Exciting new fields of physics and precision inertial navigation can be realized by reducing test mass disturbances in drag-free spacecraft orders of magnitude below what has currently been demonstrated. The mass center of an ideal drag-free test mass is a reference point traveling along a pure geodesic. The purpose of the drag-free spacecraft is to shield the test mass from all external disturbances, and at the same time, not to introduce additional disturbances. A sphere has the advantage of invariance of orientation. A spherical test mass, therefore, requires no forcing on the part of the spacecraft to control the test mass orientation. With the need for actuation eliminated, the gap between the test mass and spacecraft can be opened up to sizes on the order of the sphere's radius. Elimination of test mass forcing and a large gap reduces, or all together eliminates, the largest disturbances acting on the test mass. Furthermore, spinning the sphere can spectrally shift body-fixed features to frequencies that do-not interfere with the drag-free control or the science mission. The angular momentum vector of the spinning sphere is a quantity that is robust against residual torques providing an orientation reference for the local inertial frame.;In this dissertation a generic model for the output of a drag-free sensor with a spinning spherical test mass is developed. A measurable feature of the test mass (surface geometry with respect to the mass center, magnetic potential, etc.) is written as an expansion in spherical harmonics. The rigid body motion of the test mass relative to the sensor is assumed to obey Euler's equations on short time scales, with angular momentum decay and polhode damping due to residual disturbances modeled on longer time scales, greater than say one clay. The validity of this model is demonstrated to approximately 1% using the Gravity Probe B flight data spanning 1 year. The success of this model allows for the prediction of polhode variations in the sensor readout scale factor to ∼ 10-4, which is critical to the accurate reduction of the Gravity Probe B science data and the achievement of overall mission goals. The model is then extended to the application of an advanced gravitational reference sensor for gravitational wave observation, fundamental physics and inertial navigation. Analytical modeling and numerical simulation show that a data processing technique can produce picometer level mass center measurements and one part per million spin frequency determination on-board the spacecraft in real-time. However, dynamic range limitations of the optical displacement sensor require that the mass center offset from the geometric center be less than 100 mu, which is challenging due to test mass density inhomogeneities on the order of 10-5. In the final portion of this dissertation, a laboratory demonstration of a novel technique for measuring the mass center of a sphere to 150 nm, approaching the 100 nm requirement and nearly one order of magnitude better than previous methods, is presented. The new technique again takes advantage of the symmetry of the sphere to spectrally shift the mass center information above low frequency by rolling the sphere down a set of parallel rails.
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