Dissertation Defense
Student: Eduardo Verrone Sanches
Program: AstronomyPrograma: Astronomia
Title: Study of the Secular Paths of Planetary Migration
Advisor: Prof. Dr. Tatiana Alexandrovna Michtchenko - IAG/USP
Judging Committee:
- Prof. Dr. Tatiana Alexandrovna Michtchenko - Chair - IAG/USP
- Prof. Dr. Adrián Rodriguez Colucci - OV-UFRJ – (Videoconference)
- Prof. Dr. Jorge Luiz Melendez Moreno - IAG-USP
- Prof. Dr. Carlos Tabaré Gallardo Castro - Universidad de la República - Uruguai - (Videoconference)
Abstract: The discoveries of extra-solar systems have shown that the configuration of our Solar System is out of paradigm when we think about planetary system model, putting to test our knowledge on planetary formation and evolution. Thus, we seek to develop new theories and methods to obtain a broad view of possible configurations and movements in systems with several planets. In this work, we analyze the Planar 3 Bodies Problem and, by calculating the average of the perturbation function, we reduce the problem to 1 degree of freedom, which can be defined by the two free parameters: planetary mass ratio and orbital semi- axis ratio. Thus, we can evaluate the dynamic characteristics of the problem in a complete phase space. For this, we introduce the Representative Plane on which we determine the families of equilibrium solutions, the zones of oscillation and circulation and exclude configurations that generate instability in the short period using the concept of Hill’s Stability. By introducing small dissipative perturbations, we alter the total energy and orbital angular momentum of the system, simulating the planetary migration process. As a result, we can predict the possible Secular Migration Paths of this system, so that they do not depend on the mechanism that caused the migration. The theoretical secular paths were compared and confirmed by the results obtained through the exact equations of motion. We studied two specific migration mechanisms: stellar tide effects on planetary motion and planet interaction with the protoplanetary disk. We evaluated how the change of parameters that characterize these mechanisms alter the variation of energy and angular momentum during migration. This work can be complemented by considering the increase in the mass of planets during formation to predict more accurately the initial configurations of the system under study during the formation process.
Keywords: Three-body problem, Secular Motion, Planetary Migration, Tidal Force, Planet-Disc Interaction