On the Theory and Optimization of Global Point-Mass Expansions of Anomalous Gravity.
NAVAL SURFACE WEAPONS CENTER DAHLGREN LAB VA
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The relationship between point-mass and spherical harmonic expansions of anomalous gravity is analyzed. In particular, the spherical harmonic expansion of a point-mass set is determined and used to discuss the nature of point-mass solutions to the problem of modeling anomalous gravity. Also, a global error, which arises when a finite spherical harmonic expansion is replaced by a point-mass set, is first defined and then determined, both for the anomalous potential and its gradient. Defining an optimal point-mass set as one which minimizes the gradient error leads to a system of equations linear in the masses, but non-linear in their positions whose solution is the optimal point-mass set. Methods of solution are also discussed. Author