Kinematic model of Titan’s rotation from Cassini radar data

Abstract:

The Cassini radar data provide important constraints on the rotational kinematics of Titan. Using 2602 tie-points, spanning 9.82 years, 26 October 2004 to 20 August 2014.we have obtained a number of rotation models, with various levels of complexity and quality of fit to the data.

Our simplest model has a fixed orientation spin pole, and a fixed rate of rotation. The spin pole right ascension is (39.35034 0.0031) degree, declination is (83.43825 0.00036) degree, and the mean period of rotation is (15.94547727 ) day. The residual variance of misfit is 1.235 km².

It has long been understood that the rotation of Titan is synchronized to its orbital motion about Saturn, but with the Cassini radar data, we now see that the rate of rotation is not quite uniform. The current time span of the tie-point data is almost exactly 1/3 of Saturn’s heliocentric orbital period. We have fitted a series of additional models to the data, each of which has a fixed spin pole, and a rotation rate which is represented by a finite length Fourier series in time. The residual variance drops, with increasing harmonic degree, up to N=8, and then remains nearly constant.

The model with 8 cycles in the observation time span has a residual variance of 0.774 km², or 62% of the uniform rotation case. The maximum deviation of the rotation angle, from the uniform case, amounts to 0.08 degree, or 3.6 km displacement, on the equator.