A libration series for Ganymede

The rotation rate of Ganymede, the largest satellite of Jupiter, is equal on average to its orbital mean motion due to synchronous rotation. It cannot, however, remain strictly constant because the gravitational torque exerted by Jupiter varies along the orbit. For a purely Keplerian orbit, the torque variations, and the associated librations, occur at the orbital period. Additional perturbations arise from the mutual gravitational interactions between the Galilean satellites, the perturbation from the Sun, and the oblateness of Jupiter, producing departures from Keplerian motion and therefore additional rotational variations.

The ESA JUICE mission will measure Ganymede’s rotation with unprecedented accuracy during the orbital phase around the satellite beginning on  31 October 2034. Here, we compute the libration series of Ganymede with respect to a uniform rotation and evaluate the potential of rotational variations as probes of the satellite’s interior structure.

We use the libration equations developed by Coyette et al. (2026), correct up to second order in small quantities for satellites with or without a subsurface ocean, and including the possible effects of tidal deformations (see Van Hoolst et al. 2013). Orbital perturbations are first derived from the L1 analytical theory of the Galilean satellites (Lainey et al. 2006), and subsequently reassessed using more recent ephemerides.

The truncation threshold adopted for the libration series is 0.1 arcsec in the solid rigid case. This threshold is chosen to investigate the influence of subsurface oceans and tidal deformations and to enable identifying potentially amplified terms. The libration amplitudes obtained for a solid elastic model remain close to those of the rigid case. Similarly, the ocean-elastic solutions generally differ only slightly, except when resonant amplification occurs, notably for periods near 250 and 470 days. A non-hydrostatic equilibrium shape can have a substantial effect on the librations.

The libration solution obtained for a solid rigid Ganymede constitutes an updated version of the series presented by Rambaux et al. (2011). It provides a robust baseline for the construction of updated rotation and orientation models, such as those developed by Yseboodt et al. (this conference).

 

Coyette, A., Baland, R.-M., Van Hoolst, T., 2026. Second-order modeling of the Cassini states of large satellites: I. Influence of triaxiality and a subsurface ocean. Celestial Mechanics and Dynamical Astronomy 138:3, https://doi.org/10.1007/s10569-025-10269-9

Rambaux, N., Van Hoolst, T., Karatekin, O., 2011. Librational response of Europa, Ganymede, and Callisto with an ocean for a non-Keplerian orbit. Astron. Astrophys. 527, A118. http://dx.doi.org/10.1051/0004-6361/201015304.

Van Hoolst, T., Baland, R.-M., Trinh, A., 2013. On the librations and tides of large icy satellites. Icarus 226(1), 299–315, https://doi.org/10.1016/j.icarus.2013.05.036

Lainey, V., Duriez, L., Vienne, A.: Synthetic representation of the Galilean satellites’ orbital motions from L1 ephemerides. Astron. Astrophys. 456(2), 783–788 (2006). https://doi.org/10.1051/0004-6361:20064941

Yseboodt et al. 2026 this conference