Forma, Vol. 6 (No. 3), pp. 247-266, 1991
Original Paper

The Liesegang Model of the Titius-Bode's Law

Atsushi Toramaru, Keisuke Ito, and Shoichi Kai

1Department of Earth Sciences, Kanazawa University, 1-1 Marunouchi, Kanazawa 920, Japan
2Department of Earth Sciences, Kobe University, Nada, Kobe 657, Japan
3Kyushu Institute of Technology, Kitakyushyu 804, Japan

(Received April 16, 1991; Accepted December 11, 1991)

Keywords: Liesegang Ring, Titius-Bode's Law, Solar System, Reaction-Diffusion System

Abstract. The Titius-Bode's law for the orbital distance of planets in the solar system provides clues to understanding the dynamics of the formation processes of the solar system. In this paper we introduce the structure formation in chemical reaction systems, which has the same type of spacing law as the Titius-Bode's law. Based on the analogy between the chemical reaction process and the formation process of the solar system, this paper presents a simple model leading to the law. The model contains three elemental processes taking place in the solar nebula; the sedimentation process of dust ( grains to the central plane, the gravitational fragmentation yielding planetesimals and the diffusional transport of dust plus gas. The model argues that planetesimals formed in narrow bands in the vicinity of the present orbit of planets with a spacing law of the Titius-Bode's law.