Tidal effects on the dynamics of two- and three-body systems under gravitational forces

• Grant number: 15/26253-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2017
• End date: September 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Clodoaldo Grotta Ragazzo
• Grantee: Yeva Gevorgyan de Mendonça
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM
• Associated scholarship(s): 18/02905-4 - A rheological model for the deformation and orbital dynamics of celestial bodies, BE.EP.DR

Abstract

The goal of this project is to investigate some mathematical questions that arise in the modeling of the motion of two- and three-body systems of extended bodies under the influence of their mutual gravitational forces. Such bodies display deformations due to tides, which dissipate energy over the very long time spans typical of the evolution of planetary and related systems in Celestial Mechanics. The consequences of the tides on the total energy and angular momentum of the systems can be modeled by Euler-Lagrangelike dissipative functions together with a rheological model for the bodies. Within these settings, the equations of motion for the two-body problem possess a nine-dimensional invariant manifold of equilibria that we intend to determine using standard tools of Celestial Mechanics and dynamical systems. The extension of the formalism to different types of restricted three-body problems constitutes a further objective of this project, as well as the elaboration of estimates for the variation of rheological parameters of stars, planets and satellites, the use of paleontological data for the calibration of rheological parameters of the earth, and simulations of the earth-moon-sun system including dissipative effects of tides for comparison with observational data and literature - and their possible relevance for modern planetary dynamics and Celestial Mechanics. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GEVORGYAN, YEVA; BOUE, GWENAEL; RAGAZZO, CLODOALDO; RUIZ, LUCAS S.; CORREIA, ALEXANDRE C. M.. Andrade rheology in time-domain. Application to Enceladus' dissipation of energy due to forced libration. ICARUS, v. 343, JUN 2020. (16/25053-8, 15/26253-8, 18/02905-4)

RAGAZZO, CLODOALDO; BOUE, GWENAEL; GEVORGYAN, YEVA; RUIZ, LUCAS S.. Librations of a body composed of a deformable mantle and a fluid core. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, v. 134, n. 2, p. 83-pg., 2022-04-01. (15/26253-8, 16/25053-8, 18/02905-4)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MENDONÇA, Yeva Gevorgyan de. From the internal structure to the librations of satellites and back. 2020. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.