Benoît Noyelles

Titan's rotation - A 3-dimensional theory

Aims. We study the forced rotation of Titan seen as a rigid body at the equilibrium Cassini state, involving the spin-orbit synchronization. Methods. We used both the analytical and the numerical ways. We analytically determined the equilibrium positions and the frequencies of the 3 free librations around it, while a numerical integration associated to frequency analysis gave us a more synthetic, complete theory, where the free solution split from the forced one. Results. We find a mean obliquity of 2.2 arcmin and the fundamental frequencies of the free librations of about 2.0977, 167.4883, and 306.3360 years. Moreover, we bring out the main role played by Titan’s inclination on its rotation, and we suspect a likely resonance involving Titan’s wobble.

Theory of the rotation of Janus and Epimetheus

Abstract The saturnian coorbital satellites Janus and Epimetheus present a unique dynamical configuration in the Solar System, because of high-amplitude horseshoe orbits, due to a mass ratio of order unity. As a consequence, they swap their orbits every 4 years, while their orbital periods is about 0.695 days. Recently, Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254–261) got observational informations on the shapes and the rotational states of these satellites. In particular, they detected an offset in the expected equilibrium position of Janus, and a large libration of Epimetheus. We here propose to give a three-dimensional theory of the rotation of these satellites in using these observed data, and to compare it to the observed rotations. We consider the two satellites as triaxial rigid bodies, and we perform numerical integrations of the system in assuming the free librations as damped. The periods of the three free librations we get, associated with the three dimensions, are respectively 1.267, 2.179 and 2.098 days for Janus, and 0.747, 1.804 and 5.542 days for Epimetheus. The proximity of 0.747 days to the orbital period causes a high sensitivity of the librations of Epimetheus to the moments of inertia. Our theory explains the amplitude of the librations of Janus and the error bars of the librations of Epimetheus, but not an observed offset in the orientation of Janus.

Core-mantle interactions for Mercury

Mercury is the target of two space missions: MESSENGER (NASA) which orbit insertion is planned for March 2011, and ESA/JAXA BepiColombo, that should be launched in 2014. Their instruments will observe the surface of the planet with a high accuracy (about 1 arcsec for BepiColombo), what motivates studying its rotation. Mercury is assumed to be composed of a rigid mantle and an at least partially molten core. We here study the influence of the core-mantle interactions on the rotation perturbed by the solar gravitational interaction, by modeling the core as an ellipsoidal cavity filled with inviscid fluid of constant uniform density and vorticity. We use both analytical (Lie transforms) and numerical tools to study this rotation, with different shapes of the core. We express in particular the proper frequencies of the system, because they characterize the response of Mercury to the different solicitations, due to the orbital motion of Mercury around the Sun. We show that, contrary to its size, the shape of the core cannot be determined from observations of either longitudinal or polar motions. However, we highlight the strong influence of a resonance between the proper frequency of the core and the spin of Mercury that raises the velocity field inside the core. We show that the key parameter is the polar flattening of the core. This effect cannot be directly derived from observations of the surface of Mercury, but we cannot exclude the possibility of an indirect detection by measuring the magnetic field.

The PHEMU09 catalogue and astrometric results of the observations of the mutual occultations and eclipses of the Galilean satellites of Jupiter made in 2009

Context. In 2009, the Sun and the Earth passed through the equatorial plane of Jupiter and therefore the orbital planes of its main satellites. It was the equinox on Jupiter. This occurrence made mutual occultations and eclipses between the satellites possible. Experience has shown that the observations of such events provide accurate astrometric data able to bring new information on the dynamics of the Galilean satellites. Observations are made under the form of photometric measurements, but need to be made through the organization of a worldwide observation campaign maximizing the number and the quality of the data obtained.

Obliquity evolution of the minor satellites of Pluto and Charon

Abstract New Horizons mission observations show that the small satellites Styx, Nix, Kerberos and Hydra, of the Pluto–Charon system, have not tidally spun-down to near synchronous spin states and have high obliquities with respect to their orbit about the Pluto–Charon binary (Weaver, 2016). We use a damped mass-spring model within an N-body simulation to study spin and obliquity evolution for single spinning non-round bodies in circumbinary orbit. Simulations with tidal dissipation alone do not show strong obliquity variations from tidally induced spin-orbit resonance crossing and this we attribute to the high satellite spin rates and low orbital eccentricities. However, a tidally evolving Styx exhibits intermittent obliquity variations and episodes of tumbling. During a previous epoch where Charon migrated away from Pluto, the minor satellites could have been trapped in orbital mean motion inclination resonances. An outward migrating Charon induces large variations in Nix and Styx’s obliquities. The cause is a commensurability between the mean motion resonance frequency and the spin precession rate of the spinning body. As the minor satellites are near mean motion resonances, this mechanism could have lifted the obliquities of all four minor satellites. The high obliquities need not be primordial if the minor satellites were at one time captured into mean motion resonances.

The rotation of Mimas

Context. The Cassini mission in the Saturnian system is an outstanding opportunity to improve our knowledge of the satellites of Saturn. The data obtained thanks to this mission must be balanced with theoretical models. Aims. This paper aims at modelling the rotation of Mimas with respect to its possible internal structure. Methods. We first built different interior models, considering Mimas to be composed of two rigid layers with different porosity. Then we simulated the rotational behaviour of these models in a three-degree of freedom numerical code, considering the complete ephemerides of a Mimas whose rotation is disturbed by Saturn. We also estimated the deviation of its longitudinal orientation caused by tides. Results. We expect a signature of the internal structure up to 0.53 ◦ in the longitudinal librations and an obliquity between 2 and 3 arcmin, the exact values depend on the interior. Conclusions. The longitudinal librations should be detectable, but inverting them to arrive at clues on the internal structure of Mimas is challenging.

Interpreting the librations of a synchronous satellite – How their phase assesses Mimas’ global ocean

Abstract Most of the main planetary satellites of our Solar System are expected to be in synchronous rotation, the departures from the strict synchronicity being a signature of the interior. Librations have been measured for the Moon, Phobos, and some satellites of Saturn. I here revisit the theory of the longitudinal librations in considering that part of the interior is not hydrostatic, i.e. has not been shaped by the rotational and tidal deformations, but is fossil. This consideration affects the rotational behavior. For that, I derive the tensor of inertia of the satellite in splitting these two parts, before proposing an analytical solution that I validate with numerical simulations. I apply this new theory on Mimas and Epimetheus, for which librations have been measured from Cassini data. I show that the large measured libration amplitude of these bodies can be explained by an excess of triaxiality that would not result from the hydrostatic theory. This theory cannot explain the phase shift which has been measured in the diurnal librations of Mimas. This speaks against a solid structure for Mimas, i.e. Mimas could have a global internal ocean.

A numerical exploration of Miranda's dynamical history

The Uranian satellite Miranda presents a high inclination (4.338 ◦ ) and evidences of resurfacing. It is accepted since 20 years (e.g. Tittemore and Wisdom 1989, Malhotra and Dermott 1990) that this inclination is due to the past trapping into the 3:1 resonance with Umbriel. These last years there is a renewal of interest for the Uranian system since the Hubble Space Telescope permitted the detection of an inner system of rings and small embedded satellites, their dynamics being of course ruled by the main satellites. For this reason, we here propose to revisit the long-term dynamics of Miranda, using modern tools like intensive computing facilities and new chaos indicators (MEGNO and frequency map analysis). As in the previous studies, we find the resonance responsible for the inclination of Miranda and the secondary resonances associated, likely to have stopped the rise of Miranda’s inclination at 4.5 ◦ . Moreover, we get other trajectories in which this inclination reaches 7 ◦ . We also propose an analytical study of the secondary resonances associated, based on the study by Moons and Henrard (1993).

Behavior of nearby synchronous rotations of a Poincaré-Hough satellite at low eccentricity

This paper presents a study of the Poincaré–Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant uniform density and vorticity. In considering an Io-like body on a low eccentricity orbit, we describe the different possible behaviors of the system, depending on the size, polar flattening and shape of the core. We use for that the numerical tool. We propagate numerically the Hamilton equations of the system, before expressing the resulting variables under a quasi-periodic representation. This expression is obtained numerically by frequency analysis. This allows us to characterise the equilibria of the system, and to distinguish the causes of their time variations. We show that, even without orbital eccentricity, the system can have complex behaviors, in particular when the core is highly flattened. In such a case, the polar motion is forced by several degrees and longitudinal librations appear. This is due to splitting of the equilibrium position of the polar motion. We also get a shift of the obliquity when the polar flattening of the core is small.

The k:k+4 resonances in planetary systems

In this study we give a first description of De Haerdtl’s 3:7 inequality between the Jovian satellites Ganymede and Callisto and 1:5 inequality between the Saturnian Titan and Iapetus and the resonant arguments associated. For each inequality, 19 arguments are associated. The overlapping of resonant zones induces stochasic layers that the system might have crossed in the past thanks to tidal dissipation.