Navigation Solution to Maneuver Spacecraft Relative to Spheres Centered on Cooperative Satellites
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Abstract
A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within the overlapping spheres, with user-defined radii, centered around multiple cooperative satellites within a constrained time. The differential correction algorithm develops and utilizes the state transition matrix along with the equations of motion and multiple satellites' state information to determine the optimum trajectory to achieve the desired results. The results from the algorithm are presented for prograde orbits. The results are presented in order to allow for mission design trade-offs, including satellite separation distance and required ΔV based on the satellites' initial inclinations. The results also provide empirical methodstodetermine the miss distance and optimum ΔV solutions for the provided problem. This work ultimately provides the framework for applying the algorithm to a unique user defined responsive space scenario.