Nicolas Rambaux

Constraints on Mimas’ interior from Cassini ISS libration measurements

Like our Moon, the majority of the solar system’s satellites are locked in a 1:1 spin-orbit resonance; on average, these satellites show the same face toward the planet at a constant rotation rate equal to the satellite’s orbital rate. In addition to the uniform rotational motion, physical librations (oscillations about an equilibrium) also occur. The librations may contain signatures of the satellite’s internal properties. Using stereophotogrammetry on Cassini Image Science Subsystem (ISS) images, we measured longitudinal physical forced librations of Saturn’s moon Mimas. Our measurements confirm all the libration amplitudes calculated from the orbital dynamics, with one exception. This amplitude depends mainly on Mimas’ internal structure and has an observed value of twice the predicted one, assuming hydrostatic equilibrium. After considering various possible interior models of Mimas, we argue that the satellite has either a large nonhydrostatic interior, or a hydrostatic one with an internal ocean beneath a thick icy shell. The precise difference between rotational and orbital periods suggests an unexpected interior for one of Saturn’s moons. Whats inside Saturns tiniest moon? The icy body Mimas is the smallest of Saturns main moons, only slightly wider than Switzerland. Like our own Moon, Mimas is tidally locked in its orbit and shows nearly the same face to Saturn at all times. The rotational and orbital periods continually overtake each other slightly, however, so that the moon would appear to rock back and forth as viewed from Saturn. Tajeddine et al. measured these movements with the Cassini spacecraft to see what they reveal about the moons interior. Surprisingly, the data are consistent with models for a subsurface ocean or an elongated core. Science, this issue p. 322

Librational response of Europa, Ganymede, and Callisto with an ocean for a non-Keplerian orbit

Context. The Galilean satellites Europa, Ganymede, and Callisto are thought to harbor a subsurface ocean beneath an ice shell but its properties, such as the depth beneath the surface, have not been well constrained. Future geodetic observations with, for example, space missions like the Europa Jupiter System Mission (EJSM) of NASA and ESA may refine our knowledge about the shell and ocean. Aims. Measurement of librational motion is a useful tool for detecting an ocean and characterizing the interior parameters of the moons. The objective of this paper is to investigate the librational response of Galilean satellites, Europa, Ganymede, and Callisto assumed to have a subsurface ocean by taking the perturbations of the Keplerian orbit into account. Perturbations from a purely Keplerian orbit are caused by gravitational attraction of the other Galilean satellites, the Sun, and the oblateness of Jupiter. Methods. We use the librational equations developed for a satellite with a subsurface ocean in synchronous spin-orbit resonance. The orbital perturbations were obtained from recent ephemerides of the Galilean satellites. Results. We identify the wide frequency spectrum in the librational response for each Galilean moon. The librations can be separated into two groups, one with short periods close to the orbital period, and a second group of long-period librations related to the gravitational interactions with the other moons and the Sun. Long-period librations can have amplitudes as large as or even larger than the amplitude of the main libration at orbital period for the Keplerian problem, implying the need to introduce them in analyses of observations linked to the rotation. The amplitude of the short-period librations contains information on the interior of the moons, but the amplitude associated with long periods is almost independent of the interior at first order in the low frequency. For Europa, we identified a short-period libration with period close to twice the orbital period, which could have been resonantly amplified in the history of Europa. For Ganymede, we also found a possible resonance between a proper period and a forced period when the icy shell thickness is around 50 km. The librations of Callisto are dominated by solar perturbations.

Analytical description of physical librations of saturnian coorbital satellites Janus and Epimetheus

Abstract Janus and Epimetheus are famously known for their distinctive horseshoe-shaped orbits resulting from a 1:1 orbital resonance. Every 4 years these two satellites swap their orbits by a few tens of kilometers as a result of their close encounter. Recently Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254–261) have proposed a model of rotation based on images from the Cassini orbiter. These authors inferred the amplitude of rotational librational motion in longitude at the orbital period by fitting a shape model to Cassini ISS images. By a quasi-periodic approximation of the orbital motion, we describe how the orbital swap impacts the rotation of the satellites. To that purpose, we have developed a formalism based on quasi-periodic series with long- and short-period librations. In this framework, the amplitude of the libration at the orbital period is found proportional to a term accounting for the orbital swap. We checked the analytical quasi-periodic development by performing a numerical simulation and find both results in good agreement. To complete this study, the results obtained for the short-period librations are studied with the help of an adiabatic-like approach.

Rotational motion of Phobos

Context. Phobos is in synchronous spin-orbit resonance around Mars, like our Moon around the Earth. As a consequence, the rotational period of Phobos is equal in average to its orbital period. The variations of its rotational motion are described by oscillations, called physical librations, which yield information of its interior structure. The largest libration of Phobos rotational motion was first detected in 1981 and the determination of this libration has recently been improved using Mars EXpress observations. Aims. The objective of this paper is to present the spectrum of Phobos’ librations by using recent orbital ephemerides and geophysical knowledge of this Martian satellite. The analysis of the librational spectrum highlights the relationship between dynamical and geophysical properties of the body, but is also useful for cartographic and geodetic purposes for future space missions dedicated to Phobos. Methods. We developed a numerical model of Phobos’ rotation that includes the point-mass Mars acting on the dynamical shape of Phobos, expanded to the third degree, and the e ect of Mars’ oblateness. The forced librations spectrum is extracted through a frequency analysis. Results. We find that the libration in longitude presents a quadratic term that coincides with the secular acceleration of Phobos falling onto Mars. The primary libration in longitude has a period equal to the anomalistic mean motion, whereas the primary libration in latitude has a period equal to the draconic mean motion (node to node). Both librations have amplitudes of about one degree leading to a surface displacement of about 200 m. These two components dominate the libration spectrum by a factor one hundred. Phobos’ third degree gravity harmonics and Mars’ oblateness a ect the librations amplitude at 10 4 degree. This is small but detectable from long-term tracking of a lander. The determination of the librational spectrum would bring strong constraints on the principal torques acting on the Martian moon, as well as on the possible presence of lateral variations in density predicted by certain geophysical models of the Stickney crater formation. We also investigate the obliquity variations of Phobos and find that their amplitudes are larger than the mean value of the obliquity. Conclusions. Phobos exhibits a rich and varied set of librational oscillations. The main librations and the librations close to the proper frequencies are the most sensitive to the interior structure. On the other hand, the superimposed e ect of large amplitude oscillations is likely to make the determination of the mean obliquity challenging.

Spin-orbit coupling and chaotic rotation for circumbinary bodies - Application to the small satellites of the Pluto-Charon system

We investigate the resonant rotation of circumbinary bodies in planar quasi-circular orbits. Denoting

The various contributions in Venus rotation rate and LOD

n_b

The rotation of Mimas

and

Tides on Satellites of Giant Planets

n

The rotational motion of Vesta

the orbital mean motion of the inner binary and of the circumbinary body, respectively, we show that spin-orbit resonances exist at the frequencies

A pre-Caloris synchronous rotation for Mercury

n\pm k\nu/2