Rotation has a central place in the understanding of planets and satellites. It causes deformation (flattening) which is a key to unlocking the internal structure of a body. Rotational dynamics profoundly affects the atmosphere and climate, as well as the internal dynamics through tidal deformation and dissipation. Tides couple rotational and orbital motions, resulting in certain special resonant configurations (e.g., the synchronous rotation of the Moon) that shed light on the evolution of the orbit and spin state over billions of years. Multiple satellite systems, such as the Galilean satellites of Jupiter, show even more complex interactions. The goal of this project of Dr. Ferenc Varadi is to advance the understanding of rotational dynamics by developing new analytical theories which will be extensively tested through comparisons with the results of direct numerical simulations. As opposed to specific theories for ephemeris computations, the goal of the project is to find physical explanations for phenomena using a general framework that is not tailored to a specific planet or satellite.
The project will also provide the theoretical basis for generalizing the notion of Cassini states in which free motions are completely damped due to tides. The main motivation comes from recent results on large-amplitude physical librations, which are contrary to the prevailing view of rotational dynamics. The approach will also make it possible to determine generalized Cassini states without restrictive assumptions on orbital motions. While a large part of the work is related to synchronous rotation, physical librations and their long-term effects will also be investigated for fast rotators. The new theories will provide self-consistent dynamical equations based on perturbation computations and averaging. New, more accurate equations will be derived for spin axis evolution. Applications for the terrestrial planets, asteroids and the Jovian planets will be developed. An important component of the project will be the development of differential equations for the rotational and tidal deformations that are coupled to orbital and rotational dynamics. Rather than using a Love number formalism, which requires a spectral decomposition in time to accommodate viscoelastic behavior, the equations for the deformation of the body in time and space are recast into a system of ordinary differential equations in time. This system can then be analyzed via the same techniques of perturbation theory and averaging to develop a self consistent model for deformable bodies.
The advances made through this project will significantly contribute to several problems and projects in planetary astronomy. In particular, this project may make it possible to infer the interior properties of outer planet satellites from precise astrometric measurements, such as eclipse and occultation timings. In addition, the project is expected to provide theoretical basis for the analysis of data from ongoing and planned US space missions, such as the Messenger mission to Mercury and the Cassini mission to Saturn. ***
