Close encounters or resonances overlaps can create chaotic motion in small bodies in the Solar System. Approaches that measure the separation rate of trajectories that start infinitesimally near, or changes in the frequency power spectrum of time series, among others, can discover chaotic motion. In this paper, we introduce the ACF index (ACFI), which is based on the auto-correlation function of time series. Auto-correlation coefficients measure the correlation of a time-series with a lagged duplicate of itself. By counting the number of auto-correlation coefficients that are larger than 5% after a certain amount of time has passed, we can assess how the time series auto-correlates with each other. This allows for the detection of chaotic time-series characterized by low ACFI values.

A persistent difficulty in terrestrial planet formation models is creating Mars analogs with the appropriate mass: Mars is typically an order of magnitude too large in simulations. Some recent work found that a small Mars can be created if the planetesimal disk from which the planets form has an outermost edge at 1.0 AU. However, that work and no previous work could produce a truncation of the planetesimal disk while also explaining the mass and structure of the asteroid belt. We show that gas-driven migration of Jupiter inward to 1.5 AU, before its subsequent outward migration, can truncate the disk and repopulate the asteroid belt. This dramatic migration history of Jupiter suggests that the dynamical behavior of our giant planets was more similar to that inferred for extra-solar planets than previously thought, as both have been characterised by substantial radial migration.

In the beginning we review briefly the evolution of the ideas on the motion of the bodies in our solar system, from Newton's clockwork Universe to the presently accepted ubiquity of chaotic transport in the asteroid belt. Then we discuss the result of chaotic motion, which is transport in phase space, and we introduce the concept of diffusion of an asteroid in action space. We proceed by reviewing recent work on numerical as well as analytical study of asteroids following chaotic trajectories and we summarize the main results. We present several applications of the theoretical modelling of asteroid motion as diffusion in action space, to problems of specific interest.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html