Dynamics of small bodies in the solar system

Abstract

In this chapter we review key results on the dynamics of small solar-system bodies, such as asteroids and comets. We begin by presenting the main populations of small bodies in the solar system, in terms of their orbital characteristics. We define the different types of resonant interactions for small bodies, relating them to the orbital structure of the main belts. In the next section, we present the basic theoretical background on the dynamics of small bodies, referring to applications in selected problems. First, we introduce the reader to the basics of the three-body and N(>3)-body problem with a central mass, using a Hamiltonian framework. We then analyze the expansion of the disturbing function and discuss the classification of terms. Elements of canonical perturbation theory, with the use of Lie series, are also given. The analytical solution of the linearized secular problem (Lagrange-Laplace theory) and the definition of proper elements is then presented. The extension to higher-order/degree secular theories is discussed. Subsequently, we present a derivation of low-order resonant normal forms, suitable for studying motion in mean motion resonances (MMRs, averaged Hamiltonians). The single-resonance model and MMR multiplets (in two-body and three-body MMRs) are then analyzed. We show that the application of the resonance-overlap criterion explains the origin of chaos and chaotic diffusion in resonances; an analytical description of the different diffusion regimes is also given. This section ends with a discussion on extended chaos in the outer asteroid belt and on the origin of the Kirkwood gaps. In the last part of this chapter, we discuss the evolution of small-body reservoirs during the early phases of solar system evolution, namely the epoch of planet migration. We present different models of planet migration (i. e. "smooth vs. chaotic") and discuss resonant capture, which can explain the origin of different small-body resonant populations. These results show how the observed orbital distribution of small bodies, combined with suitable dynamical modeling, can be used as a proxy to unveil the evolutionary history of the Solar System. A short discussion devoted to open problems concludes this chapter. © 2010 EDP Sciences and Springer.