MOD SRLS
The Stochastic Three-body problem: Stochastic Resonances and Diffusion in small-body dynamics
Determinism is an idealization: real dynamical systems cannot be isolated from their environments and thus always experience stochastic influence. This work focuses on the implications of this in celestial mechanics. Inspired by the recently introduced Stochastic Two-Body problem, we here introduce the Stochastic Three-Body problem, in which the motion of the point mass is both influenced by the gravitational attraction of the primaries and by a stochastic perturbation, arising from random fluctuations of mass distributions in the solar system. Restricting our analysis on the planar, circular case, after deriving the equations of motion, we discuss the effect of the stochastic perturbation on the symplectic structure of the original dynamical system, and the relations with deterministic nearly-integrable dynamical systems in general. We show the implications of the stochastic perturbation, particularly via Ito’s lemma, for diffusion processes and the existence of weak first integrals. We conjecture and give numerically-assisted proof of the existence of stochastic resonances associated with the formation of heteroclinic connections between L4 and L5. We discuss the consequence of these findings for the stochastic Sun-Jupiter system, particularly regarding the evolution of the Trojan population, the formation of Potentially Hazardous Asteroids, and the origin of the Moon.
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The Stochastic Three-body problem: Stochastic Resonances and Diffusion in small-body dynamics
