Resonance Sweeping in the Solar System

Abstract

In this paper, we would like to show how the Adiabatic Invariant theory and its extension to the problems of capture into resonance can be an effective tool to understand some basic mechanism in the long term evolution of the Solar System. After summarizing the principal results of this theory in Section 1, we describe briefly two applications. The first one concerns the Kirkwood’s Gaps in the Asteroid belt (section 2). We show how a small displacement of the location of the Jovian resonance in the belt can lead to the formation of gaps similar to the ones observed. The second application (section 3) concerns the rotation of Mercury. We analyze a fixed orbit, two dimensional model of the capture of Mercury in a 3/2 resonance. This model has been considered by previous authors. We recover their results in a very simple way with almost no computations.