Influence of orbital perturbations on the Polar Motion of the Galilean satellites

The oblateness of Jupiter, the perturbations induced by the Sun, and the mutual perturbations between the Galilean satellites, cause their orbital motion to deviate from a purely Keplerian orbit. In particular, the inclination, eccentricity, node and pericenter precession rates of each moon vary with time. These non-uniform orbital motions can be represented through periodic series expansions. From these series, corresponding periodic terms in the rotational response of the satellites can be derived. In the case of orbital node precession, the spin axis response consists of a dominant precessional motion accompanied by smaller nutation terms.

In this work, we extend the rotation model presented by Coyette et al. (2026), in which we assumed osculating orbits, to account for these orbital perturbations. Our dynamical model, based on an angular momentum formalism, couples the polar motion to the precession and nutation of the spin axis. Solving the equations up to second order in small quantities for osculating orbits allowed us to identify two polar motions: one at the diurnal frequency and another associated with the frequency of the precession of the pericenter longitude.

Using periodic series expansions for the orbital elements, we further identify additional polar motion terms superimposed on the two previously identified contributions. Some of these newly identified terms can reach amplitudes comparable to, or even larger than, those of the original polar motions.

References:

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