An introduction to the dynamics of trojan asteroids

Abstract

The dynamics of Trojan asteroids constitutes one of the richest fields of celestial mechanics, as a real application of the three-body problem. It involves the L 4 and L 5 Lagrange points and the conditions of stability around these two points. In this chapter we propose to present the fundamentals of the dynamics of Trojan asteroids. After a brief historical overview, we come back to the definitions and characteristics of the collinear Lagrange points L 1, L 2, and L 3, as well as the triangular ones, L 4 and L 5. We show how observational data of Trojan asteroids have confirmed the existence of real bodies librating around these two last points. Then we focus on the linearization of the equations of motion around L 4 and L 5 from a general and purely theoretical point of view. In addition, we show how qualitative results can be extracted to describe the properties of Trojan asteroids. We complete our study by summarizing many previous and up-to-date investigations, which focus on their dynamical behavior. © 2010 Springer-Verlag Berlin Heidelberg.