Prevalence of Earth-size Planets Orbiting Sun-like Stars

In this thesis, I explore two topics in exoplanet science. The first is the prevalence of Earth-size planets in the Milky Way Galaxy. To determine the occurrence of planets having different sizes, orbital periods, and other properties, I conducted a survey of extrasolar planets using data collected by NASA's Kepler Space Telescope. This project involved writing new algorithms to analyze Kepler data, finding planets, and conducting follow-up work using ground-based telescopes. I found that most stars have at least one planet at or within Earth's orbit and that 26% of Sun-like stars have an Earth-size planet with an orbital period of 100 days or less. The second topic is the connection between the properties of planets and their host stars. The precise characterization of exoplanet hosts helps to bring planet properties like mass, size, and equilibrium temperature into sharper focus and probes the physical processes that form planets. I studied the abundance of carbon and oxygen in over 1000 nearby stars using optical spectra taken by the California Planet Search. I found a large range in the relative abundance of carbon and oxygen in this sample, including a handful of carbon-rich stars. I also developed a new technique called SpecMatch for extracting fundamental stellar parameters from optical spectra. SpecMatch is particularly applicable to the relatively faint planet-hosting stars discovered by Kepler