Applications of the hydrodynamical tide - Investigations on the rotational and orbital dynamics of the Solar System's moons

• Grant number: 25/15218-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2025
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Astronomy - Solar System Astronomy
• Principal Investigator: Nelson Callegari Júnior
• Grantee: Raphael Alves Silva
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Associated research grant: 25/02325-1 - Orbital and Rotational Resonances in Systems of Natural Satellites and Planetary Systems, AP.R

Abstract

The fundamental basis of the rheophysical tide theory - also known as the creep tide theory or hydrodynamical tide - was established by the seminal work of Ferraz-Mello (2013). Later on, Folonier et al. (2025) extended the creep theory to tridimensional systems, including both the orbital and axial inclinations dynamics, which allowed the analysis of other motions such as the equatorial nodal precession, and the nutation and libration of the spin axes of the bodies under the influence of tides.This project intends to apply the recently published theoretical tools to the study of the rotational and orbital dynamics of the Solar System's natural satellites. Although some of these satellites are very small, they present interesting regimes of motion, still to be better comprehended. Methone, Aegaeon, and Prometheus (Saturn), with their secondary rotational resonances, constitute some examples (Callegari 2024). The understanding of the current configurations of such systems must be achieved by considering the evolution under tidal forces.A direct consequence of applying tidal forces is analyzing the energy dissipation within these systems, since tides contribute directly to the maintenance of the orbital and rotational regimes of motion, through mutual exchanges in the mechanical energy and the orbital and spin angular momenta. The study of tidal heating may help in the conception of the internal structures of these moons, giving hints on their composition, being rocky, icy, and/or metallic.Applying the creep tide theory will also allow a better qualification of the chaoticity and stability within those systems that will be studied in this project.Callegari, N. Jr.. A Hamiltonian for 1/1 rotational secondary resonances, and application to small satellites of Saturn and Jupiter. Commun Nonlinear Sci Numer Simulat 138 (2024) 108224.Ferraz-Mello S.. Tidal synchronization of close-in satellites and exoplanets. A rheophysical approach. Celest Mech Dyn Astron 2013;116:109-40.H Folonier, H., Ferraz-Mello, S. Alves-Silva, R.. Extension of the creep tide theory to exoplanet systems with high stellar obliquity. The dynamic tide of CoRoT-3b. Celest Mech Dyn Astron 137 (2), 1-25, 2025 (AU)