Titan's Hydrostatic Figure and a Possible Dynamic Tidal Variation

An archive of radio Doppler data from the Cassini mission can be found in NASA's PDS Atmospheres Node as a series of binary files called Orbit Data Files (ODF). We have downloaded six ODFs from the Cassini mission for six Titan gravity passes T11 (27-Feb-2006), T22 (28-Dec-2006), T33 (29-Jun-2007), T45 (31-Jul-2008), T68 (20-May-2010) and T74 (18-Feb-2011). After converting to text files with JPL space-navigation software (ODDUMP), we convert the observed Doppler shift for the Cassini spacecraft to radial velocity along the line of sight (LOS) at one-second sample interval. These data can be fit by a numerical integration of the equations of motion for the craft with respect to Titan, and a subsequent projection of the velocity so obtained along the LOS. The orbital parameters are represented by six standard Kepler elements with the plane of sky as the fundamental reference system, the system used for spectroscopic binary stars. While the systemic velocity V_s is taken as a constant for binary stars, it is represented for spacecraft by six parameters in a function developed for the Doppler detection of gravitational waves. We adopt well-determined values for the GM of Titan and Saturn and add a 13th gravity parameter C₂₂ for an ellipsoidal hydrostatic Titan distorted by the Saturn tide and synchronous rotation (J₂ = (10/3) C₂₂). Also, we adopt the IAU definition for the pole and prime meridian of Titan in the ICRF/J2000 reference system. The interval of observation for each flyby is held to two hours, centered as closely as possible on the time of closest approach to Titan. This interval is sufficiently long for purposes of including all the detectable signal from C₂₂, but short enough that spacecraft-generated translational forces can be neglected. By iterating on a linear least-squares system, 13 converged parameters and associated covariance matrix are found by singular-value decomposition of the least-squares design matrix for each of the six flybys. With reasonably good starting conditions from JPL's Horizons web site, convergence is achieved in about 10 iterations. The weighted mean of the six independent values of C₂₂ is (10.479 ± 0.074) × 10^-6, in good agreement with published values by the Cassini Radio Science Team, especially SOL1a at (10.121 ± 0.029) × 10^-6. However, our independent analysis of the data does not result in a significantly improved fit when a 14th parameter, the Love number k₂, is added to the parameter list. It seems that a dynamic tidal variation is not required in order to fit the data, even though it might very well represent a more realistic fitting model.