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Anelastic tidal dissipation in multi-layer planets
F. Remus,S. Mathis,J. -P. Zahn,V. Lainey
Physics , 2012, DOI: 10.1051/0004-6361/201118595
Abstract: Earth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. The tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on their rheology and on the tidal frequency. Therefore, modelling tidal interactions presents a high interest to provide constraints on planets' properties and to understand their history and their evolution, in our Solar System or in exoplanetary systems. We examine the equilibrium tide in the anelastic parts of a planet whatever the rheology, taking into account the presence of a fluid envelope of constant density. We show how to obtain the different Love numbers that describe its tidal deformation. Thus, we discuss how the tidal dissipation in solid parts depends on the planet's internal structure and rheology. Finally, we show how the results may be implemented to describe the dynamical evolution of planetary systems. The first manifestation of the tide is to distort the shape of the planet adiabatically along the line of centers. Then, the response potential of the body to the tidal potential defines the complex Love numbers whose real part corresponds to the purely adiabatic elastic deformation, while its imaginary part accounts for dissipation. This dissipation is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which we derive the characteristic evolution times. The rate at which the system evolves depends on the physical properties of tidal dissipation, and specifically on how the shear modulus varies with tidal frequency, on the radius and also the rheological properties of the solid core. The quantification of the tidal dissipation in solid cores of giant planets reveals a possible high dissipation which may compete with dissipation in fluid layers.
The surface signature of the tidal dissipation of the core in a two-layer planet
F. Remus,S. Mathis,J. -P. Zahn,V. Lainey
Physics , 2014, DOI: 10.1051/0004-6361/201424472
Abstract: Tidal dissipation, which is directly linked to internal structure, is one of the key physical mechanisms that drive systems evolution and govern their architecture. A robust evaluation of its amplitude is thus needed to predict evolution time for spins and orbits and their final states. The purpose of this paper is to refine recent model of the anelastic tidal dissipation in the central dense region of giant planets, commonly assumed to retain a large amount of heavy elements, which constitute an important source of dissipation. The previous paper evaluated the impact of the presence of the static fluid envelope on the tidal deformation of the core and on the associated anelastic tidal dissipation, through the tidal quality factor Qc. We examine here its impact on the corresponding effective anelastic tidal dissipation, through the effective tidal quality factor Qp. We show that the strength of this mechanism mainly depends on mass concentration. In the case of Jupiter- and Saturn-like planets, it can increase their effective tidal dissipation by, around, a factor 2.4 and 2 respectively. In particular, the range of the rheologies compatible with the observations is enlarged compared to the results issued from previous formulations. We derive here an improved expression of the tidal effective factor Qp in terms of the tidal dissipation factor of the core Qc, without assuming the commonly used assumptions. When applied to giant planets, the formulation obtained here allows a better match between the an elastic core's tidal dissipation of a two-layer model and the observations.
The anelastic equilibrium tide in exoplanetary systems
F. Remus,S. Mathis,J. -P. Zahn,V. Lainey
Physics , 2012,
Abstract: Earth-like planets have anelastic mantles, whereas giant planets may have anelastic cores. As for the fluid parts of a body, the tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on its internal friction, and thus on its internal structure. Therefore, modelling this kind of interaction presents a high interest to provide constraints on planet interiors, whose properties are still quite uncertain. Here, we examine the equilibrium tide in the solid central region of a planet, taking into account the presence of a fluid envelope. We first present the equations governing the problem, and show how to obtain the different Love numbers that describe its deformation. We discuss how the quality factor Q depends on the rheological parameters, and the size of the core. Taking plausible values for the anelastic parameters, and examinig the frequency-dependence of the solid dissipation, we show how this mechanism may compete with the dissipation in fluid layers, when applied to Jupiter- and Saturn-like planets. We also discuss the case of the icy giants Uranus and Neptune.
Constraining multiple systems with GAIA
L. Beauvalet,V. Lainey,J. -E. Arlot,D. Bancelin,R. P. Binzel,F. Marchis
Physics , 2012, DOI: 10.1016/j.pss.2012.01.006
Abstract: GAIA will provide observations of some multiple asteroid and dwarf systems. These observations are a way to determine and improve the quantification of dynamical parameters, such as the masses and the gravity fields, in these multiple systems. Here we investigate this problem in the cases of Pluto's and Eugenia's system. We simulate observations reproducing an approximate planning of the GAIA observations for both systems, as well as the New Horizons observations of Pluto. We have developed a numerical model reproducing the specific behavior of multiple asteroid system around the Sun and fit it to the simulated observations using least-square method, giving the uncertainties on the fitted parameters. We found that GAIA will improve significantly the precision of Pluto's and Charon's mass, as well as Petit Prince's orbital elements and Eugenia's polar oblateness.
Cassini ISS Mutual Event Astrometry of the Mid-sized Saturnian Satellites 2005-2012
N. J. Cooper,C. D. Murray,V. Lainey,R. Tajeddine,M. W. Evans,G. A. Williams
Physics , 2014, DOI: 10.1051/0004-6361/201424555
Abstract: We present astrometric observations of the Saturnian satellites Mimas, Enceladus, Tethys, Dione and Rhea from Cassini Imaging Science Subsystem (ISS) narrow-angle camera (NAC) images. Image sequences were designed to observe mutual occultations between these satellites. The positions of satellite centres were estimated by fitting ellipsoidal shape models to the measured limbs of the imaged satellites. Spacecraft pointing corrections were computed using the UCAC2 star catalogue. We provide a total of 2303 astrometric observations, resulting in 976 pairs, the remainder consisting of observations of a single satellite. Mean residuals for the individual satellite positions relative to the SAT360 ephemeris were 4.3 km in the line direction and -2.4 km in the sample direction, with standard deviations of 5.6 and 7.0 km respectively, an order of magnitude improvement in precision compared to published HST observations. By considering inter-satellite separations, uncertainties in camera pointing and spacecraft positioning along with possible biases in the individual positions of the satellites can be largely eliminated, resulting in an order-of-magnitude increase in accuracy compared to that achievable using the individual satellite positions. We show how factors relating to the viewing geometry cause small biases in the individual positions of order 0.28 pixel to become systematic across the dataset as a whole and discuss options for reducing their effects . The reduced astrometric data are provided in the form of individual positions for each satellite, together with the measured positions of reference stars, in order to allow more flexibility in the processing of the observations, taking into account possible future advances in limb-fitting techniques as well as the future availability of more accurate star catalogues, such as those from the GAIA mission.
Astrometric observations of Phobos and Deimos during the 1971 opposition of Mars
V. Robert,V. Lainey,D. Pascu,J. -E. Arlot,J. -P. De Cuyper,V. Dehant,W. Thuillot
Physics , 2015, DOI: 10.1051/0004-6361/201424384
Abstract: Accurate positional measurements of planets and satellites are used to improve our knowledge of their dynamics and to infer the accuracy of planet and satellite ephemerides. In the framework of the FP7 ESPaCE project, we provide the positions of Mars, Phobos, and Deimos taken with the U.S. Naval Observatory 26-inch refractor during the 1971 opposition of the planet. These plates were measured with the digitizer of the Royal Observatory of Belgium and reduced through an optimal process that includes image, instrumental, and spherical corrections to provide the most accurate data. We compared the observed positions of the planet Mars and its satellites with the theoretical positions from INPOP10 and DE430 planetary ephemerides, and from NOE and MAR097 satellite ephemerides. The rms residuals in RA and Dec. of one position is less than 60 mas, or about 20 km at Mars. This accuracy is comparable to the most recent CCD observations. Moreover, it shows that astrometric data derived from photographic plates can compete with those of old spacecraft (Mariner 9, Viking 1 and 2).
Testing Gravitation in the Solar System with Radio Science experiments
A. Hees,P. Wolf,B. Lamine,S. Reynaud,M. T. Jaekel,C. Le Poncin-Lafitte,V. Lainey,V. Dehant
Physics , 2011,
Abstract: The laws of gravitation have been tested for a long time with steadily improving precision, leading at some moment of time to paradigmatic evolutions. Pursuing this continual effort is of great importance for science. In this communication, we focus on Solar System tests of gravity and more precisely on possible tests that can be performed with radio science observations (Range and Doppler). After briefly reviewing the current tests of gravitation at Solar System scales, we give motivations to continue such experiments. In order to obtain signature and estimate the amplitude of anomalous signals that could show up in radio science observables because of modified gravitational laws, we developed a new software that simulates Range/Doppler signals. We present this new tool that simulates radio science observables directly from the space-time metric. We apply this tool to the Cassini mission during its cruise from Jupiter to Saturn and derive constraints on the parameters entering alternative theories of gravity beyond the standard Parametrized Post Newtonian theory.
The Lense-Thirring effect in the Jovian system of the Galilean satellites and its measurability
Lorenzo Iorio,Valery Lainey
Physics , 2005, DOI: 10.1142/S0218271805008133
Abstract: In this paper we investigate the possibility of measuring the post-Newtonian general relativistic gravitomagnetic Lense-Thirring effect in the Jovian system of its Galilean satellites Io, Europa, Ganymede and Callisto in view of recent developments in processing and modelling their optical observations spanning a large time interval (125 years). The present day best observations have an accuracy between several kilometers to few tens of kilometers, which is just the order of magnitude of the Lense-Thirring shifts of the orbits of the Galilean satellites over almost a century. From a comparison between analytical development and numerical integration it turns out that, unfortunately, most of the secular component of the gravitomagnetic signature is removed in the process of fitting the initial conditions. Indeed, an estimation of the magnitude of the Lense-Thirring effect in the ephemerides residuals is given; the resulting residuals have a maximum magnitude of 20 meters only (over 125 years).
The Physics of Bodily Tides in Terrestrial Planets, and the Appropriate Scales of Dynamical Evolution
Michael Efroimsky,Valery Lainey
Physics , 2007, DOI: 10.1029/2007JE002908
Abstract: Any model of tides is based on a specific hypothesis of how lagging depends on the tidal-flexure frequency. For example, Gerstenkorn (1955), MacDonald (1964), and Kaula (1964) assumed constancy of the geometric lag angle, while Singer (1968) and Mignard (1979, 1980) asserted constancy of the time lag. Thus, each of these two models was based on a certain law of scaling of the geometric lag. The actual dependence of the geometric lag on the frequency is more complicated and is determined by the rheology of the planet. Besides, each particular functional form of this dependence will unambiguously fix the appropriate form of the frequency dependence of the tidal quality factor, Q. Since at present we know the shape of the dependence of Q upon the frequency, we can reverse our line of reasoning and single out the appropriate actual frequency-dependence of the angular lag. This dependence turns out to be different from those employed hitherto, and it entails considerable alterations in the time scales of the tide-generated dynamical evolution. Phobos' fall on Mars is an example we consider.
Radioscience simulations in General Relativity and in alternative theories of gravity
A. Hees,B. Lamine,S. Reynaud,M. -T. Jaekel,C. Le Poncin-Lafitte,V. Lainey,A. Füzfa,J. -M. Courty,V. Dehant,P. Wolf
Physics , 2012, DOI: 10.1088/0264-9381/29/23/235027
Abstract: In this paper, we focus on the possibility to test General Relativity in the Solar System with radioscience measurements. To this aim, we present a new software that simulates Range and Doppler signals directly from the space-time metric. This flexible approach allows one to perform simulations in General Relativity and in alternative metric theories of gravity. In a second step, a least-squares fit of the different initial conditions involved in the situation is performed in order to compare anomalous signals produced by a given alternative theory with the ones obtained in General Relativity. This software provides orders of magnitude and signatures stemming from hypothetical alternative theories of gravity on radioscience signals. As an application, we present some simulations done for the Cassini mission in Post-Einsteinian Gravity and in the context of MOND External Field Effect. We deduce constraints on the Post-Einsteinian parameters but find that the considered arc of the Cassini mission is not useful to constrain the MOND External Field Effect.
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