Indirect Optimization of End-of-Life Disposal for Galileo Constellation Using Low Thrust Propulsion

In this work, the end-of-life disposal of satellites in the Galileo constellation using low thrust propulsion is studied. Indirect optimization methods are employed to design transfer maneuvers to remove the satellite from its original operational orbit into previously computed orbits leading to its natural re-entry within 100 years due to lunisolar perturbation effects. The dynamics are formulated using the modified equinoctial elements, which allow expressing the boundary conditions in a simple way at the cost of more complex equations compared to the use of Cartesian coordinates. A special focus is placed in defining an efficient and robust algorithm for solving the two point boundary value problem arising from the first order optimality conditions, including the integration of the analytically-derived variational equations to obtain the State Transition Matrix, and the accurate detection of thrust-switching events. The numerical results obtained for several test cases show the practical feasibility of this end-of-life disposal approach at thrust levels compatible with electric thrusters likely to be used by the next generation of Galileo satellites.