metric theories of
gravity are derived from an integration of the null geodesic differential
equations. However, the solution of the geodesic equations requires heavy
calculations when one has to take into account the presence of mass multipoles
in the gravitational field or the tidal effects due to the planetary motions,
and the calculations become quite complicated in the post-post-Minkowskian
approximation. This difficult task can be avoided using the time transfer
function's formalism. We present here our last advances in the formulation of
the one-way frequency shift using this formalism up to the
post-post-Minkowskian approximation.Comment: 4 pages, submitted to proceedings of SF2
Relativistic formulation of coordinate light time, Doppler and astrometric observables up to the second post-Minkowskian order
Given the extreme accuracy of modern space science, a precise relativistic
modeling of observations is required. In particular, it is important to
describe properly light propagation through the Solar System. For two decades,
several modeling efforts based on the solution of the null geodesic equations
have been proposed but they are mainly valid only for the first order
Post-Newtonian approximation. However, with the increasing precision of ongoing
space missions as Gaia, GAME, BepiColombo, JUNO or JUICE, we know that some
corrections up to the second order have to be taken into account for future
experiments. We present a procedure to compute the relativistic coordinate time
delay, Doppler and astrometric observables avoiding the integration of the null
geodesic equation. This is possible using the Time Transfer Function formalism,
a powerful tool providing key quantities such as the time of flight of a light
signal between two point-events and the tangent vector to its null-geodesic.
Indeed we show how to compute the Time Transfer Functions and their derivatives
(and thus range, Doppler and astrometric observables) up to the second
post-Minkowskian order. We express these quantities as quadratures of some
functions that depend only on the metric and its derivatives evaluated along a
Minkowskian straight line. This method is particularly well adapted for
numerical estimations. As an illustration, we provide explicit expressions in
static and spherically symmetric space-time up to second post-Minkowskian
order. Then we give the order of magnitude of these corrections for the
range/Doppler on the BepiColombo mission and for astrometry in a GAME-like
observation.Comment: 22 pages, 5 figures, accepted in Phys. Rev.
Light propagation in the field of a moving axisymmetric body: theory and application to JUNO
Given the extreme accuracy of modern space science, a precise relativistic
modeling of observations is required. We use the Time Transfer Functions
formalism to study light propagation in the field of uniformly moving
axisymmetric bodies, which extends the field of application of previous works.
We first present a space-time metric adapted to describe the geometry of an
ensemble of uniformly moving bodies. Then, we show that the expression of the
Time Transfer Functions in the field of a uniformly moving body can be easily
derived from its well-known expression in a stationary field by using a change
of variables. We also give a general expression of the Time Transfer Function
in the case of an ensemble of arbitrarily moving point masses. This result is
given in the form of an integral easily computable numerically. We also provide
the derivatives of the Time Transfer Function in this case, which are mandatory
to compute Doppler and astrometric observables. We particularize our results in
the case of moving axisymmetric bodies. Finally, we apply our results to study
the different relativistic contributions to the range and Doppler tracking for
the JUNO mission in the Jovian system.Comment: 17 pages, 4 figures, submitted to Phys. Rev. D, some corrections
after revie
Impact of the frequency dependence of tidal Q on the evolution of planetary systems
Context. Tidal dissipation in planets and in stars is one of the key physical
mechanisms that drive the evolution of planetary systems.
Aims. Tidal dissipation properties are intrisically linked to the internal
structure and the rheology of studied celestial bodies. The resulting
dependence of the dissipation upon the tidal frequency is strongly different in
the cases of solids and fluids.
Methods. We compute the tidal evolution of a two-body coplanar system, using
the tidal quality factor's frequency-dependencies appropriate to rocks and to
convective fluids.
Results. The ensuing orbital dynamics comes out smooth or strongly erratic,
dependent on how the tidal dissipation depends upon frequency.
Conclusions. We demonstrate the strong impact of the internal structure and
of the rheology of the central body on the orbital evolution of the tidal
perturber. A smooth frequency-dependence of the tidal dissipation renders a
smooth orbital evolution while a peaked dissipation can furnish erratic orbital
behaviour.Comment: Accepted for publication as a letter in Astronomy And Astrophysic
Scaling laws to understand tidal dissipation in fluid planetary regions and stars I - Rotation, stratification and thermal diffusivity
Tidal dissipation in planets and stars is one of the key physical mechanisms
driving the evolution of star-planet and planet-moon systems. Several
signatures of its action are observed in planetary systems thanks to their
orbital architecture and the rotational state of their components. Tidal
dissipation inside the fluid layers of celestial bodies are intrinsically
linked to the dynamics and the physical properties of the latter. This complex
dependence must be characterized. We compute the tidal kinetic energy
dissipated by viscous friction and thermal diffusion in a rotating local fluid
Cartesian section of a star/planet/moon submitted to a periodic tidal forcing.
The properties of tidal gravito-inertial waves excited by the perturbation are
derived analytically as explicit functions of the tidal frequency and local
fluid parameters (i.e. the rotation, the buoyancy frequency characterizing the
entropy stratification, viscous and thermal diffusivities) for periodic normal
modes. The sensitivity of the resulting possibly highly resonant dissipation
frequency-spectra to a control parameter of the system is either important or
negligible depending on the position in the regime diagram relevant for
planetary and stellar interiors. For corresponding asymptotic behaviors of
tidal gravito-inertial waves dissipated by viscous friction and thermal
diffusion, scaling laws for the frequencies, number, width, height and contrast
with the non-resonant background of resonances are derived to quantify these
variations. We characterize the strong impact of the internal physics and
dynamics of fluid planetary layers and stars on the dissipation of tidal
kinetic energy in their bulk. We point out the key control parameters that
really play a role and demonstrate how it is now necessary to develop ab-initio
modeling for tidal dissipation in celestial bodies.Comment: 24 pages, 14 figures, accepted for publication in Astronomy &
Astrophysic
How to test SME with space missions ?
In this communication, we focus on possibilities to constrain SME
coefficients using Cassini and Messenger data. We present simulations of
radioscience observables within the framework of the SME, identify the linear
combinations of SME coefficients the observations depend on and determine the
sensitivity of these measurements to the SME coefficients. We show that these
datasets are very powerful for constraining SME coefficients.Comment: Presented at the Sixth Meeting on CPT and Lorentz Symmetry,
Bloomington, Indiana, June 17-21, 2013. 4 pages, 1 figur
Lorentz symmetry and Very Long Baseline Interferometry
Lorentz symmetry violations can be described by an effective field theory
framework that contains both General Relativity and the Standard Model of
particle physics called the Standard-Model extension (SME). Recently, post-fit
analysis of Gravity Probe B and binary pulsars lead to an upper limit at the
level on the time-time coefficient of the pure-gravity
sector of the minimal SME. In this work, we derive the observable of Very Long
Baseline Interferometry (VLBI) in SME and then we implement it into a real data
analysis code of geodetic VLBI observations. Analyzing all available
observations recorded since 1979, we compare estimates of and
errors obtained with various analysis schemes, including global estimations
over several time spans and with various Sun elongation cut-off angles, and
with analysis of radio source coordinate time series. We obtain a constraint on
, directly fitted to the observations and
improving by a factor 5 previous post-fit analysis estimates.Comment: 5 pages, 3 figures, version accepted for publicatio
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