Complements to the longitudinal librations of an elastic 3-layer Titan on a non-Keplerian orbit

Titan longitudinal librations are dependent on the satellite internal structure and the elastic behavior of the surface. The elastic deformation of the surface is related to the perturbing potential through the Love theory. In a previous paper, we described the deformation as a response to the tidal potential exerted by Saturn at orbital frequency. Here we improve the tidal deformation reponse by including the effect of the libration angle and the orbital perturbations. We then provide the libration amplitudes associated with the rotational model of a tidally deformed three-layer Titan evolving on a non-Keplerian orbit.

Investigation on a Flexible Tether Slackness Based on In- and Out-of Plane Libration Angles

Tethered Satellite Systems (TSS) have been used in various applications such as in performing space interferometry, orbit transfer and other relevant fields. As far as the operation system of a TSS is concerned, it is crucial to ensure that the tether will not go slack as its slackness would adversely affects the overall operation outcome due to an undesirable system dynamics. Therefore, it is important to investigate the types of conditions that will cause the tether slackness. Investigations on in-plane and out-of plane libration angles can be utilized to measure at what point that the tether will go slack. Based on previous research works, usually a rigid tether comprising of a uniformed mass is considered while the connecting two satellites are regarded as point masses in order to simplify the governing dynamics equation of motion. However, in order to develop a much more accurate modeling, a flexible tether is chosen by further incorporating the reeling mechanism, attitude dynamics of rigid bodies and tether deformations. Furthermore, a tether has a tendency to go slack if the in-plane and out-of plane libration angle exceeds 65° and 60° respectively regardless of the types of tether utilized whether it being a rigid or a flexible one. Thus, the tension of the tether will serves as a constraint and plotted against the in-plane and out-of plane libration motions that would be attained via the generalized forces. The results will then be analyzed to establish in-plane and out-of plane libration boundaries. Subsequently, the in-plane and out-of plane operation contrains are established for TSS corresponding to a reference mission.

A Synthetic Theory of Motion for Titan-Hyperion

We present an iterative method allowing to synthetize a semi-numerical solution for the equations of motion of the resonant Saturn's satellites Titan-Hyperion (limited now to the planar problem). The current theory of Hyperion by Taylor, Sinclair & Message (1987) gives the greatest terms of the long-period part of the solution (depending on two angles: the libration angle τ, and the angular distance of the pericenters ζ). Using it as a first approximation, this solution is substituted numerically in the exact Lagrange equations of motion for Titan and Hyperion, computed for many values of the three angles: τ, ζ and ϕ (the mean synodic longitude). Then, a multivariable Fourier transform allows to reconstruct the equations in these three angles, that is in same form as the initial one with, in addition, the short-period terms. Then, a solution may be obtained and used as a better approximation in an iterative process. Besides a complete determination of the short-period perturbations of Hyperion obtained here completely for the first time, some long-period perturbations of Titan by Hyperion are also found which would be non negligible at the 10 km level.