This paper presents a novel approach for the preliminary design of Low-Thrust, many-revolution transfers. The main feature of\r\nthe novel approach is a considerable reduction in the control parameters and a consequent gain in computational speed. Each\r\nspiral is built by using a predefined pattern for thrust direction and switching structure. The pattern is then optimised to minimise\r\npropellant consumption and transfer time. The variation of the orbital elements due to the thrust is computed analytically from\r\na first-order solution of the perturbed Keplerian motion. The proposed approach allows for a realistic estimation of ?V and time\r\nof flight required to transfer a spacecraft between two arbitrary orbits. Eccentricity and plane changes are both accounted for.\r\nThe novel approach is applied here to the design of missions for the removal of space debris by means of an Ion Beam Shepherd\r\nSpacecraft. In particular, two slightly different variants of the proposed low-thrust control model are used for the different phases\r\nof the mission. Thanks to their low computational cost they can be included in a multiobjective optimisation problem in which\r\nthe sequence and timing of the removal of five pieces of debris are optimised to minimise propellant consumption and mission\r\nduration.
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