This paper presents a novel approach for the preliminary design of Low-Thrust, many-revolution transfers. The main feature of the novel approach is a considerable reduction in the control parameters and a consequent gain in computational speed. Each spiral is built by using a predefined pattern for thrust direction and switching structure. The pattern is then optimised to minimise propellant consumption and transfer time. The variation of the orbital elements due to the thrust is computed analytically from a first-order solution of the perturbed Keplerian motion. The proposed approach allows for a realistic estimation of V and time of flight required to transfer a spacecraft between two arbitrary orbits. Eccentricity and plane changes are both accounted for. The novel approach is applied here to the design of missions for the removal of space debris by means of an Ion Beam Shepherd Spacecraft. In particular, two slightly different variants of the proposed low-thrust control model are used for the different phases of the mission. Thanks to their low computational cost they can be included in a multiobjective optimisation problem in which the sequence and timing of the removal of five pieces of debris are optimised to minimise propellant consumption and mission duration. 1. Introduction One of the most critical issues related to the exploitation of space around the Earth is the threat posed by space debris. Since the beginning of the space era in the late 1950s, an increasing number of man-made, inert objects has been orbiting the Earth. Recent statistics revealed around 15000 trackable objects, for a total of some 6000 tons of material. Some of these objects are simply spent upper stages of launch vehicles, some others are satellites which are no longer active due to failures or to having reached their end of life. Others, however, are the results of past collisions. It is easy to imagine that even a single collision between two objects is likely to generate tens of smaller objects as a result. The outcome of a collision in an already crowded environment could generate a cascade of collisions generating an exponentially increasing volume of space debris. In fact, the debris produced by a collision is itself likely to collide with other objects, thereby producing other debris which will generate further collisions, and so on. This chain reaction, known as the Kessler Syndrome [1], occurs once the rate of generation of debris due to collisions or simple human-driven additions exceeds the natural debris removal rate. According to Kessler et al., this
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