The Physics of Bodily Tides in Terrestrial Planets, and the Appropriate Scales of Dynamical Evolution

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.Comment: arXiv admin note: substantial text overlap with arXiv:astro-ph/060552

Cassini ISS mutual event astrometry of the mid-sized Saturnian satellites 2005-2012

Reproduced with permission from Astronomy & Astrophysics, © ES

The need of long time series of observations for the natural planetary satellites

Program available at: http://www.imcce.fr/hosted_sites/naroo/program.htmlInternational audienceAt the time of spacecraft era, it is a rather common though to question the relevance of old astrometric data. Images performed from space probes provide absolute position within an uncertainty of about one to ten kilometers for most planetary satellites. Observations of Mars' moon Phobos can even achieve an accuracy about 500 meters sometimes..

The Physics of Bodily Tides in Terrestrial Planets, and the Appropriate Scales of Dynamical Evolution

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.Comment: arXiv admin note: substantial text overlap with arXiv:astro-ph/060552

Le prétendu wampum offert à Champlain et l’interprétation des objets muséifiés

Outre son fameux astrolabe ou encore son légendaire tombeau, d’autres objets et lieux ont été associés à Samuel de Champlain. C’est le cas d’un des wampums conservés au musée du quai Branly à Paris ayant fait partie de la récente exposition « Premières Nations, Collections royales de France » de passage au Musée Pointe-à-Callière de Montréal à l’été 2007. Assez bien connu du public pour avoir paru dans diverses publications et expositions depuis les cent dernières années, on a affirmé jusqu’à récemment que ce wampum avait été donné par les Hurons à Champlain lui-même en 1611 afin de forger une alliance qui allait garantir le développement de la Nouvelle-France. Bien qu’il eût été intéressant de détenir une « trace » de cette alliance fondatrice, l’apparence des perles et du wampum en général, le silence de Champlain à son égard, la constitution des collections royales et la façon dont cette interprétation erronée s’est développée nous font croire que Champlain n’a jamais vu ni touché ce wampum. Tout en appelant les chercheurs à questionner les objets avec la même rigueur appliquée aux documents écrits, la réflexion entourant un objet en particulier permettra du même coup de parler de la difficulté de documenter et d’interpréter les objets amérindiens muséifiés.Aside from his famous astrolabe and his legendary tomb, other objects and places have been associated with Samuel de Champlain. Such is the case with the wampum band held in the collections of the Quai Branly Museum in Paris, which was part of the recent exhibition titled « First Nations, Royal Collections of France ». The exhibition visited the Pointe-à-Callière Museum in Montreal during the summer of 2007. Fairly well known for having appeared in various publications and exhibitions over the last century, until recently it was claimed that this wampum had been given to Champlain himself by the Hurons in 1611, in order to forge an alliance which would ensure the development of New France. As interesting as it would have been to identify this founding alliance, the appearance of the individual beads and of the wampum band in general, Champlain’s silence on the subject, the constitution of the royal collections and the way in which this mistaken interpretation developed makes it clear that Champlain never saw or touched this wampum. While underscoring the need for researchers to question objects with the same rigour they apply to written documents, a reflection on this particular object also provides a context for discussing the difficulty of documenting and interpreting Amerindian objects which have been integrated into museum collections

The surface signature of the tidal dissipation of the core in a two-layer planet

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.Comment: 5 pages, 2 figures, Accepted for publication in Astronomy & Astrophysic

Constraining multiple systems with GAIA

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.Comment: 5 pages, accepted by Planetary and Space Science, Gaia GREAT-SSO-Pis

The equilibrium tide in viscoelastic parts of planets

International audienceEarth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic 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 the tidal frequency, as well as on the rheology. Therefore, modelling tidal interactions presents a high interest to provide constraints on planet properties, and to understand their history and their evolution. Here, we examine the equilibrium tide in the solid core of a planet, taking into account the presence of a fluid envelope. We explain how to obtain the different Love numbers that describe its deformation. Next, we discuss how the quality factor Q depends on the chosen viscoelastic model. Finally, we show how the results may be implemented to describe the dynamical evolution of planetary systems