This thesis develops and establishes several methods to determine the detailed geometric architecture of transiting exoplanetary systems (planets orbiting around, and periodically passing in front of, stars other than the sun) using high-precision photometric data collected by the Kepler space telescope. It highlights the measurement of stellar obliquity – the tilt of the stellar equator with respect to the planetary orbital plane(s) – and presents methods for more precise obliquity measurements in individual systems of particular interest, as well as for measurements in systems that have been out of reach of previous methods. Such information is useful for investigating the dynamical evolution of the planetary orbit, which is the key to understanding the diverse architecture of exoplanetary systems. The thesis also demonstrates a wide range of unique applications of high-precision photometric data, which expand the capability of future space-based photometry.

The discovery of more than a thousand planets orbiting stars other than the Sun (i.e. exoplanets) over the past 20 years has shown that planetary systems are commonplace in the Milky Way galaxy. However, these discoveries are only a starting point in the quest to answer one of the most compelling questions posed by mankind for centuries -- "are we alone in the universe?". This research aims to help build the foundation needed to search for that answer by optimizing data reduction techniques, determining and refining fundamental properties of known exoplanets, and searching for new exoplanets. Many exoplanets have been discovered using the radial velocity (RV) technique to measure small variations in a star's motion that are gravitational induced by an orbiting planet. The RV signal reveals the planetary mass, orbital period, and orbital eccentricity. If an exoplanet crosses the face of its host star (i.e. transits) from the perspective of the observer, it causes an apparent periodic dimming of the star. The depth and shape of those brightness variations reveal the planet's radius, its transit time, and some orbital characteristics. Combining the mass and radius measurements, a planet's mean density can be calculated, thus constraining its composition. During transit, part of the star's light passes through the planetary atmosphere on its way to Earth, facilitating atmospheric measurements. Monitoring a planet's transit timing variations (TTVs) on many epochs may reveal the presence of another planet in the system due to gravitational interactions. I report the development of a new tool, AstroImageJ (AIJ), that provides an interactive environment for the optimal extraction and analysis of high-precision photometry from time-series observations. Based on AIJ photometry, I report high-precision measurements of system parameters and tight upper limits on TTVs derived from global analyses of 23 WASP-12b and 18 Qatar-1b complete transits. I also report the detection of sodium in the atmosphere of the exoplanet HD 189733b, the detection of z' band emission from the recently discovered hot brown dwarf, KELT-1b, and the discovery and characterization of the transiting hot-Saturn exoplanet, KELT-6b. Data for this research have been collected using the research-grade 0.6 m Moore Observatory RC (MORC) telescope, which is located near Louisville, Kentucky, and operated by the University of Louisville.

The Transiting Exoplanet Survey Satellite (TESS) is an MIT-led, NASA-funded Explorer-class planet finder with the primary mission of detecting transiting exoplanets in a 2-year all-sky survey. The TESS instrument consists of four wide-field optical cameras, mounted in a stacked configuration. During science operations, TESS uses the instrument cameras in the loop for attitude determination as part of the fine-pointing system in order to achieve the desired photometric precision of the mission. In this work, we present our approach toward improving and quantifying the fine-pointing performance of TESS and assessing the impact of pointing errors on the overall photometric precision of the mission. First, a guide-star selection method was developed to generate a set of desirable stars for guidance during any arbitrary observation sector based on stellar properties and their proximities to neighboring objects. Next, a comprehensive testing and validation framework was developed to assess the attitude determination flight software as well as to quantify the attitude determination performance of the instrument cameras during key mission scenarios. This framework allows the attitude determination system to be significantly improved, leading to a reduction in open-loop attitude errors by more than 65%. The final attitude determination performance was estimated to meet all relevant open-loop pointing requirements with margin. To assess the closed-loop fine-pointing performance of the system, multiple mission scenarios were simulated and analyzed using a comprehensive framework including both instrument performance as well as spacecraft control and dynamics, showing that the relevant closed-loop pointing requirements at multiple time scales are met with margin. The performance of the system over longer time scales and in temporary camera unavailability periods was also quantified through end-to-end simulations and is in agreement with analytical predictions. Finally, a high-fidelity simulation and analysis framework was developed to assess the photometric precision of the system, including realistic optical responses of the cameras, major photometry noise processes, and expected fine-pointing errors. The simulation results show that with basic co-trending techniques, the impact of pointing errors on science data can be significantly reduced, resulting in shot-noise-limited stellar photometry signals over the magnitude range of interest.

The methods used in the detection and characterisation of exoplanets are presented in this unique textbook for advanced undergraduates.

Very precise photometry of transiting extrasolar planets can be used to learn about the physical structure of Jupiter-like planets in an exoplanetary systems. The fraction of light reflected from the planet (albedo) provides crucial insight into the chemical structure of atmospheres and global thermal properties of a planet, including heat dissipation and global weather patterns. Measuring the albedo of an exoplanet requires very precise photometry with high time sampling and nearly continuous time coverage spanning may orbits, which can be achieved at present only from space. We present space-based photometry of the transiting exoplanetary system HD 209458 obtained with the MOST (Microvariablity and Oscillations of STars) satellite during 2004 and 2005. The data span 14 and 44 days respectively, and have nearly complete time coverage for both spans. The HD 209458 photometry was obtained in MOST's Direct Imaging mode, not part of the original mission but implemented to make possible measurements of stars in the brightness range 6.5