Enceladus’ long-period physical librations

The predicted long-period librational response of Saturn’s moon Enceladus proceeds on the assumption that the spin pole is inertially fixed. Actually, the spin pole is expected to occupy a Cassini state where it tracks the motion of the precessing orbit pole. Here we show that this would result in additional long-period libration frequencies with appreciable amplitudes

On the oscillations in Mercury's obliquity

One major objective of MESSENGER and BepiColombo spatial missions is to accurately measure Mercury's rotation and its obliquity in order to obtain constraints on internal structure of the planet. Which is the obliquity's dynamical behavior deriving from a complete spin-orbit motion of Mercury simultaneously integrated with planetary interactions? We have used our SONYR model integrating the spin-orbit N-body problem applied to the solar System (Sun and planets). For lack of current accurate observations or ephemerides of Mercury's rotation, and therefore for lack of valid initial conditions for a numerical integration, we have built an original method for finding the libration center of the spin-orbit system and, as a consequence, for avoiding arbitrary amplitudes in librations of the spin-orbit motion as well as in Mercury's obliquity. The method has been carried out in two cases: (1) the spin-orbit motion of Mercury in the 2-body problem case (Sun-Mercury) where an uniform precession of the Keplerian orbital plane is kinematically added at a fixed inclination (S2K case), (2) the spin-orbit motion of Mercury in the N-body problem case (Sun and planets) (Sn case). We find that the remaining amplitude of the oscillations in the Sn case is one order of magnitude larger than in the S2K case, namely 4 versus 0.4 arcseconds (peak-to-peak). The mean obliquity is also larger, namely 1.98 versus 1.80 arcminutes, for a difference of 10.8 arcseconds. These theoretical results are in a good agreement with recent radar observations but it is not excluded that it should be possible to push farther the convergence process by drawing nearer still more precisely to the libration center.Comment: 30 pages, 3 tables, 8 figures, accepted to Icarus (26 Jul 2007

Interior properties of the inner saturnian moons from space astrometry data

International audienc

About the various contributions in Venus rotation rate and LOD

% context heading (optional) {Thanks to the Venus Express Mission, new data on the properties of Venus could be obtained in particular concerning its rotation.} % aims heading (mandatory) {In view of these upcoming results, the purpose of this paper is to determine and compare the major physical processes influencing the rotation of Venus, and more particularly the angular rotation rate.} % methods heading (mandatory) {Applying models already used for the Earth, the effect of the triaxiality of a rigid Venus on its period of rotation are computed. Then the variations of Venus rotation caused by the elasticity, the atmosphere and the core of the planet are evaluated.} % results heading (mandatory) {Although the largest irregularities of the rotation rate of the Earth at short time scales are caused by its atmosphere and elastic deformations, we show that the Venus ones are dominated by the tidal torque exerted by the Sun on its solid body. Indeed, as Venus has a slow rotation, these effects have a large amplitude of 2 minutes of time (mn). These variations of the rotation rate are larger than the one induced by atmospheric wind variations that can reach 25-50 seconds of time (s), depending on the simulation used. The variations due to the core effects which vary with its size between 3 and 20s are smaller. Compared to these effects, the influence of the elastic deformation cause by the zonal tidal potential is negligible.} % conclusions heading (optional), leave it empty if necessary {As the variations of the rotation of Venus reported here are of the order 3mn peak to peak, they should influence past, present and future observations providing further constraints on the planet internal structure and atmosphere.}Comment: 12 pages, 10 figures, Accepted in A&

Impact of tidal Poisson terms on nonrigid Earth rotation

Context. The tidal potential generated by bodies in the solar system contains Poisson terms, i.e., periodic terms with linearly time-dependent amplitudes. The influence of these terms on the Earth's rotation, although expected to be small, is of interest for high accuracy modeling. Aims. Therefore, we study their contribution to the rotation of a non-rigid Earth with an elastic mantle and liquid core. Methods. Starting from Liouville's equations, and following an analytical treatment, we obtain the relations accounting for Poisson terms in the forcing and providing the solution for the wobble. Results. We show that the transfer function between rigid and non rigid nutation amplitudes, as usually defined in the literature, must be supplemented by additional terms proportional to the amplitude of the Poisson term of the potential. These new terms are inversely proportional to (sigma - sigma(N))(2) where sigma is the forcing frequency and sigma(N) are the eigenfrequencies associated with the retrograde free core nutation and the Chandler wobble. The highest contribution to the nutation is 6 mu as (Delta psi) on the term 2l' - 2F + 2D - 2 Omega and remains below 1 mu as for the other terms. A contribution of 88 mu as/cy is found to the obliquity rate. We evaluate the variations of the third component of the wobble of the Earth and of the core in response to a zonal tidal potential, and show that there is no significant change

Librational response of Enceladus

Physical librations could significantly contribute to Enceladus' geophysics through their influence on tidal stress. Therefore it is important to determine their behavior and the present paper is devoted to estimating Enceladus' libration in longitude. In a rotational model of Enceladus with no global ocean, we introduce the main perturbative terms of its orbital longitude and the tidal coupling. The main librations of Enceladus are related to indirect perturbations of the orbit of Enceladus by Dione (11 years and 3.7 years periods) with amplitudes of 933.4″ (1.14 km) and 676.6″ (827 m), respectively. These amplitudes are almost independent of the body's triaxiality. The third main libration is due to the direct gravitational attraction of Saturn and its period is equal to that of the mean anomaly of Enceladus with an amplitude between 93.1″ and 113.5″ (i.e., 112 and 139 m), depending on triaxiality. These amplitudes are consistent with the upper bound of 1.5° (6.6 km) inferred from observations with the Cassini‐Huygens spacecraft. The nonrigid body libration amplitudes due to tidal coupling are negligible. Nevertheless, tidal dissipation induces a small phase shift up to 0.57° corresponding to a displacement of Enceladus' figure of 1 m along the moon's equator at the mean anomaly period