The stochastisation hypothesis and the spacing of planetary systems

Jacky Cresson (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We introduce the stochastisation hypothesis which aims to provide a framework to deal with physical systems in random environment. We apply the stochastisation hypothesis in two different cases: in the study of the dynamics of a protoplanetary nebula and in the chaotic long-term behaviour of a generic planetary system using previous works of Albeverio et al. ["A stochastic model for the orbits of planets and satellites: an interpretation of Titius-Bode law," Expo. Math.4, 363-373 (1983)], Nottale ["The quantization of the solar system," Astron. Astrophys.315, L9 (1996)], and Laskar ["On the spacing of planetary systems," Phys. Rev. Lett.84(15), 3240-3243 (2000)10.1103/PhysRevLett.84.3240]. These results give both a particular law for the distribution of planetary orbits. © 2011 American Institute of Physics.

Domaines: Equations aux dérivées partielles [math.AP]

Jacky Cresson. The stochastisation hypothesis and the spacing of planetary systems. Journal of Mathematical Physics, 2011, 52 (11), ⟨10.1063/1.3658279⟩. ⟨hal-00865009⟩