Titan's Orbital Expansion: A Combined Analysis of Cassini Radio Science Normal Points and Astrometry

The rapid outward migration of Titan presents a challenge to classical tidal theories, with recent analyses yielding conflicting results regarding its rate and the underlying mechanisms within Saturn.

Lainey et al. (2020) presented evidence for rapid migration, potentially driven by resonance locking, based on two independent analyses: 1) Radio science data from Cassini Titan flybys analyzed with MONTE software, and 2) Classical astrometry data spanning over a century analyzed with NOE software. While both methods produced statistically coherent results suggesting a low tidal quality factor (Q), the radio science solution yielded significantly more precise results, finding Q =124±9 (1-sigma).

However, a subsequent comprehensive analysis (Jacobson, 2022) merging astrometry and radio science data from Cassini, Voyager, and Pioneer 11 obtained a result for Q that diverged by an order of magnitude (Q=1224±119, 1-sigma). When considering only the astrometry dataset (removing Cassini and Voyager radio science), the estimated central value of Q from this later work became compatible with the Lainey et al. (2020) astrometry-only method (method 2), yielding Q=91±101 (1-sigma), though still statistically consistent with zero. It was noted that, to determine Saturn's dissipation at Titan's frequency, radio science data was essential, but only by combining Voyager 1 data with Cassini's, given that Cassini data alone proved insufficient in that analysis. This made the radio science data result an important discrepancy to resolve with respect to Lainey et al. (2020).

To address this discrepancy, we conducted a new analysis combining long-term astrometric observations (spanning over a century ) with Cassini radio science data processed into reduced normal points for Titan flybys. These normal points, derived using a multi-arc local approach, provide Titan's state vector at each closest approach, minimizing dependence on specific dynamical models.  This combined dataset was analyzed within a unified dynamical framework using the NOE software, solving for Saturn's gravitational field, pole orientation, moon masses, and tidal parameters (k₂​ and k₂​/Q) for major satellites, including Titan. 

Our combined analysis yields a Saturn’s tidal quality factor fully compatible with Lainey et al. (2020), confirming the rapid migration rate of Titan and further supporting the resonance locking hypothesis. The results reinforce the need for non-classical dissipation mechanisms to explain gas giant planet satellites tidal evolution, as they may be incompatible with standard equilibrium tide models.