Valery Lainey

Strong tidal dissipation in Io and Jupiter from astrometric observations

Io is the volcanically most active body in the Solar System and has a large surface heat flux. The geological activity is thought to be the result of tides raised by Jupiter, but it is not known whether the current tidal heat production is sufficiently high to generate the observed surface heat flow. Io’s tidal heat comes from the orbital energy of the Io–Jupiter system (resulting in orbital acceleration), whereas dissipation of energy in Jupiter causes Io’s orbital motion to decelerate. Here we report a determination of the tidal dissipation in Io and Jupiter through its effect on the orbital motions of the Galilean moons. Our results show that the rate of internal energy dissipation in Io (k2/Q = 0.015u2009±u20090.003, where k2 is the Love number and Q is the quality factor) is in good agreement with the observed surface heat flow, and suggest that Io is close to thermal equilibrium. Dissipation in Jupiter (k2/Q = (1.102u2009±u20090.203)u2009×u200910-5) is close to the upper bound of its average value expected from the long-term evolution of the system, and dissipation in extrasolar planets may be higher than presently assumed. The measured secular accelerations indicate that Io is evolving inwards, towards Jupiter, and that the three innermost Galilean moons (Io, Europa and Ganymede) are evolving out of the exact Laplace resonance.

Strong Tidal Dissipation in Saturn and Constraints on Enceladus' Thermal State from Astrometry

Tidal interactions between Saturn and its satellites play a crucial role in both the orbital migration of the satellites and the heating of their interiors. Therefore, constraining the tidal dissipation of Saturn (here the ratio k2/Q) opens the door to the past evolution of the whole system. If Saturn’s tidal ratio can be determined at different frequencies, it may also be possible to constrain the giant planet’s interior structure, which is still uncertain. Here, we try to determine Saturn’s tidal ratio through its current effect on the orbits of the main moons, using astrometric data spanning more than a century. We find an intense tidal dissipation (k2/Q = (2.3 ± 0.7) × 10 −4 ), which is about 10 times higher than the usual value estimated from theoretical arguments. As a consequence, eccentricity equilibrium for Enceladus can now account for the huge heat emitted from Enceladus’ south pole. Moreover, the measured k2/Q is found to be poorly sensitive to the tidal frequency, on the short frequency interval considered. This suggests that Saturn’s dissipation may not be controlled by turbulent friction in the fluid envelope as commonly believed. If correct, the large tidal expansion of the moon orbits due to this strong Saturnian dissipation would be inconsistent with the moon formations 4.5 Byr ago above the synchronous orbit in the Saturnian subnebulae. But it would be compatible with a new model of satellite formation in which the Saturnian satellites formed possibly over a longer timescale at the outer edge of the main rings. In an attempt to take into account possible significant torques exerted by the rings on Mimas, we fitted a constant rate da/dt on Mimas’ semi-major axis as well. We obtained an unexpected large acceleration related to a negative value of da/dt =− (15.7 ± 4.4) × 10 −15 AU day −1 . Such acceleration is about an order of magnitude larger than the tidal deceleration rates observed for the other moons. If not coming from an astrometric artifact associated with the proximity of Saturn’s halo, such orbital decay may have significant implications on the Saturn’s rings.

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 lagt. Thus, each of these two models was based on a certain law of scaling of the geometric lag: the Gerstenkorn-MacDonald-Kaula theory implied that � ∼ � 0 , while the Singer-Mignard theory postulated � ∼ � 1 . 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 function Q(�), we can reverse our line of reasoning and single out the appropriate actual frequency-dependence of the lag, �(�): as within the frequency range of our concern, Q ∼ � � , � = 0.2 − 0.4, then � ∼ � � . 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.

Accretion of Saturn's mid-sized moons during the viscous spreading of young massive rings: Solving the paradox of silicate-poor rings versus silicate-rich moons

Abstract The origin of Saturn’s inner mid-sized moons (Mimas, Enceladus, Tethys, Dione and Rhea) and Saturn’s rings is debated. Charnoz et al. [Charnoz, S., Salmon J., Crida A., 2010. Nature 465, 752–754] introduced the idea that the smallest inner moons could form from the spreading of the rings’ edge while Salmon et al. [Salmon, J., Charnoz, S., Crida, A., Brahic, A., 2010. Icarus 209, 771–785] showed that the rings could have been initially massive, and so was the ring’s progenitor itself. One may wonder if the mid-sized moons may have formed also from the debris of a massive ring progenitor, as also suggested by Canup [Canup, R., 2010. Nature 468, 943–946]. However, the process driving mid-sized moon accretion from the icy debris disks has not been investigated in details. In particular, Canup’s (2010) model does not seem able to explain the varying silicate contents of the mid-sized moons (from 6% to 57% in mass). Here, we explore the formation of large objects from a massive ice-rich ring (a few times Rhea’s mass) and describe the fundamental properties and implications of this new process. Using a hybrid computer model, we show that accretion within massive icy rings can form all mid-sized moons from Mimas to Rhea. However in order to explain their current locations, intense dissipation within Saturn (with Q p

The tidal history of Iapetus: Spin dynamics in the light of a refined dissipation model

[1]xa0We study the tidal history of an icy moon, basing our approach on a dissipation model, which combines viscoelasticity with anelasticity and takes into account the microphysics of attenuation. We apply this approach to Iapetus, the most remote large icy moon in the Saturnian system. Different authors provide very different estimates for Iapetuss despinning timescale, by several orders of magnitude. One reason for these differences is the choice of the dissipation model used for computing the spin evolution. As laboratory data on viscoelastic properties of planetary ices are sparse, many studies relied on dissipation models that turned out to be inconsistent with experiment. A pure water ice composition, generally assumed in the previous studies of the kind, yields despinning times of the order of 3.7 Gyr for most initial conditions. We demonstrate that through accounting for the complexity of the material (like second-phase impurities) one arrives at despinning times as short as 0.9 Gyr. A more exact estimate will remain unavailable until we learn more about the influence of impurities on ice dissipation. By including the triaxial-shape-caused torque, we encounter a chaotic behavior at the final stage of despinning, with the possibility of entrapments in the intermediate resonances. The duration of these entrapments turns out to be sensitive to the dissipation model. No long entrapments have been found for Iapetus described with our laboratory-based dissipation model.

Long-term evolution of orbits about a precessing oblate planet: 3. A semianalytical and a purely numerical approach

Construction of an accurate theory of orbits about a precessing and nutating oblate planet, in terms of osculating elements defined in a frame associated with the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2004, 2005, 2006a, b). Here we continue this line of research by combining that analytical machinery with numerical tools. Our model includes three factors: the J2 of the planet, its nonuniform equinoctial precession described by the Colombo formalism, and the gravitational pull of the Sun. This semianalytical and seminumerical theory, based on the Lagrange planetary equations for the Keplerian elements, is then applied to Deimos on very long time scales (up to 1 billion years). In parallel with the said semianalytical theory for the Keplerian elements defined in the co-precessing equatorial frame, we have also carried out a completely independent, purely numerical, integration in a quasi-inertial Cartesian frame. The results agree to within fractions of a percent, thus demonstrating the applicability of our semianalytical model over long timescales. Another goal of this work was to make an independent check of whether the equinoctial-precession variations predicted for a rigid Mars by the Colombo model could have been sufficient to repel its moons away from the equator. An answer to this question, in combination with our knowledge of the current position of Phobos and Deimos, will help us to understand whether the Martian obliquity could have undergone the large changes ensuing from the said model (Ward 1973; Touma and Wisdom 1993, 1994; Laskar and Robutel 1993), or whether the changes ought to have been less intensive (Bills 2006; Paige etxa0al. 2007). It has turned out that, for low initial inclinations, the orbit inclination reckoned from the precessing equator of date is subject only to small variations. This is an extension, to non-uniform equinoctial precession given by the Colombo model, of an old result obtained by Goldreich (1965) for the case of uniform precession and a low initial inclination. However, near-polar initial inclinations may exhibit considerable variations for up to ±10 deg in magnitude. This result is accentuated when the obliquity is large. Nevertheless, the analysis confirms that an oblate planet can, indeed, afford large variations of the equinoctial precession over hundreds of millions of years, without repelling its near-equatorial satellites away from the equator of date: the satellite inclination oscillates but does not show a secular increase. Nor does it show secular decrease, a fact that is relevant to the discussion of the possibility of high-inclination capture of Phobos and Deimos.

On the Theory of Bodily Tides

Different theories of bodily tides assume different forms of dependence of the angular lag δ upon the tidal frequency χ. In the old theory (Gerstenkorn 1955, MacDonald 1964, Kaula 1964) the geometric Iag angle is assumed constant (i.e., δ ∼ χ0), while the new theory (Singer 1968; Mignard 1979, 1980) postulates constancy of the time lag Δt (which is equivalent to saying that δ ∼ χ1).Each particular functional form of δ(χ) unambiguously determines the form of the frequency dependence of the tidal quality factor, Q(χ), and vice versa. Through the past 20 years, several teams of geophysicists have undertaken a large volume of experimental research of attenuation at low frequencies. This research, carried out both for mineral samples in the lab and for vast terrestrial basins, has led to a complete reconsideration of the shape of Q(χ). While in late 70s – early 80s it was universally accepted that at low frequencies the quality factor scales as inverse frequency, by now it is firmly established that Q ∼ χα, wh...

Impact analysis of the transponder time delay on radio-tracking observables

Abstract Accurate tracking of probes is one of the key points of space exploration. Range and Doppler techniques are the most commonly used. In this paper we analyze the impact of the transponder delay, i . e . the processing time between reception and re-emission of a two-way tracking link at the satellite, on tracking observables and on spacecraft orbits. We show that this term, only partially accounted for in the standard formulation of computed space observables, can actually be relevant for future missions with high nominal tracking accuracies or for the re-processing of old missions. We present several applications of our formulation to Earth flybys, the NASA GRAIL and the ESA BepiColombo missions.