Abstract: Rubble pile asteroids are thought to form in the aftermath of cataclysmic collisions between proto-planets. The details of how the detritus from such collisions reaccumulate to form these bodies are not well understood, yet can play a fundamental role in the subsequent evolution of these bodies in the solar system. Simple items such as how particle sizes and porosity is distributed within a body can have a significant influence on how they subsequently evolve. Current space missions are just starting to gain limited insight into these fundamental questions, but require a better theoretical understanding to fully explain their observations.
To that end, this work studies how the initial energy and angular momentum of a random collection of gravitating bodies is partitioned and redistributed between escaping components and bound multiple body systems. A generic initial distribution of N bodies will naturally lose many components due to multi-body dynamical interactions. If the bodies have finite density, some components will also form condensed distributions, becoming single, binary or multiple component rubble pile asteroids. We derive and apply rigorous results from the Full N-body problem to place limits and constraints on how the energy and angular momentum of such systems can evolve, which controls the formation of stable rubble pile asteroids.
We are able to establish some of our constraints analytically, providing unique insight into this process. Ultimately, however, we require numerical simulations to elucidate certain aspects of the ejection process. As will be shown, these gravitational ejections will always reduce the system energy yet can cause significant fluctuations in the total angular momentum of the remaining bodies. Some possible implications of these trends will be discussed.