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EPSC-DPS2011-516, 2011 EPSC-DPS Joint Meeting 2011 C Author(S) 2011 EPSC Abstracts Vol. 6, EPSC-DPS2011-516, 2011 EPSC-DPS Joint Meeting 2011 c Author(s) 2011 Rotational signature of Mimas’ interior B. Noyelles (1,2), Ö. Karatekin (3) and N. Rambaux (4,2) (1) NAmur Center for Complex SYStems (NAXYS), FUNDP-The University of Namur, Belgium (2) IMCCE - Paris Observatory, France (3) Royal Observatory of Belgium (4) Université Pierre & Marie Curie (UPMC), France ([email protected]) Abstract iments support the hypothesis of a 2-layer rigid Mi- mas [6], this differentiation being due to variations of The Cassini space mission gives the opportunity to porosity. Due to the lack of contraints for Mimas, we have a better knowledge of the properties of the main built two interior models. The first one is an hydro- Saturnian satellites. Among them, Mimas is up to now static equilibrium model whereas the second one con- poorly known, and was considered as a cold rigid body tains non-hydrostatic anomalies as suggested by John- until Cassini observed surface temperature inhomo- son et al. 2006 [2] based on shape model. geneities. The scope of this study is to model the rota- tion of Mimas with different interior models, based on For a two layer interior model the core radius Rc can compaction experiments by Yasui et al. 2009 [6], al- be determined if the densities of the rocky core ρc and 1/3 lowing to consider Mimas as a rigid body composed of ρ ρs the icy mantle ρs are known, i.e. Rc = R ρ − ρ . 2 solid layers. We also considered 2 different hypothe- c− s 2 ses for the interior model: a model based on Mimas’ The moment of Inertia factor (MOI =Ip/(MR )) 5/3 2 (ρ ρs) ρs observed shape, and another one based on the hydro- is given as MOI = − + . Once the 5 ρ(ρ ρ )2/3 ρ static approximation. The rotation has been numeri- c− s MOI and Rc are determined, we can either use hydro- cally computed using the 3 degree of freedom model static approximation or the observed shape to calculate of rigid rotation of Henrard. Physical longitudinal li- the moment of inertia differences. brations of 4 km are to be expected, and an obliquity ≈ of 2 arcmin, while the deviation of the equilibrium ≈ MOI is related to the fluid Love number kf which position because of tides is expected to be negligible. describes the reaction of the satellite to a perturb- ing potential after all viscous stresses have relaxed: 2 2 4 kf MOI = 1 − , and the gravity coeffi- 1 Introduction 3 − 5 1+kf h q i kf As most of the main Solar System satellites, the Satur- cients C22 and J2 are determined from C22 = 4 qr 5kf 2 3 nian satellite Mimas is assumed to be in synchronous and J2 = 6 qr, where qr = Ω R /(Gm), Ω being rotation. The period of the free librations and the am- the spin velocity of Mimas, equal to its mean motion plitudes of the forced ones around the exact spin-orbit n since Mimas is in synchronous rotation. resonance are known to be signatures of the internal structure (see e.g. [3],[4]), that is the reason why we The differences between the three principal mo- here propose a theoretical study of its rotation, based ments of inertia A < B < C are determined from the 2 on a modern view of Mimas on the light of Cassini definitions of C22 and J2, i.e. B A = 4C22MR , 2 − data and recent compaction experiments. C A = (J2 + 2C22)MR , and C B = (J2 − 2 − − We first model the internal structure of Mimas, in 2C22)MR . The relationship between the mean mo- A+B+C assuming the hydrostatic equilibrium, or not. Then we ment of inertia I = 3 and the polar moment 2 2 estimate the dynamical signature of this internal struc- of inertia C is C = I + 3 J2MR , so we can then ture, before estimating the influence of tides. calculate all the three moment of inertia A, B and C. 2 Internal structure From all these calculations, we get 23 models of in- terior, 22 being based on the hydrostatic approxima- Modeling the rotation of a body requires to estimate tion with different densities and sizes of the core, and its moments of inertia. Laboratory compaction exper- the last one being based on the shape of Mimas. 3 The rotation The Fig.1 & 2 give the amplitude the physical li- brations of Mimas associated with the orbital period, We use the model extensively presented in [1]. It con- and the mean obliquity, with respect to the densities sists in considering a 3 degree of freedom rotation of of the core, for a hydrostatic Mimas. For the physical Mimas, modeled by the following Hamiltonian : librations, this represents a motion of 4 km. This H ≈ quantity has to be compared with the deviation of the equilibrium position due to tidal dissipation. A study nP 2 n = + 4P ξ2 η2 similar to the one performed by Rambaux et al.[3] for H 2 8 − q − q Enceladus gives a deviation smaller than 1 meter. γ + γ γ γ 1 2 ξ2 + 1− 2 η2 × 1 γ γ q 1 γ + γ q − 1 − 2 − 1 2 4 Conclusion h M i 3 G 2 2 2 2 3 γ1(x + y ) + γ2(x y ) , Physical longitudinal librations have already been ob- −2n d Y − served for the Moon, for the Martian satellite Phobos, Y Y Y Y Y and for the small Saturnian satellite Janus. 4 km libra- in which P is the norm of the angular momentum nor- tions of Mimas should be able to be detected. Invert- malized to 1, ξq and ηq are canonical variables related ing them to improve our knowledge of the interior is to the polar motion of Mimas, and γ1,2 are related to challenging. the differences of the moments of inertia. x and y are the first 2 coordinates of the perturber,Y here Sat-Y urn ( ), in a reference frame bound to the principal Acknowledgements axes ofY inertia of Mimas. These coordinates have been obtained thanks to TASS1.6 ephemerides [5] and 5 ro- Numerical simulations were made on the local com- tations containing the other degrees of freedom, espe- puting ressources (Cluster URBM-SYSDYN) at the cially the longitudinal motion and the obliquity of Mi- University of Namur. This work has been sup- mas. ported by EMERGENCE-UPMC grant (contract num- ber: EME0911). BN is F.R.S.-FNRS post-doctoral re- search fellow. References [1] Henrard, J.: The rotation of Io, Icarus, 178, 144-153 (2005) [2] Johnson, T.V., Castillo-Rogez, J., and Matson, D.L.: Mimas’ interior models, prospects for constraining Ence- ladus’ thermal evolution, DPS Meeting 38, 69.03, BAAS, 38, 621 (2006) Figure 1: Physical librations of Mimas. [3] Rambaux, N., Castillo-Rogez, J., Williams, J.G., and Karatekin, Ö.: Librational response of Enceladus, GRL, 37, L04202 (2010) [4] Rambaux, N., van Hoolst, T., Karatekin, Ö.: Libra- tional response of Europa, Ganymede, and Callisto with an ocean for a non-Keplerian orbit, Astronomy and As- trophysics, 527, A118 (2011) [5] Vienne, A. and Duriez, L.: TASS1.6: Ephemerides of the major Saturnian satellites, Astronomy and Astro- physics, 297, 588-605 (1995) [6] Yasui, M., and Arakawa, M.: Compaction experiments on ice-silica particle mixtures: Implication for resid- ual porosity of small icy bodies, J. Geophys. Res., 114, Figure 2: Obliquity of Mimas. E09004 (2009).
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