Numerical integration accuracy and modeling for future geodetic missions
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As technological advances throughout the field of satellite geodesy improve the accuracy of satellite measurements, numerical methods and algorithms must be able to keep pace. This becomes increasingly important for high precision applications, such as high degree/order gravity field recovery. Currently, the Gravity Recovery and Climate Experiment's (GRACE) dual one-way microwave ranging system can determine changes in inter-satellite range to a precision of a few microns; however, with the advent of laser measurement systems nanometer precision ranging is a realistic possibility. With this increase in measurement accuracy, a reevaluation of the accuracy inherent in the numerical integration algorithms is necessary. This study attempts to quantify and minimize these numerical errors in an effort to improve the accuracy of modeling and propagation of various orbital perturbations; helping to provide further insight into the behavior and evolution of the Earth's gravity field from the more capable gravity missions in the future. The numerical integration errors are examined for a variety of satellite accelerations. The propagation of orbits similar to those of the GRACE satellites using a gravitational model that assumes the Earth is a perfect sphere show integration errors, using double precision numerical representations, on the order of 1 micron in inter-satellite range and 0.1 nanometers per second in inter-satellite range-rate. In addition, when the Earth's gravitational field is formulated in spherical harmonics these numerical integration errors begin to contaminate signals to due harmonics approximately above degree 220, for an orbit at GRACE altitudes. Also, when examining the effect of mass anomalies on the Earth's surface, simulated as point masses, it is apparent that numerical integration methods are easily capable of resolving point mass anomalies as small as 0.05 gigatonnes. Finally, a numerical integration procedure is determined to accurately simulate the effect of numerous, small step accelerations applied to the satellite's center of mass due to misalignment and misfiring of the attitude thrusters. Future studies can then use this procedure as a metric to evaluate the accuracy and effectiveness of an accelerometer in reproducing these non-gravitational forces and how these errors might affect gravity field recovery.