Evasion maneuvers with double lunar flyby for interplanetary missions

The purpose of this thesis is to describe and analyze a particular evasion maneuver with double lunar gravity assist (LGA) for interplanetary missions. Lunar flybys are a means to free increase the hyperbolic escape energy (C3) of an escape maneuver for a modest increase in flight time. Two approaches are applied: 1) the first one is the approximate analytical approach; 2) the second one gives the exact numerical solutions, because it takes into account all the main perturbations. The approximate model, it is easier than the other because is based on simplifying as- sumptions such as: no gravitational influence of Sun and Moon on the spacecraft, no solar radiation pressure, no eccentricity of Moon’s orbit (i.e. circular orbit), only Earth’s gravitational pull. It is just a preliminary study but extremely helpful because it gives you a macro view of the whole trajectory. Even without going into too much detail, it provides all the most important information in terms of times, positions and velocities. In particular, the solution obtained from this model, is used as the tentative solution for the more detailed analysis. Only short maneuvers, which should be less affected by solar perturbation are treated. For preliminary analysis of the interplanetary transfers, usually, is adopted the patched conic approximation. The analysis of the heliocentric leg provides us the escape condi- tions. In particular, our conditions refer to an Asteroid Redirect Mission (ARM ), also known as the Asteroid Retrieval and Utilization (ARU) mission. It is a NASA space mission, proposed in 2013. An ARRM spacecraft (Asteroid Retrieval Robotic Mission) would rendezvous with a large near-Earth asteroid and use robotic arms in order to collect a multi-ton boulder from its surface and return it to a stable orbit around the Moon or the Earth. This Asteroid Redirect Mission is part of NASA’s plan to advance the new technologies and spaceflight experience needed for a human mission to the Martian system in the 2030s. All the solutions presented in the following chapters were obtained from these escape conditions as boundary conditions. At the boundary of the Earth’s sphere of influence, are known the escape date, positions and escape velocity components of the spacecraft. Solutions are then compared between the two different approaches and between the different escape conditions (Chapter 5 and 6). Escape conditions that differ either by the escape date or by the escape velocity. Comparison between the two different models it is useful in order to verify the ap- proximation committed by the simplest one, taking into consideration that this solution is obtained in less than 1 second (limited computational effort), compared to the much larger effort required to obtain the exact solution.