C. Le Poncin-Lafitte

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 di erent 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.

Tidal dynamics of extended bodies in planetary systems and multiple stars

Context. With the discovery during the past decade of a large number of extrasolar planets orbiting their parent stars at distances lower than 0.1 astronomical unit (and the launch and the preparation of dedicated space missions such as CoRoT and KEPLER), with the position of inner natural satellites around giant planets in our Solar System and with the existence of very close but separated binary stars, tidal interaction has to be studied carefully. Aims. This interaction is usually studied with a punctual approximation for the tidal perturber. The purpose of this paper is to examine the step beyond this traditional approach by considering the tidal perturber as an extended body. To achieve this, we studied the gravitational interaction between two extended bodies and, more precisely, the interaction between mass multipole moments of their gravitational fields and the associated tidal phenomena. Methods. We use cartesian symmetric trace free tensors, their relation with spherical harmonics and Kaulas transform enables us to analytically derive the tidal and mutual interaction potentials, as well as the associated disturbing functions in extended body systems. Results. The tidal and mutual interaction potentials of two extended bodies are derived. In addition, the external gravitational potential of such a tidally disturbed extended body is obtained, using the Love number theory, as well as the associated disturbing function. Finally, the dynamical evolution equations for such a system are given in their more general form without any linearization. We also compare, under a simplified assumption, this formalism to the punctual case. We show that the non-punctual terms have to be taken into account for strongly deformed perturbers (J 2 > 10 -2 ) in very close systems (a B /R B ≤ 5). Conclusions. We show how to derive the dynamical equations for the gravitational and tidal interactions between extended bodies and associated dynamics. The conditions for applying this formalism are given.

Radioscience simulations in general relativity and in alternative theories of gravity

This paper deals with tests of general relativity (GR) in the Solar System using tracking observables from planetary spacecraft. We present a new software that simulates the Range and Doppler signals resulting from a given spacetime metric. This flexible approach allows one to perform simulations in GR as well as in alternative metric theories of gravity. The outputs of this software provide templates of anomalous residuals that should show up in real data if the underlying theory of gravity is not GR. Those templates can be used to give a rough estimation of constraints on additional parameters entering alternative theory of gravity and also signatures that can be searched for in data from past or future space missions aiming at testing gravitational laws in the Solar System. As an application of the potentiality of this software, we present some simulations performed for Cassini-like mission in post-Einsteinian gravity and in the context of MOND external field effect. We derive signatures arising from these alternative theories of gravity and estimate expected amplitudes of the anomalous residuals.

Test of special relativity using a fiber network of optical clocks

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α|≲1.1×10^{-8}, quantifying a violation of time dilation, thus improving by a factor of around 2 the best known constraint obtained with Ives-Stilwell type experiments, and by 2 orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this Letter will improve by orders of magnitude in the near future.

Testing Lorentz Symmetry with Lunar Laser Ranging

Lorentz symmetry violations can be parametrized by an effective field theory framework that contains both general relativity and the standard model of particle physics called the standard-model extension (SME). We present new constraints on pure gravity SME coefficients obtained by analyzing lunar laser ranging (LLR) observations. We use a new numerical lunar ephemeris computed in the SME framework and we perform a LLR data analysis using a set of 20 721 normal points covering the period of August, 1969 to December, 2013. We emphasize that linear combination of SME coefficients to which LLR data are sensitive and not the same as those fitted in previous postfit residuals analysis using LLR observations and based on theoretical grounds. We found no evidence for Lorentz violation at the level of 10^{-8} for s[over ¯]^{TX}, 10^{-12} for s[over ¯]^{XY} and s[over ¯]^{XZ}, 10^{-11} for s[over ¯]^{XX}-s[over ¯]^{YY} and s[over ¯]^{XX}+s[over ¯]^{YY}-2s[over ¯]^{ZZ}-4.5s[over ¯]^{YZ}, and 10^{-9} for s[over ¯]^{TY}+0.43s[over ¯]^{TZ}. We improve previous constraints on SME coefficient by a factor up to 5 and 800 compared to postfit residuals analysis of respectively binary pulsars and LLR observations.

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.

Determination of the relativistic parameter gamma using very long baseline interferometry

Relativistic bending in the vicinity of a massive body is characterized only by the post-Newtonian parameter

Time and frequency transfer with a MicroWave Link in the ACES/PHARAO mission

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The impact of rotation on turbulent tidal friction in stellar and planetary convective regions

within the standard parameterized post-Newtonian formalism, which is unity in General Relativity. Aiming at estimating this parameter, we use very long baseline interferometry (VLBI) to measure the gravitational deflection of radio waves emitted by distant compact radio sources, by Solar System bodies. We analyze geodetic VLBI observations recorded since 1979. We compare estimates of

Determining the relativistic parameter γ using very long baseline interferometry

\gamma