The measurement of Titan rotational state by means of SAR imaging

The rotational state of a planet or satellite bears crucial physical information on the bodypsilas dynamical evolution and deep internal structure. For planets or satellites in a Cassini state the obliquity (the angle between the rotational and orbital angular momentum) and physical librations, combined with the measurement of the second degree coefficients of the gravity field, could provide the value of the moments of inertia and reveal the existence of a fluid core (as in the case of Mercury). As ground measurements by means of radar or optical observations are usually not sufficiently accurate and long-life landers have rarely been available, one must rely on orbiting spacecraft for building a body-fixed frame and linking it to a celestial inertial frame. This paper presents a method for estimating the obliquity by comparing image pairs of surface landmarks, taken by an orbiter at different positions along the bodypsilas orbit. The algorithm estimates the vectorial angular velocity, thus providing a body-fixed reference frame. While optical imaging is preferred due to the high angular resolution of planetary cameras, for bodies with a thick atmosphere one has to rely on SAR data. This work presents the result of the estimation of Titanpsilas obliquity and length of day using a combination of SAR imaging of surface landmarks and precise spacecraft positioning of the Cassini spacecraft. We show that the Cassini data provide the pole position and length of day with an accuracy suitable for geophysical interpretation. The main results are a non-synchronous rotation and a pole position compatible with the occupancy of a Cassini state.