| Summary: | Understanding asteroid collisional and dynamical evolution necessitates the use of statistical methods, since an asteroid's physical and orbital characteristics are modified throughout its lifetime by collisions and planetary perturbations. Thus, my thesis investigates evolutionary trends for asteroids by calculating and applying parameters such as collision probabilities, impact velocities, and collisional and dynamical lifetimes. I found that previous calculations of collision probabilities between pairs of asteroids on independent Keplerian orbits often yielded inconsistent results. By correcting and improving the formalism, I obtained results which should be accurate for all cases. Applying this formalism, I calculated collision probabilities and impact velocity distributions for single asteroids (e.g. Gaspra, Ida), asteroid populations, and the terrestrial planets with other asteroid populations. These results allowed me to determine asteroid comminution and planetary impact rates. I also examined the dynamical evolution of asteroids, using a modified Monte-Carlo code. The accuracy of these codes are frequently questioned since, for some planetary encounters on tangential orbits, the two-body scattering approximation is inconsistent with numerical integration results. Thus, to verify the validity of Monte-Carlo results in general, I tracked particle-planetary encounters using a new mapping technique to determine the role of distant perturbations. My results show that Monte-Carlo results yield statistically similar results to numerical integration for all but the most pathological cases, and my model shows why. Finally, I used this Monte-Carlo model, modified to include impact disruption, asteroid fragmentation after disruption, and observational selection effects to determine the most likely source for a population of small asteroids near the Earth. My results show that main-belt asteroids (via the 3:1 or v₆ resonances) are an unlikely source for these objects, as are small bodies ejected from Mars after a large cratering event. However, planetary ejecta from either the Earth-Moon system or Venus is dynamically consistent with these orbits. Of these three, the Moon is the most likely source since its escape velocity is significantly lower than either Earth or Venus.
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