Optimization of sequences for space debris removal

The gradual increase in space missions brings with it not only countless benefits for mankind, but also several problems that cannot be ignored nowadays. The most relevant problem is the constant increase in space debris. These, also commonly called "space junk", include: non-functional satellites, mission remnants such as abandoned launch vehicle stages and fragments of various types, which orbit the earth and represent a real risk to new space missions. This issue has led space agencies to define different solutions to mitigate both the risk of orbital accidents and the increase of space debris, thus decreasing the probability of collisions. These solutions are: extending the operational life of satellites with a consequent reduction in the number of launches, design the satellite for end-of- life deorbiting, and the active removal of already orbiting debris. In particular, this thesis focuses on the latter solution, analyzing and comparing two mission strategies for space debris removal through deorbiting via chemical propulsion. The mission focuses on the removal of four debris generated by the Russian ’Kosmos 3M’ launchers, which during their operational phase produced two clusters of debris at orbital inclinations of 74° (120 debris) and 82° (155 debris). The case studied foresees that the spacecraft is already on the first debris, on which the spacecraft waits for the time necessary to apply the deorbiting kit, and then makes a transfer to the next debris. This operation is repeated until the arrival on the fourth debris, where the mission is considered to be concluded. This thesis aims at optimizing the transfers between debris by minimizing propellant consumption. In order to do that, the most efficient of the two following strategies is applied: (i) the first consists in performing the transfer if the condition of orbit coplanarity is verified in a predefined time span; (ii) the second strategy, instead, is applied in the case in which the condition of coplanarity is not verified in the predefined time. The first strategy is performed using a single impulse, while the second one, since the orbits are non-coplanar, requires two impulses. The second strategy exists since the coplanarity condition may not be reached in a short period of time. The objective is therefore to optimize the mission, both in terms of mission time and ??V (speed impulse) cost. Furthermore, a simplified formulation is applied, thus obtaining a computationally efficient algorithm. The results obtained are compared with those obtained from the application of other possible strategies and with those derived from the non-simplified formulation, the purpose being to verify the validity of the proposed approach.