Numerical integration of ordinary differential equations resulting from the gravitation of nearby celestial small bodies is the subject of this thesis. We present three methods that alleviate the computational burden of evaluating gravitational force near a small body: i) adaptive polynomial interpolation, ii) adaptive polynomial least squares approximation, and iii) acceleration via specialized, commodity hardware. Each method is evaluated on its quantitative accuracy with respect to a reference model, and its observance of qualitative features of gravity. We conclude with a summary of methods available for computing small body gravitation, and recommendations for different scenarios.
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