Dynamics of Energy Dissipation in the Three-Body Problem.

• Grant number: 25/12420-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2025
• End date: August 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Clodoaldo Grotta Ragazzo
• Grantee: Claudio Fernando Sierpe Sierpe
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/07076-4 - Dynamics and geometry in low dimensions, AP.TEM

Abstract

This research project focuses on the dynamics of energy dissipation in the three-body problem, a fundamental challenge in celestial mechanics. The study investigates how tidal forces, which arise from gravitational interactions between bodies, influence the long-term evolution of systems like the Earth-Moon-Sun or exoplanetary systems. Tidal effects can deform celestial bodies, leading to energy dissipation and significant changes in their orbits and spins. Historically, the problem has been explored by pioneers like George Darwin and A.E.H. Love, with modern advancements by researchers such as Ferraz-Mello, Efroimsky, and Correia. However, the dissipative aspects of the problem remain debated.The project employs theoretical and numerical methods to address key questions, including the dissipation of the Jacobi integral in the restricted-circular problem, the role of energy dissipation in capturing smaller bodies, and the existence of slow manifolds. The methodologies include global surfaces of section, invariant manifold theory, and numerical integrations using software like Mercury and Rebound. The work builds on equations from Ragazzo and Ruiz (2017), excluding deformation inertia terms.The three-year timeline involves collaboration with international experts, such as Alexandre Correia and Gwenael Boue, and aims to produce at least three publications. The researcher will spend the first year developing a theoretical foundation and initiating numerical simulations, the second year collaborating abroad, and the final year concluding the research at USP. The project encourages independent publications, fostering academic growth. (AU)