Fundamental parameters of exoplanets and their host stars

For much of human history we have wondered how our solar system formed, and whether there are any other planets like ours around other stars. Only in the last 20 years have we had direct evidence for the existence of exoplanets, with the number of known exoplanets dramatically increasing in recent years, especially with the success of the Kepler mission. Observations of these systems are becoming increasingly more precise and numerous, thus allowing for detailed studies of their masses, radii, densities, temperatures, and atmospheric compositions. However, one cannot accurately study exoplanets without examining their host stars in equal detail, and understanding what assumptions must be made to calculate planetary parameters from the directly derived observational parameters. In this thesis, I present observations and models of the primary transits and secondary eclipses of transiting exoplanets from both the ground and Kepler in order to better study their physical characteristics and search for additional exoplanets. I then identify, observe, and model new eclipsing binaries to better understand the stellar mass-radius relationship and stellar limb-darkening, compare these observations to the predictions of stellar models, and attempt to define to what extent these fundamental stellar characteristics can impact derived planetary parameters. I also present novel techniques for the direct determination of exoplanet masses and stellar inclinations via multi-wavelength astrometry, the ground-based photometric observation of stars at sub-millimagnitude precision, the reduction of Kepler photometry from pixel-level data, the extraction of radial velocities from spectroscopic observations, and the automatic identification, period analysis, and modeling of eclipsing binaries and transiting planets in large datasets.