Evidence for Levy random walks in the evolution of comets from the Oort cloud

With a simple map model, derived within the framework of the planar circular restricted three-body problem (Sun-Jupiter-comet), we study the dynamical evolution of near-parabolic comets under the perturbation of Jupiter. The commonly adopted random walk assumption about the energy evolution of the comets is examined. Numerical results show that for the comets on Jupiter-crossing orbits, due to the large energy changes with Jupiter per passage, the statistical evolution of the cometary energy follows a Levy random walk, thus statistically the final energy parameter that a comet reaches is linked to the number of passages by a power law K-f similar to n(f). The mechanism that generates the Levy random walk is explained in this model.