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

Abstract

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.

A Libration Model for Enceladus Based on Geodetic Control Point Network Analysis

“…In the first step we use the nominal libration model (Rambaux et al, 2011), which includes 3 terms with different periods (Table 1). This step gives us the errors in spacecraft positions after adjustment.…”

“…The libration amplitude  predicted for Enceladus was described as (Rambaux, et al, 2011): (Rambaux et al, 2011).…”

“…The point accuracies vary from 55 m to 2900 m (average point accuracy  221 m). From tracking of the control points we detect a librational motion described by a model which includes 3 different periods and amplitudes (Rambaux et al, 2011). We determine the amplitudes for each term.…”

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

“…Planetary libration represents an important dynamic characteristic that has recently been employed to examine the physical properties of planetary interiors (see e.g. Margot et al 2007;Dufey et al 2009;Rambaux, Van Hoolst & Karatekin 2011).…”

The rotation of Mimas

“…≈86 • peak-topeak) caused by the librations of the argument of the orbital resonance between Mimas and Tethys. As explained in Rambaux et al (2010Rambaux et al ( , 2011, the amplitude of the long-period librations are equal to the magnitude of the orbital perturbations because at long period the body is oriented towards the central planet. As a consequence, by analysing the tidal librations, the long period librations vanish.…”