Transient states in dissipative planetary dynamics

• Grant number: 24/15052-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2025
• End date: December 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Clodoaldo Grotta Ragazzo
• Grantee: Matheus Jean Lazarotto
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Among the known planetary systems, despite their apparent stability lasting for millions or billions of years, a rather complex scenario is observed. Although it is well known that any set of celestial bodies orbiting each other is not a fully conservative system, due to different dissipation sources, the time required to reach the final dissipated states is often unattainable. What is seen instead are many-body systems remaining in long transient configurations. In this project, we propose a simple mathematical model emulating the dissipation of energy due to tidal effects. We will study the effect that a weak central dissipative force has on the conservative structures of phase space and how it impacts the dynamics to produce states of long transient. The proposed model while dissipates energy preserves the angular momentum, which is the main physical feature of tidal forces. We plan to study the model for simple planetary systems, for 2 and 3 point masses, with a further extension to 2 and 3 extended bodies, evaluating how well our simpler model simulates more realistic scenarios. We hope to observe how the weak dissipation affects key components of the conservative phase space, such as its periodic orbits and central configurations, and evaluate how they influence transient times that may explain the resilient orbital behaviors seen throughout the plethora of planetary systems we know. The project will develop over 3 years with an extra year in international collaboration with Daniel Scheeres, from the University of Colorado, an specialist on astrodynamics and asteroid dynamics.