The Gravity Recovery and Climate Experiment (GRACE) project is a unique mission that involves formation flying of two co-planar low-Earth-orbiting satellites. The nature of the mission requires a detailed understanding of the relative motion between the GRACE spacecraft. From launch to mission termination, several events critical to the success of the mission require relative motion modeling. As a result, a need has arisen to develop an accurate yet simple tool capable of modeling relative motion. Because the tool is to be designed for mission-planning and optimization, it should be both simple and flexible while providing reasonably accurate solutions. The first portion of this study overviews the development of a computer code written to model relative motion for the GRACE mission. The equations of motion are developed using accelerations due only to thrust and the 2-body and J_2 gravitational terms. This is determined to be a sufficient level of accuracy for purposes of maneuver sequence planning. The second portion of this study presents results of the analysis of several relative motion events that occur during the GRACE mission. These events include the separation of the twin satellites from the BREEZE insertion vehicle, the drift attenuation maneuver, the BREEZE de-orbit maneuver, and a simulated scenario involving the GRACE satellites being placed into the exact same nominal orbit, only delayed by a constant time. An optimization procedure is presented to minimize final local-vertical periodic drifts given the prescribed thrusting constraints. The code and optimization procedures developed in this study can be easily configured for future use to perform further analyses for GRACE and/or any other relative motion application.
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