Close approach problems in orbital dynamics

Abstract

Close Encounters in orbital dynamics occur when, under the gravitational force, one body has a trajectory that takes it to a position close to another body. The orbital evolution of these two bodies will depend on the dynamical and geometrical parameters of the encounter. The outcome can be, for example: i) a collision between the two bodies; ii) a drastic change in the trajectory of one (or both) of them; iii) a smooth exchange of angular momentum between them, keeping both on similar trajectories they had before the encounter, such that the encounter repeat itself sistematically and the system remains stable. The outcome of a close encounter may be highly dependent on the initial conditions of the system, characterizing the existence of chaotic regions in the phase space. The phenomena of close encounters are extremely recurrent in orbital dynamics, with application on the dynamics of artificial bodies (satellites, spacecraft, etc) as well as on solar system dynamics (planets, satellites, asteroids, rings, etc). The goal of this Thematic Project is to group together researchers with solid scientific experience in Orbital Dynamics to approach the theme of close encounters in a sistematic and coordenated way. In this project will be made studies from the fundaments, as the delimitation of the gravitational sphere of influence of a body in a multibody system, going through a detailed analysis of the dependence of the geometrical and dynamical parameters of the encounter up to a variety of important applications in astrodynamics (orbital evolution, transference maneuvers of swing-by type, gravitational capture maneuvers, and others) and in planetary dynamics (gravitational capture of planetesimals, stability and origin of coorbital systems, formation and structures of narrow planetary rings and planetary migration, and others). The project is distributed into six connected parts classified by: A) Fundaments: sphere of influence, capture radius, chaotic and colisional regions - Coordinated by Othon Cabo Winter; B) Orbital Maneuvers - Coordinated by Antonio Fernando Bertachini de Almeida Prado; C) Gravitational Capture - Coordinated by Ernesto Vieira Neto; D) Resonance and Orbital Migration - Coordinated by Tadashi Yokoyama; E) Coorbital Systems - Coordinated by Ana Paula Marins Chiaradia; F) Space Debris and Rings - Coordinated by Silvia Maria Giuliatti Winter. Each one of the six parts of the project will be developed by at least three of the main researchers, beyond the colaborators (associated researchers and students). The parts will all be developed simultaneously, there are direct connections between them. In special, the studies to be developed in the part of Fundaments (A) will be applied in all the other five parts and will receive feedback inputs from each one of them along the work. For example, the sphere of influence (A) is a basic question in many studies of maneuvers and gravitational capture (of artificial and natural bodies). The studies of Orbital Maneuvers will involve the works of part (B) with results and applications to parts (C), (E) and (F). Another topic that is interconnected between several parts of the project is the study of Resonances (D), which will have direct implications in parts (C), (E) and (F). There are also other connections between specific topics of each part of the project. The main researchers listed above will coordinate the activities of the corresponding part of the project, while the project as a whole will be coordinated by Rodolpho Vilhena de Moraes. (AU)