Theses

Asteroids and other small objects throughout the Solar System are known to exhibit many of the oddities of classical Newtonian gravitation, and these oddities vastly increase the difficulty of analysis in N-body modeling and simulation. Recently, there has been developments in the study of binary asteroids which orbit each other simultaneously in the broader Sun-Planet field. We use a modified four-body model to analyze the evolution of two asteroids in a broader field of two primaries of arbitrary mass. We show the existence of relative equilibria and periodic orbits of Hill, Comet, Lyapunov, and Binary type in our model. We also present the spectra of the reported equilibria.

During its prime mission, the Kepler Space Telescope found over 700 systems with more than one transiting planet. These multiple planet systems (multis) are the most information rich and dynamically interesting of all exoplanets. We picked 46 multis where one planet was experiencing transit timing variations (TTVs) not obviously caused by the other known planets. TTVs are caused by interactions between planets and therefore can provide evidence of additional, hidden planets in these systems. We first tried to determine if the TTVs could be reasonably explained by the known planets. We then projected six possible hidden planets for each system and performed the same analysis on the hidden planet in the strongest resonance with the TTV-experiencing planet that was estimated to be stable. Five of our systems have good fits with the known planets, 39 have good fits with the hidden planet added, and two require more work to find a satisfactory answer. This work significantly improves our understanding of the architectures of some of the most interesting multis from Kepler.

The solar system is filled with collisional families, each consisting of several objects all generated though a single historical collision. There are hundreds of known familes in the asteroid belt, but only one known family in the Kuiper Belt (an icy, rocky region beyond Neptune). The age of young asteroid collisional families is often determined by using reversed simulations (i.e. backwards integration) of the solar system. This method is not used for discovering young asteroid families and is limited by unpredictable factors unique to the Asteroid Belt (e.g. the Yarkovsky Effect). The Kuiper Belt is absent of these unpredictabilities, and thus it was theorized that backwards integrations could be an advantageous method for both Kuiper Belt Object (KBO) family finding and characterization. Such integrations are ambitious and would require high accuracy over long timescales (∼ billions of years). This thesis outlines work done examining the feasibility of backwards integration as a method of family-finding, and specifically delves into the associated challenges.