Theses

Orbital systems of two or more Trans-Neptunian Objects (TNOs) are valuable for investigating formation processes of the early Solar System. Because TNOs exist below the diffraction limit of current telescopes, they are rendered as point spread functions (PSFs) in observational images. To correctly understand the orbital dynamics of TNO systems, the PSFs must be modeled according to telescope, camera, and observational parameters. These models can then be fit to images to produce the precise relative astrometry that is needed to fit the orbits. The software package nPSF was designed to fit modeled PSFs to images containing an n number of PSFs using Bayesian parameter inference methods, specifically the Markov Chain Monte Carlo process. The relative astrometry of the system can then be derived from the posterior distribution. We test the capabilities of nPSF by fitting images of 2PSF Trans-Neptunian Binaries and comparing our results to the published astrometry for those systems. We show that nPSF produces good astrometry in the tested systems. Additionally, we apply nPSF to the search of a tertiary object in various potential hierarchical triple systems. The results produced by nPSF do not indicate the detection of a third component in these systems.

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.