Solar radiation pressure (SRP) is one of the major non-gravitational forces acting on spacecraft. Acceleration by radiation pressure depends on the radiation flux; on spacecraft shape, attitude, and mass; and on the optical properties of the spacecraft surfaces. Precise modeling of SRP is needed for dynamic satellite orbit determination, space mission design and control, and processing of data from space-based science instruments. During Earth penumbra transitions, sunlight is passing through Earth's lower atmosphere and, in the process, its path, intensity, spectral composition, and shape are significantly affected. This dissertation presents a new method for highly physical SRP modeling in Earth's penumbra called Solar radiation pressure with Oblateness and Lower Atmospheric Absorption, Refraction, and Scattering (SOLAARS). The fundamental geometry and approach mirrors past work, where the solar radiation field is modeled using a number of light rays, rather than treating the Sun as a single point source. This dissertation aims to clarify this approach, simplify its implementation, and model previously overlooked factors. The complex geometries involved in modeling penumbra solar radiation fields are described in a more intuitive and complete way to simplify implementation. Atmospheric effects due to solar radiation passing through the troposphere and stratosphere are modeled, and the results are tabulated to significantly reduce computational cost. SOLAARS includes new, more efficient and accurate approaches to modeling atmospheric effects which allow us to consider the spatial and temporal variability in lower atmospheric conditions. A new approach to modeling the influence of Earth's polar flattening draws on past work to provide a relatively simple but accurate method for this important effect. Previous penumbra SRP models tend to lie at two extremes of complexity and computational cost, and so the significant improvement in accuracy provided by the complex models has often been lost in the interest of convenience and efficiency. This dissertation presents a simple model which provides an accurate alternative to the full, high precision SOLAARS model with reduced complexity and computational cost. This simpler method is based on curve fitting to results of the full SOLAARS model and is called SOLAARS Curve Fit (SOLAARS-CF). Both the high precision SOLAARS model and the simpler SOLAARS-CF model are applied to the Gravity Recovery and Climate Experiment (GRACE) satellites. Modeling results are compared to the sub-nm/s^2 precision GRACE accelerometer data and the results of a traditional penumbra SRP model. These comparisons illustrate the improved accuracy of the SOLAARS and SOLAARS-CF models. A sensitivity analyses for the GRACE orbit illustrates the significance of various input parameters and features of the SOLAARS model on results. The SOLAARS-CF model is applied to a study of penumbra SRP and the Earth flyby anomaly. Beyond the value of its results to the scientific community, this study provides an application example where the computational efficiency of the simplified SOLAARS-CF model is necessary. The Earth flyby anomaly is an open question in orbit determination which has gone unsolved for over 20 years. This study quantifies the influence of penumbra SRP modeling errors on the observed anomalies from the Galileo, Cassini, and Rosetta Earth flybys. The results of this study prove that penumbra SRP is not an explanation for or significant contributor to the Earth flyby anomaly. / Ph. D.