Nonlocal instabilities for the planar 3-body problem

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The Newtonian three-body problem consists in studying the dynamics of three point masses moving in Euclidean space and mutually attracted under Newtonian gravitation. The description of instabilities in this system is one of the classical problems of mechanics. This project investigates instabilities for the model of the Sun-Jupiter-Asteroid system, assuming that the third body (the asteroid) has zero mass, that the second (Jupiter) is tiny in comparison with the first (the Sun), and that all three bodies move in a plane. Using the well-known Mather theory, the principal investigator seeks a mathematical proof of instability for this system. The stability of the Solar System is a fundamental issue in astronomy and mathematics. The general belief is that the system is not stable. As a first step toward understanding the physical situation it is extremely important to look for instabilities within mathematical models of the Solar System. The main thrust of this project represents an attempt to shed light on the complicated behavior of a mathematical model for the Sun-Jupiter-Asteroid system. The fundamental question for this model is whether a trajectory of the asteroid can be unstable (in oversimplified terms, whether its positions relative to the Sun and Jupiter can change a great deal over time). The principal investigator will try to find such instabilities and give a detailed mathematical description of them. This could eventually lead to a deeper understanding of instabilities in the entire Solar System, since the Sun and Jupiter are the bodies in it that have the largest impact on the motion of most of the planets.