Current astrodynamics applications require a rapid evaluation of the gravity field and an efficient approach to gravity estimation. The commonly used spherical harmonic model does not meet either of these needs. To address these issues, this research considers two new gravity representations: the cubed-sphere and the MRQSphere models. Offering a means for rapid evaluation, the cubed-sphere model yields an effectively constant computation time for any degree of the modeled gravity field. Analyzing the model's performance in a series of Monte-Carlo-like tests characterizes its effects on both orbit propagation and determination. When compared to the spherical harmonic gravity model, the cubed-sphere model improves computational efficiency without causing any significant deviation in resulting trajectories. Using this new model in sequential orbit determination improves the computational efficiency of the time update. As a result, the measurement update now dominates the filter execution time for near real-time applications. Since cubed-sphere models of higher degree require only a slight change in computation time, orbit propagation and determination systems may now use this model to improve fidelity without any significant change in cost. To address the gravity estimation problem, combining a new multiresolution technique with nearly optimal quadratures (for the sphere) invariant under the icosahedral group defines the MRQSphere model. This new multiresolution representation allows for gravity estimation via a naturally staged approach to a celestial body with an unknown gravity field, which aids in the design of missions to small bodies. To test the new model's capabilities, this research simulates a mission to an asteroid. Tests include the characterization of a MRQSphere model derived from the asteroid's spherical harmonic model, and the estimation of a model via observations of the gravity potential. For such a simplified scenario, the results indicate that the MRQSphere model meets the estimation accuracy requirements; future work is recommended to fully explore its capabilities.