Consistent satellites tidal and rotational models for ephemerides estimation

Tidal dissipation is fundamental to provides the energy that sustain natural satellites’ internal oceans, as identified in Europa and Enceladus, or Io’s volcanic activity. A proper modeling of the dissipative phenomena is crucial to correctly infer internal structure properties and composition.

Tidal dissipation is responsible for orbital expansion of satellites. From the orbital expansion it is possible to estimate the amount of dissipation in the planet or the satellite, exploiting astrometric and radiometric observations.

The two most used tidal models of satellites parametrize the tidal dissipation using a time lag (e.g. Mignard, 1980) or a phase lag (e.g. Eanes et al., 1983), respectively. Applying the models to ephemerides propagation, we found that they produce slightly different orbital effects for the satellite, with a difference of 3% in  semimajor axis and 15% in eccentricity. In this work we provide a possible strategy to reconciliate the two models.

Moreover, regarding synchronous satellites tides, classical theoretical formulas from Yoder et al. (1981), Segatz et al. (1988), which assume that the prime meridian of the moon points to the empty focus of its orbit, predict an orbital energy dissipation which is equivalent to the following evolution of semimajor axis and eccentricity of the moon’s orbit:

where Eq. (2) is found from conservation of the angular momentum.

However, computing the secular orbital evolutions using Gauss planetary equations and considering the same rotational and tidal models, we found a difference in the derivative of the semi-major axis, which is directly related to the orbital energy, by almost a factor 3. This may bias the estimation of dissipation parameters from the orbital evolution by the same factor. In addition, during the orbital evolution the angular momentum is not conserved. In this work we analyze these inconsistencies between the energetic approach and the direct propagation of the dynamical equations from tidal potential. We argue that the difference may originate from the effect of the tidal dissipation on the moons rotational state, not considered in the classical approach were the prime meridian is imposed to point the empty focus.  Finally, we identify possible strategies to reconcile the propagation with theoretical predictions, ensuring the conservation of angular momentum.

This may have important consequences in the estimation of the satellite ephemerides and tidal dissipation of the Jupiter system with the upcoming JUICE and Europa Clipper missions, whose unprecedented accuracy will require high-accuracy models of the dynamics inside the system.