On the relevance of small bodies in orbital dynamics
In orbital dynamics, minor bodies are those that have size (and mass) much smaller than at least one of the other bodies (called primaries) of the system that belong to. One case very common in astronautics is the case of a spacecraft traveling within the Sun-Earth-Moon system. This kind of characteristic makes the dynamics of the system to present some peculiarities. One of them is the fact that the minor body, in general, does not significantly affect the orbital evolution of the primaries. However, in the case of having an expressive amount of minor bodies interacting with a primary body, an accumulative effect of the angular momentum exchange occurs, leading the primary body to significant orbital changes (orbital migrations). In the case of gravitational interactions between minor bodies, there can happen a variety of different outcomes, depending on physical and dynamical parameters of these bodies. Among the possibilities of outcomes is the collision between the bodies, which can result in fragmentation and/or accretion of the bodies involved. Other possibility is the scattering of these bodies, resulting in expressive orbital changes for both of them. In orbital dynamics there are many fields of study based on collective of minor bodies. This apply to satellite constellations, formation flight, clouds of space debris, families of irregular satellites, proto-planetary discs and planetary rings, for example. In this project will be developed studies that tackle from the question of fundamentals, as the phenomenon of collision and the development of gravitational potential of minor bodies (which, in general, are highly irregular), up to the most varied and relevant applications in astronautics (orbital evolution of satellites and spacecrafts, orbital maneuvers, evolution of space debris clouds, space missions to explore asteroids, etc) and planetary dynamics (origin and formation of planetary systems, of families of irregular satellites, of groups of asteroids, orbital evolution of planetary rings systems, etc). The project is structured in four interconnected parts classified as: A) Gravitational Potential, Periodic Orbits and Stable Regions; B) Collision, Fragmentation and Accretion; C) Orbital Maneuvers; D) Clouds, Rings and Discs. Each one of the four parts of the project will be developed by at least three of the five main researchers, together with other collaborators (researchers and students). All parts will be developed simultaneously, existing direct connections among them. In special, the studies to be developed in parts (A) Gravitational Potential, Periodic Orbits and Stable Regions, and B) Collision, Fragmentation and Accretion will be applied in the other two parts and will receive inputs from them along their developments. For example, collision is a basic question in the generation and evolution of space debris, as well as, in the studies of planetary formation and formation of families of irregular planetary satellites. In the case of the gravitational potential of irregular bodies, the development of these potentials will be fundamental in the studies of the orbital evolution and maneuvers of spacecraft exploring these bodies, as well as, in the studies of natural satellites and particles that orbit around them. Most of the problems to be studied will be preceded by or followed by a dynamical systems approach, analyzing the existence of equilibrium points, periodic orbits and stable regions. In particular, the occurrence of the resonance phenomena will be explored in many of the sub-projects.