Online

Pearl, Jason

Mechanical Engineering

2019

Ph. D.

A number of missions to comets and asteroids have been undertaken by major space organizations driving a need to accurately characterize their gravitational fields. This is complicated however by their irregular shapes. To accurately and safely navigate spacecraft in these environments, a simple point-mass gravity model is insufficient and instead higher-fidelity models are required. Several such models exist for this purpose but all posess drawbacks. Moreover, there are some applications for which the currently available models are not particular well suited. In this dissertation, numerical quadrature and curvilinear meshing techniques are applied to the small body gravity problem. The goal of this work is to to create a gravitational model suitable for integating large numbers of low altitude trajectories and rapidly characterizing the near-surface potential field. In total three new models are developed. The first applies two-dimensional quadrature formulas to calculate the gravitational field of an arbitrary triangular surface mesh. The second extends this result to curvilinear surface meshes that more accurately approximate the surface topology. The third applies three-dimensional quadrature to curvilinear tetrahedral meshes to generate accurate distributions of point-masses. The accuracy of the new models is fully characterized and simple relations are presented for predicting the error of integrated trajectories. The efficiency of the models is then compared to other high-fidelity models currently in use. The new models perform well between the body's circumsphere and a thin layer that surrounds the surface.